Word Class Representations Spontaneously Emerge from Successor Representations Trained on Natural Language

# Word Class Representations Spontaneously Emerge from Successor Representations Trained on Natural Language
Source: [https://arxiv.org/html/2605.24585](https://arxiv.org/html/2605.24585)
\[1,2\]\\fnmMathis\\surImmertreu

\[1\]\\orgdivCognitive Computational Neuroscience Group,\\orgnameFriedrich\-Alexander\-Universität Erlangen–Nürnberg \(FAU\),\\countryGermany

\[2\]\\orgdivMannheim Center for Neuromodulation and Neuroprosthetics \(MCNN\),\\orgnameUniversity Hospital Mannheim, University Heidelberg,\\countryGermany

###### Abstract

Language models are typically trained to predict the next token in a sequence\. Here, we explore an alternative predictive principle derived from reinforcement learning: Successor Representations, which model not the immediate next state but the expected discounted distribution of future states\. We transfer this framework to natural language and train neural networks to predict, for each word, the distribution of words expected to follow across multiple temporal horizons\. In contrast to conventional next\-token prediction, this objective learns representations of the long\-range transition structure of language\. We train a deep residual neural network on WikiText\-103 \(103 million tokens, 20,000\-word vocabulary\)\. The model predicts successor representations at multiple predictive horizons and is optimized by treating SR targets as probability distributions using KL divergence rather than direct regression\. We show that linguistic structure emerges spontaneously from this predictive objective without explicit supervision or annotation of linguistic categories\. After training, the representation space develops a clear geometric organization with respect to part\-of\-speech \(POS\) categories: initially unstructured representations reorganize into separated regions, with nouns, verbs, and adjectives showing particularly strong separation and recoverability by unsupervised clustering\. Cluster agreement with ground\-truth POS labels is highest for short predictive horizons and decreases for longer horizons, suggesting a shift from local syntactic regularities toward broader contextual and semantic organization\. At finer clustering resolutions, additional interpretable lexical substructure emerges\. Adjectives decompose into subclasses including scalar, color, and quantificational modifiers; verbs organize into motion, communication, and outcome\-related groups; nouns separate into domains such as temporal expressions, measurement units, and media\-related concepts\. These findings suggest that predictive successor dynamics recover not only broad syntactic categories but also functional and construction\-like organization\. Overall, our results argue that syntactic categories need not be explicitly encoded or supervised but may emerge as a consequence of predictive sequence learning\. More broadly, this work provides, to our knowledge, the first systematic application of successor representations to natural language and establishes a conceptual bridge between reinforcement learning, linguistics, and cognitive neuroscience\.

###### keywords:

Successor Representations, Natural Language Processing, Emergent Linguistic Structure, Part\-of\-Speech Representations, Representation Learning, Reinforcement Learning

## 1Introduction

Modern language models have achieved remarkable success by learning to predict the next token in a sequence\. Across architectures ranging from recurrent neural networks to transformers, this predictive objective has become the dominant paradigm for representation learning in natural language processing\. Beyond their practical performance, such models have also become increasingly relevant as computational models of cognition and language processing, as they often develop internal structures that align with linguistic and neural phenomena despite receiving only weak supervision from raw text\.

A recurring observation across machine learning and cognitive science is that structured representations can emerge spontaneously from predictive learning objectives\. Neural language models have been shown to develop internal representations related to syntax, semantics, and hierarchical linguistic structure without explicit symbolic encoding of these categories\. This raises a broader question: to what extent are linguistic categories intrinsic components of language, and to what extent do they emerge as efficient predictive abstractions over sequential structure?

Most existing language models formulate prediction as a local problem: given a context, predict the immediate next token\. While this objective has proven highly effective, it emphasizes short\-range dependencies and does not explicitly represent how future states unfold over extended horizons\. In contrast, reinforcement learning offers an alternative predictive framework through Successor Representations \(SRs\)\. Originally introduced by Dayan, successor representations decompose prediction into environmental dynamics and reward structure by encoding the expected discounted occupancy of future states under a policy\. Rather than predicting what comes next, SRs model what is expected to occur in the future and how often\.

Although successor representations have been extensively studied in reinforcement learning and have received increasing attention in computational neuroscience as models of predictive coding, planning, and hippocampal representations, their application to natural language remains largely unexplored\. Language can itself be viewed as a sequential environment in which words define transitions through a high\-dimensional state space\. From this perspective, the successor representation provides a natural way to describe linguistic structure as the long\-term geometry of future transitions rather than immediate co\-occurrence\.

In this work, we transfer successor representations to natural language and investigate whether linguistic structure emerges from this predictive objective alone\. Instead of training a model to predict the next token, we train neural networks to predict the expected discounted distribution of future words across multiple temporal horizons\. Concretely, we train a deep residual neural network on WikiText\-103 to learn successor representations as probability distributions over future token occupancy\.

Our central finding is that structured linguistic organization emerges spontaneously without explicit supervision\. After training, the learned representation space develops a pronounced geometric organization with respect to part\-of\-speech \(POS\) categories: nouns, verbs, and adjectives become recoverable through unsupervised clustering despite the absence of linguistic labels during training\. Increasing cluster granularity reveals additional interpretable substructure, including semantically and functionally coherent lexical subclasses\. Furthermore, we observe that the temporal prediction horizon systematically shapes representation geometry: short horizons preserve local syntactic regularities most strongly, whereas longer horizons increasingly integrate broader contextual and semantic information\.

These findings suggest that syntactic categories need not be explicitly encoded or supervised but may arise as emergent consequences of predictive sequence learning\. More broadly, our work establishes a conceptual bridge between reinforcement learning, computational linguistics, and cognitive neuroscience and, to our knowledge, provides the first systematic application of successor representations to natural language\.

The main contributions of this work are threefold: First, we introduce successor representations as a predictive framework for natural language modeling\. Second, we demonstrate that word class representations emerge spontaneously from successor\-based learning without linguistic supervision\. Finally, we show that varying predictive horizons reveal a transition from local syntactic organization to broader contextual and semantic structure\.

## 2Methods

### 2\.1Successor Representation

In reinforcement learning, value\-based methods such as Q\-learning estimate long\-term returns by propagating reward information through the Bellman equation\[barto2021reinforcement,mnih2013playing\]\. An alternative perspective, introduced by Dayan\[dayan1993improving\], is to decompose value learning into two components: \(i\) a predictive model of the environment’s dynamics, and \(ii\) a reward model\. This idea is formalized in the Successor representation \(SR\), which captures how future states are expected to unfold under a fixed policy, independently of the particular reward function\.

For a Markov decision process over statess∈𝒮s\\in\\mathcal\{S\}under a fixed policyπ\\pi, the SRM​\(s,s′\)M\(s,s^\{\\prime\}\)is defined as the expected discounted future occupancy of states′s^\{\\prime\}when starting fromss:

M\(s,s′\)=𝔼π\[∑t=0∞γt𝕀\(st\+1=s′\)\|s0=s\],M\(s,s^\{\\prime\}\)=\\mathbb\{E\}\_\{\\pi\}\\left\[\\sum\_\{t=0\}^\{\\infty\}\\gamma^\{t\}\\mathbb\{I\}\(s\_\{t\+1\}=s^\{\\prime\}\)\\,\\middle\|\\,s\_\{0\}=s\\right\],\(1\)whereγ∈\[0,1\]\\gamma\\in\[0,1\]is a discount factor and𝕀​\(⋅\)\\mathbb\{I\}\(\\cdot\)denotes the indicator function\. Intuitively,M​\(s,s′\)M\(s,s^\{\\prime\}\)quantifies how often \(in a discounted sense\) the agent is expected to arrive at states′s^\{\\prime\}in the future when starting fromss, thereby encoding the predictive structure of the environment independently of any specific reward function\. Thus, the discount factorγ\\gammacontrols the time horizon our SRtakes into account\. We adopt the arrival SR formulation, as predicting occupancy of future states from the next state onwards is more natural as the current state is already observed and carries no predictive value\.

This representation yields a simple linear factorization of the value function\. For a state\-dependent reward functionr​\(s′\)r\(s^\{\\prime\}\), the value function can be written as

v​\(s\)=∑s′M​\(s,s′\)​r​\(s′\)\.v\(s\)=\\sum\_\{s^\{\\prime\}\}M\(s,s^\{\\prime\}\)\\,r\(s^\{\\prime\}\)\.\(2\)Unlike Q\-learning, which directly bootstraps on observed rewards, the SR separates dynamics \(captured byMM\) from rewards \(captured by𝐫\\mathbf\{r\}\), enabling efficient transfer across tasks that share the same transition structure but differ in their reward functions\[stachenfeld2017hippocampus,gershman2018successor\]\. This idea can be extended to successor features which predicts feature representation of states instead of pure states\[barreto2017successor\]\.

### 2\.2Successor Representation Updates

![Refer to caption](https://arxiv.org/html/2605.24585v1/x1.png)Figure 1:Figure: TD learning targets for successor representations\.1\-Step TD \(blue\),nn\-Step TD shown forn=4n=4\(teal\), and TD\(λ\\lambda\) \(gold\) differ in how many future token positions contribute discounted features before bootstrapping and how the individual steps are weighted\. They range from a single step to an infinite exponentially\-weighted horizon\.In practice, the dynamics of the environment are typically unknown, making it impossible to compute the successor representation analytically\. Moreover, for large or continuous state spaces, we cannot maintain tabular representations and must resort to function approximators such as neural networks\. These constraints necessitate a sample\-based learning approach\.

The SRcan be learned via temporal difference \(TD\)learning\[russek2017predictive\], similar to the classical TDlearning algorithm\[barto2021reinforcement\]\. Letϕ​\(st\)\\phi\(s\_\{t\}\)denote the feature representation \(e\.g\., a one\-hot vector encoding which token is observed\) of the state at timett, and letα\\alpharepresent the learning rate\.

The simplest TDlearning is done via a 1\-step Bellman update\. This method uses bootstrapping, where the successor representation estimateM^​\(st,:\)\\hat\{M\}\(s\_\{t\},:\)is updated based on the feature observation of the next stateϕ​\(st\+1\)\\phi\(s\_\{t\+1\}\)combined with the agent’s own current estimate of the next state’s successor representationM^​\(st\+1,:\)\\hat\{M\}\(s\_\{t\+1\},:\), rather than waiting for complete trajectories:

M^​\(st,:\)←M^​\(st,:\)\+α​\(ϕ​\(st\+1\)\+γ​M^​\(st\+1,:\)⏟Target−M^​\(st,:\)\)\\hat\{M\}\(s\_\{t\},:\)\\leftarrow\\hat\{M\}\(s\_\{t\},:\)\+\\alpha\\Big\(\\underbrace\{\\phi\(s\_\{t\+1\}\)\+\\gamma\\hat\{M\}\(s\_\{t\+1\},:\)\}\_\{\\text\{Target\}\}\-\\hat\{M\}\(s\_\{t\},:\)\\Big\)\(3\)However, certain domains such as natural language are inherently non\-Markovian\. To reasonably model dependencies in such environments, the algorithm is extended tonn\-step updates\. Instead of relying solely on the immediate next state, thenn\-step update accumulates discounted features over a horizon ofnnsteps and bootstraps from the value at statest\+ns\_\{t\+n\}:

G^t:t\+n\\displaystyle\\hat\{G\}\_\{t:t\+n\}=∑k=0n−1γk​ϕ​\(st\+k\+1\)\+γn​M^​\(st\+n,:\)\\displaystyle=\\sum\_\{k=0\}^\{n\-1\}\\gamma^\{k\}\\phi\(s\_\{t\+k\+1\}\)\+\\gamma^\{n\}\\hat\{M\}\(s\_\{t\+n\},:\)\(4\)M^​\(st,:\)\\displaystyle\\hat\{M\}\(s\_\{t\},:\)←M^​\(st,:\)\+α​\(G^t:t\+n−M^​\(st,:\)\)\\displaystyle\\leftarrow\\hat\{M\}\(s\_\{t\},:\)\+\\alpha\\left\(\\hat\{G\}\_\{t:t\+n\}\-\\hat\{M\}\(s\_\{t\},:\)\\right\)\(5\)
This approach can be further generalized to TD\(λ\\lambda\), which provides a smooth interpolation between 1\-step bootstrapping \(λ=0\\lambda=0\) and full Monte Carlo returns \(λ=1\\lambda=1\)\. Since we operate on fixed sequences rather than a stream of online interactions, we compute theλ\\lambda\-return via a backward pass, initialised at the final position as

G^T−2=ϕ​\(sT−1\)\+γ​M^​\(sT−1,:\),\\hat\{G\}\_\{T\-2\}=\\phi\(s\_\{T\-1\}\)\+\\gamma\\,\\hat\{M\}\(s\_\{T\-1\},:\),\(6\)and recursed backwards as

G^t=ϕ​\(st\+1\)\+γ​\(\(1−λ\)​M^​\(st\+1,:\)\+λ​G^t\+1\),\\hat\{G\}\_\{t\}=\\phi\(s\_\{t\+1\}\)\+\\gamma\\\!\\left\(\(1\-\\lambda\)\\,\\hat\{M\}\(s\_\{t\+1\},:\)\+\\lambda\\,\\hat\{G\}\_\{t\+1\}\\right\),\(7\)withλ=0\\lambda=0recovering the 1\-step target andλ=1\\lambda=1the full Monte Carlo return\. An example of how future states are included and weighted before bootstrapping is illustrated in Figure[9](https://arxiv.org/html/2605.24585#S3.F9)\.

### 2\.3Architecture

Our SRmodel follows the broad residual network paradigm\[he2016deep,he2016identity\], adapted to a fully\-connected setting with a shared trunk and separate output heads per discount factorγ\\gammapredicting the SRbased on a single input token\. All components are built from a common building block, theResidualBlock, which applies a two\-layer MLP with pre\-normalisation and an additive skip connection\. Given an input vector𝐱∈ℝ512\\mathbf\{x\}\\in\\mathbb\{R\}^\{512\}, each block computes

𝐱′=𝐱\+W2​GELU​\(W1​LayerNorm​\(𝐱\)\+𝐛1\)\+𝐛2,\\mathbf\{x\}^\{\\prime\}=\\mathbf\{x\}\+W\_\{2\}\\,\\mathrm\{GELU\}\\\!\\left\(W\_\{1\}\\,\\mathrm\{LayerNorm\}\(\\mathbf\{x\}\)\+\\mathbf\{b\}\_\{1\}\\right\)\+\\mathbf\{b\}\_\{2\},\(8\)whereW1,W2∈ℝ512×512W\_\{1\},W\_\{2\}\\in\\mathbb\{R\}^\{512\\times 512\}and𝐛1,𝐛2∈ℝ512\\mathbf\{b\}\_\{1\},\\mathbf\{b\}\_\{2\}\\in\\mathbb\{R\}^\{512\}are learned weight matrices and bias vectors, respectively\. Applying LayerNorm to the input before the first linear transformation \(pre\-norm\) yields more stable gradients in deep networks compared to post\-norm variants\[xiong2020layer\], and GELU is preferred over ReLU for its smoother gradient signal\[hendrycks2016gaussian\]\. No nonlinearity is applied to the block output prior to the residual addition, preserving unobstructed gradient flow through all layers\.

The full model begins by mapping each token IDt∈\{0,…,19,999\}t\\in\\\{0,\\ldots,19\{,\}999\\\}to a learnable 512\-dimensional dense vector via an embedding tableE∈ℝ20000×512E\\in\\mathbb\{R\}^\{20000\\times 512\}\. The embedded sequence then passes through a shared backbone of eight ResidualBlocks, yielding a context representationH∈ℝB×80×512H\\in\\mathbb\{R\}^\{B\\times 80\\times 512\}that is consumed by all prediction heads\.

Three independent heads are attached to this shared representation, one for each discount factorγ∈\{0\.2,0\.5,0\.8\}\\gamma\\in\\\{0\.2,0\.5,0\.8\\\}\. Each head consists of seven further ResidualBlocks followed by a linear projectionWout∈ℝ512×20000W\_\{\\mathrm\{out\}\}\\in\\mathbb\{R\}^\{512\\times 20000\}as the eighth layer, producing raw logits over the full vocabulary,

ψγ=Wout​BlockStackγ​\(H\)∈ℝB×80×20000\.\\psi\_\{\\gamma\}=W\_\{\\mathrm\{out\}\}\\;\\mathrm\{BlockStack\}\_\{\\gamma\}\(H\)\\;\\in\\;\\mathbb\{R\}^\{B\\times 80\\times 20000\}\.\(9\)The heads share no parameters with one another, allowing each to specialise for its temporal horizon\. This mirrors the increasing scale of place fields along the hippocampal longitudinal axis\[stachenfeld2017hippocampus\]\.

To stabilise training, a frozen shadow copy of the entire model is maintained alongside the actively trained parameters\. After every gradient update, the shadow parametersθema\\theta\_\{\\mathrm\{ema\}\}are updated via

θema←α​θema\+\(1−α\)​θactive,\\theta\_\{\\mathrm\{ema\}\}\\leftarrow\\alpha\\,\\theta\_\{\\mathrm\{ema\}\}\+\(1\-\\alpha\)\\,\\theta\_\{\\mathrm\{active\}\},\(10\)and it is these slowly\-moving parameters that supply the bootstrap targets for the TD loss\. This prevents the moving\-target instability that arises when the model simultaneously updates its own bootstrap targets, analogous to the target network in reinforcement learning \(RL\)\[mnih2015human,haarnoja2018soft\]\. The architecture is illustrated in Figure[2](https://arxiv.org/html/2605.24585#S2.F2)\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x2.png)Figure 2:Architecture and Training Flow\.Input tokens are embedded and passed through a shared backbone that branches into three discount\-specific heads, each producing a successor representation prediction\. The Residual Block, the main building unit of both backbone and heads, is illustrated top\-left\. Training targets are computed via aλ\\lambda\-return formulation that bootstraps from the one\-hot encodings of all future tokens and a frozen EMA target network, which maintains a slowly updating copy of the live network weights \(lock symbols indicate no gradient flow\)\. The model is optimized by minimizing the KL divergence between predictions and targets, summed across all heads\. At inference, the true Successor Representation is recovered by a simple rescaling\.
### 2\.4Training

We train the SRmodel on a lowercased version of WikiText\-103\[merity2016pointer\], a medium\-sized corpus \(103M tokens\) of high\-quality Wikipedia articles, using the spaCy tokenizer\[honnibal2020spacy\]\. The vocabulary consists of the 20,000 most frequent tokens; all remaining words are mapped to diversified unknown tags derived from their part\-of\-speech category \(e\.g\.,UNK\_NOUN,UNK\_VERB\), preserving coarse syntactic structure even for out\-of\-vocabulary words similar to the ideas of\[petrov2006perceptual\]\.

Rather than a standard mean squared error \(MSE\)loss, we used Kullback\-Leibler \(KL\)divergence\[kullback1951information\], by re\-framing the learning objective as matching a probability distribution over future states\. Since the unscaled SR sums to11−γ\\frac\{1\}\{1\-\\gamma\}, we scale the one\-hot featureϕ​\(st\+1\)\\phi\(s\_\{t\+1\}\)by\(1−γ\)\(1\-\\gamma\)and replace the raw bootstrap withsoftmax​\(ψema\)\\mathrm\{softmax\}\(\\psi\_\{\\mathrm\{ema\}\}\), so that the resultingλ\\lambda\-return targetGtG\_\{t\}sums to\(1−γ\)\+γ=1\(1\-\\gamma\)\+\\gamma=1and constitutes a valid distribution over the vocabulary\. The model outputs are treated as logits, converted to log\-probabilities vialog\_softmax, and trained against this normalized target,

ℒγ=DKL​\(Gγ∥softmax​\(ψγ\)\),\\mathcal\{L\}\_\{\\gamma\}=D\_\{\\mathrm\{KL\}\}\\\!\\left\(G\_\{\\gamma\}\\;\\Big\\\|\\;\\mathrm\{softmax\}\\\!\\left\(\\psi\_\{\\gamma\}\\right\)\\right\),\(11\)with the total lossℒ=∑γℒγ\\mathcal\{L\}=\\sum\_\{\\gamma\}\\mathcal\{L\}\_\{\\gamma\}summing over all three heads\. The final SRis recovered by applying softmax to the logits and rescaling by11−γ\\frac\{1\}\{1\-\\gamma\}, restoring the expected discounted occupancy interpretation\. This formulation is more stable than MSEfor large vocabularies, where target magnitudes can vary drastically, and encourages the SR to focus on the relative structure of future visitations rather than their absolute magnitude\. Gradients are clipped to unit norm before each optimizer step, and the model is trained with a cosine learning rate schedule with linear warm\-up over the first 1,000 steps; all hyperparameters are reported in Table[1](https://arxiv.org/html/2605.24585#S2.T1)and the training flow is illustrated in Figure[2](https://arxiv.org/html/2605.24585#S2.F2)\.

Table 1:Training hyperparameters for the Successor Representation model\.
### 2\.5Preprocessing

To analyze the structure learned by the SRmodel, we first construct a part\-of\-speech \(POS\)lexicon by processing the WikiText\-103 corpus with spaCy’s large English model \(en\_core\_web\_lg\)\. Each token in the vocabulary is assigned its majority POStag across all occurrences in the corpus, resolving lexical ambiguity \(e\.g\., bank as noun vs\. verb\) by majority voting\. We then extract SRsfor up to 200 tokens per part\-of\-speech category, selecting the most frequent tokens within each category, considering either only nouns, verbs, and adjectives \(NVA\) or all major POScategories, excluding tags:X, SYM, SPACE, PUNCT, INTJ\. Prior to clustering, the high\-dimensional SRvectors are denoised and reduced via principal component analysis \(PCA\)\[pearson1901liii,hotelling1933analysis\], retaining 99\.99% of the variance, reducing the influence of spurious dimensions while preserving the dominant structure and reducing computational costs\. This led to 600 tokens in the NVA and 1377 tokens considered in the extended set\. The token distribution is illustrated in Table[2](https://arxiv.org/html/2605.24585#S2.T2)\.

Table 2:Token counts by POS tag\.
### 2\.6Consensus Clustering

To identify stable structural groupings robust to the choice ofKK, we employed a variant of consensus clustering\[monti2003consensus\]over 240 trials per algorithm\. Rather than perturbing the sample through resampling as in the original formulation, we perturb the resolution: we draw the baseKKfrom the set of 24 prime numbers ranging from 3 to 97, repeating each value ten times with independently sampled random seeds, so that the resulting co\-association matrix reflects structure that is robust across scales rather than robust to data perturbation\.

We ran two disjoint sets of trials using different base clustering algorithms:KK\-Means\[bishop2006pattern\], which partitions tokens intoKKclusters by iteratively assigning each token to its nearest centroid, producing compact and geometrically regular partitions; and Bayesian Gaussian mixture models \(BGMs\), which model the data as a mixture ofKKfull\-covariance Gaussian components with Dirichlet process priors over component weights, enabling soft assignments and suppression of superfluous components unsupported by the data\. Each set of trials produces its own consensus clustering independently, yielding two complementary clusterings per target resolution\. The former favours hard, spherical boundaries and the latter capturing probabilistic, ellipsoidal structure\.

Within each set, a co\-association matrix is accumulated recording how frequently each pair of tokens is assigned to the same cluster across all base clusterings\. Agglomerative hierarchical clustering with average linkage is then applied to this matrix: starting from singleton clusters, the algorithm iteratively merges the pair of clusters with the highest average pairwise co\-association until all tokens are joined into a single cluster\. The resulting dendrogram is cut at several target resolutions \(K=3,10,20,30,40,50,60,80,100K=3,10,20,30,40,50,60,80,100for the NVA setting;K=13,20,40,60,80,100,120,160,200K=13,20,40,60,80,100,120,160,200for the extended setting\), enabling simultaneous analysis at multiple levels of granularity\.

### 2\.7Cluster Evaluation

Clustering quality is assessed against POStags using three complementary metrics over a clustering𝒞=\{C1,…,CK\}\\mathcal\{C\}=\\\{C\_\{1\},\\dots,C\_\{K\}\\\}and reference partitionℒ=\{L1,…,LJ\}\\mathcal\{L\}=\\\{L\_\{1\},\\dots,L\_\{J\}\\\}overNNtokens\. Purity is the fraction of tokens in a cluster belonging to its majority class,

purity​\(Ck\)=1\|Ck\|​maxj⁡\|Ck∩Lj\|,\\mathrm\{purity\}\(C\_\{k\}\)=\\frac\{1\}\{\|C\_\{k\}\|\}\\max\_\{j\}\|C\_\{k\}\\cap L\_\{j\}\|,\(12\)and provides an intuitive per\-cluster measure of homogeneity, allowing inspection of which clusters align well with POStags and which do not\. To compare clustering quality across different values ofKKandγ\\gamma, we employ two global metrics\. Normalized Mutual Information \(NMI\)\[strehl2002cluster\],

NMI​\(𝒞,ℒ\)=2​I​\(𝒞;ℒ\)H​\(𝒞\)\+H​\(ℒ\),\\mathrm\{NMI\}\(\\mathcal\{C\},\\mathcal\{L\}\)=\\frac\{2\\,I\(\\mathcal\{C\};\\mathcal\{L\}\)\}\{H\(\\mathcal\{C\}\)\+H\(\\mathcal\{L\}\)\},\(13\)penalizes fragmentation and lies in\[0,1\]\[0,1\], but does not correct for chance, so finer partitions can still achieve spuriously elevated scores\. Adjusted Rand Index \(ARI\)\[hubert1985comparing\]corrects for chance agreement under a hypergeometric model,

ARI​\(𝒞,ℒ\)=RI−𝔼​\[RI\]max⁡\(RI\)−𝔼​\[RI\],\\mathrm\{ARI\}\(\\mathcal\{C\},\\mathcal\{L\}\)=\\frac\{\\mathrm\{RI\}\-\\mathbb\{E\}\[\\mathrm\{RI\}\]\}\{\\max\(\\mathrm\{RI\}\)\-\\mathbb\{E\}\[\\mathrm\{RI\}\]\},\(14\)yielding a score in\[−1,1\]\[\-1,1\]that is approximately resolution\-independent, making it the most reliable basis for comparison across values ofKK\.

### 2\.8Visualization

For visualization, SRvectors are projected into 2D via uniform manifold approximation and projection \(UMAP\)\[mcinnes2018umap\]\(nneighbors=15n\_\{\\text\{neighbors\}\}=15,min\_dist=0\.1\\text\{min\\\_dist\}=0\.1\)\. UMAP assumes the data lies on a low\-dimensional manifold embedded in the high\-dimensional space, constructs a weightedkk\-nearest neighbor graph whose edge weights reflect manifold connectivity, and optimizes a 2D embedding by minimizing the cross\-entropy between the high\- and low\-dimensional fuzzy graph representations\. Thenneighborsn\_\{\\text\{neighbors\}\}parameter controls the neighborhood size used during graph construction, trading local against global structure, whilemin\_distgoverns the minimum distance between points in the embedding, affecting cluster compactness\. Clusters are colored by their majority POStag, with lightness and hue variants distinguishing multiple clusters sharing the same category\.

### 2\.9Transition Networks

To examine the sequential structure captured by the SR, we compute inter\-cluster transition weightsMi​jM\_\{ij\}as the average normalized SRmass flowing from clusteriito clusterjj, and visualize these as both heatmaps and directed graphs\. In the graph representation, each cluster forms a node, and edges correspond to the top 3 outgoing transitions with edge width proportional to transition strength\.

## 3Results

![Refer to caption](https://arxiv.org/html/2605.24585v1/x3.png)Figure 3:Training and Validation Losses\.Mean and per\-head training \(solid black\) and validation \(dashed red\) losses over 10 epochs\.### 3\.1Training Dynamics and Emergent Embedding Geometry

Figure[3](https://arxiv.org/html/2605.24585#S3.F3)illustrates the training and validation KLdivergence loss curves across 10 epochs for each output head, alongside the mean loss aggregated over all heads\. All configurations exhibit a sharp initial decline in the first epoch, followed by a steady decrease that approaches convergence by epoch 10, suggesting that additional training could yield marginal further improvements\. Notably, the training and validation curves remain closely aligned throughout, indicating that the model generalises well without significant overfitting\.

The per\-head loss curves reveal a consistent pattern across allγ\\gammavalues, differing primarily in their baseline KLdivergence\. Higherγ\\gammavalues correspond to substantially lower absolute losses —γ=0\.8\\gamma=0\.8converges to approximately2\.532\.53\(train\) and2\.542\.54\(validation\), compared to3\.973\.97and4\.004\.00forγ=0\.5\\gamma=0\.5, and4\.644\.64and4\.704\.70forγ=0\.2\\gamma=0\.2— suggesting that heads associated with higherγ\\gammavalues represent easier or more predictable sub\-tasks, whose target distributions are more amenable to learning\. The mean loss curve summarises this behaviour, declining fromℒtrain=3\.99\\mathcal\{L\}\_\{\\text\{train\}\}=3\.99to3\.713\.71and fromℒval=3\.81\\mathcal\{L\}\_\{\\text\{val\}\}=3\.81to3\.753\.75over the course of training, confirming stable and consistent learning across all heads\.

Beyond the loss trajectories, the emergence of structure is directly visible in the geometry of the SRembeddings themselves\. Figure[4](https://arxiv.org/html/2605.24585#S3.F4)shows UMAPprojections before and after training for both the NVA subset and the extended vocabulary\. Prior to training, embeddings occupy a structureless cloud with no systematic organization by POScategory, consistent with randomly initialised representations carrying no distributional information\. After training, the geometry changes substantially\. In the NVA case, the three categories separate into spatially distinct regions, indicating that the learned SRsassign systematically different representations to nouns, verbs, and adjectives purely on the basis of their successor statistics\. In the extended vocabulary, the picture is more complex: most categories converge into a central region with emergent substructure reflecting the overlapping distributional profiles of the included POScategories, while a subset, most notably numerals, project as isolated peripheral strands, consistent with their more uniform and construction\-specific successor distributions\. The degree of separation varies across categories and is not uniform, suggesting that the embedding space encodes a gradient rather than a discrete categorical structure\. The following subsections examine this internal organisation systematically, moving from the coarse three\-way NVA structure through increasingly fine\-grained sub\-class distinctions to the construction\-specific transition profiles recoverable at higher cluster resolutions\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x4.png)Figure 4:Emergence of Syntactic Structure in SR Geometry\.UMAP projections of SRembeddings for the untrained model \(left\) and after training \(epoch 10, right\), colored by ground\-truth POStag\. Prior to training, embeddings form a structureless cloud with no systematic POSorganisation\.a\)NVA subset \(NOUN, VERB, ADJ\): after training, embeddings decompose into three spatially separated regions corresponding to the three POScategories\.bExtended vocabulary \(13 POScategories\): after training, most categories converge into a central region with emergent substructure, while a subset project as isolated peripheral strands; numerals show the most distinct separation\.![Refer to caption](https://arxiv.org/html/2605.24585v1/x5.png)Figure 5:Unsupervised Clustering of Successor Representations and Connectivity Structure \(NVA, k=3\)\.To assess the geometric structure of the main syntactic categories in embedding space, SRs’ withγ=0\.2\\gamma=0\.2of the 200 most frequent tokens were sampled from each of three part\-of\-speech categories \(nouns, verbs, and adjectives\), yielding a balanced dataset of 600 tokens\.a\)UMAP projections of token embeddings, colored by KMeans cluster assignment \(left\), Bayesian Gaussian Mixture \(BGM\) cluster assignment \(center\), and ground\-truth Part\-of\-Speech \(POS\) tags \(right\), enabling direct visual comparison between unsupervised cluster solutions and known syntactic categories\.b\)Cluster purity heatmaps for KMeans clusters, showing the raw POS tag frequency per cluster \(left\) and the fractional POS tag composition per cluster \(right\), quantifying the degree to which each cluster captures a coherent syntactic category\.c\)Directed inter\-cluster successor representation \(SR\) connectivity network\. Nodes represent KMeans clusters and are colored according to their majority POS tag; directed edges indicate the magnitude of SR connectivity from source to target cluster, with edge thickness proportional to connection strength\.d\)SR connectivity matrix corresponding to the network in \(c\)\. Rows denote source clusters and columns denote target clusters; each entry reports the fraction of total directed SR connectivity from the source to the target cluster\.
### 3\.2Recovering Basic Syntactic Categories

The three\-way separation visible in Figure[4](https://arxiv.org/html/2605.24585#S3.F4)a\) suggests that the SRgeometry encodes POScategory information recoverable by unsupervised means\. To quantify this, we applied KMeans and BGMclustering \(k=3k=3\) to the NVA embeddings atγ=0\.2\\gamma=0\.2, targeting the 600 most frequent nouns, verbs, and adjectives\. Both methods confirm that the geometric structure of the SRspace closely mirrors syntactic category boundaries\. As shown by the color\-coded UMAPprojections in Figure[5](https://arxiv.org/html/2605.24585#S3.F5)a\), both KMeans and BGMclustering withk=3k=3recover groupings that align well with ground\-truth POStags, and the two methods yield only minor differences in cluster assignment, suggesting the three\-cluster solution is robust to the choice of algorithm \(full token\-level assignments are provided in Appendix[A](https://arxiv.org/html/2605.24585#A1)\)\. The confusion matrices between the KMeans clustering and the POStags in Figure[5](https://arxiv.org/html/2605.24585#S3.F5)b\) further illustrate this\. KMeans achieves per\-cluster POSpurities of 0\.89 \(C0→\\toADJ\), 0\.91 \(C1→\\toVERB\), and 0\.85 \(C2→\\toNOUN\) with all clusters consisting of around 200 tokens\. The coarse three\-way structure identified here raises the question of whether the SRspace contains further internal organization within each category\. The following subsection examines this by increasing cluster resolution tok=30k=30\.

Beyond cluster identity, the inter\-cluster SRnetwork and connectivity matrix \(Figures[5](https://arxiv.org/html/2605.24585#S3.F5)c\),d\)\) reveal interpretable syntactic transition patterns: adjectives transition predominantly toward nouns \(67%\) and rarely toward verbs \(7%\), consistent with the adjective\-noun modifier relationship\. Verbs distribute their SRmass roughly equally between adjectives \(40%\) and nouns \(47%\), with only minor self\-connectivity \(13%\), reflecting that verbs seldom succeed other verbs in natural language\. Notably, auxiliary verbs are assigned a dedicated POStag \(AUX\) in the Universal Dependencies tag set and are therefore excluded from theVERBcategory; the expected auxiliary\-to\-main\-verb transitions consequently do not contribute to the verb cluster’s self\-connectivity, making the low value all the more interpretable\. Nouns show the strongest tendency to transition to verbs \(52%\), with moderate self\-connectivity \(32%\), consistent with subject–predicate structure\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x6.png)Figure 6:Unsupervised Clustering of Successor Representations \(NVA, k=30\)\.SRsforγ=0\.2\\gamma=0\.2were extracted for a balanced sample of the 200 most frequent tokens per part\-of\-speech category \(nouns, verbs, and adjectives\), yielding a dataset of 600 tokens in total\.\(a\)UMAP projections of token embeddings, colored by KMeans cluster assignment \(left\), BGM cluster assignment \(center\), and ground\-truth POS tags \(right\)\. Clusters are aligned across algorithms by maximizing cluster overlap\. They receive a base color for their joint majority POS tag, with distinct shades differentiating individual clusters within the same syntactic category to facilitate comparison\.\(b\)Cluster purity heatmaps evaluating the alignment between KMeans clusters and POS categories\. The left heatmap shows the raw POS tag frequency across the 30 clusters, and the right heatmap shows the fractional purity, i\.e\. the proportion of each POS category assigned to each cluster, illustrating the degree of syntactic specialization achieved at higher cluster granularity \(K=30K=30\)\.
### 3\.3Fine\-Grained Clustering: Lexical Sub\-Classes as Constructional Slots

Increasing the number of clusters tok=30k=30reveals that the coarse three\-way ADJ/NOUN/VERB structure identified above is itself composed of finer\-grained distributional sub\-classes, many of which correspond to recognizable lexical or semantic groupings\. Figure[6](https://arxiv.org/html/2605.24585#S3.F6)a\) shows the UMAPprojections colored by KMeans and BGM cluster assignment alongside the ground\-truth POSlabels; at this granularity the embedding space decomposes into a mosaic of localised sub\-regions, each corresponding to a distinct cluster, while the broad three\-way POStopology of thek=3k=3solution is preserved\. The purity heatmaps in Figure[6](https://arxiv.org/html/2605.24585#S3.F6)b\) quantify this specialisation: the frequency panel \(left\) shows that most clusters are strongly dominated by a single POScategory, and the fraction panel \(right\) confirms that 24 of 30 clusters reach a majority\-category fraction of≥0\.8\\geq 0\.8, with 12 of them attaining 1\.0\. The full token\-level assignments for all 30 clusters are listed in Appendix[B](https://arxiv.org/html/2605.24585#A2)\.

The adjective clusters decompose into semantically coherent sub\-types: ordinal and rank modifiers \(first, second, third, final; C0\), scalar size adjectives \(large, small, larger, largest; C5\), colour and non\-gradable property terms \(white, black, male, female; C4\), and quantifier\-like modifiers \(many, several, various, numerous; C10\)\. Verb clusters similarly separate into distinct event\-type classes: motion and change\-of\-state verbs \(moved, returned, fell, launched; C13\), epistemic and communicative verbs \(said, stated, found, suggested; C18\), and competitive outcome verbs \(won, win, scored; C12\)\. Noun clusters capture domain\-coherent groupings including temporal expressions \(days, months, years, night; C25\), measurement units \(km, ft, mph, mm; C28\), and cultural/media artefacts \(film, album, song, episode; C24\)\.

The qualitative sub\-class structure observed here holds atγ=0\.2\\gamma=0\.2andk=30k=30, but the degree to which it generalises across SR horizon values and cluster granularities remains to be assessed\. The following subsection addresses this systematically\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x7.png)Figure 7:Clustering quality metrics \(ARI and NMI\) across SR configurations for the NVA subset\.ARIand NMImeasure the agreement between a clustering solution and the ground\-truth POS labels, correcting for chance and label permutation respectively\.\(a\)ARI\(left\) and NMI\(right\) as a function of the SRscale parameterγ\\gamma, evaluated on the NVA \(Noun\-Verb\-Adjective\) subset\. Trends are shown for varying cluster granularities \(KK\), comparing KMeans \(solid lines\) and BGM\(dashed lines\)\.\(b\)ARIand NMIas a function of cluster countKKat fixedγ=0\.2\\gamma=0\.2, illustrating how cluster resolution affects the recovery of prescribed syntactic structure from the restricted NVA vocabulary\.
### 3\.4Clustering Quality as a Function of SR Horizon and Cluster Granularity

To assess how well SRembeddings recover syntactic structure across temporal horizon parameterγ\\gammaand cluster countKK, we evaluated ARIand NMIagainst ground\-truth POSlabels across a grid of configurations as illustrated in Figure[7](https://arxiv.org/html/2605.24585#S3.F7)\.

Both ARIand NMIdecrease monotonically asγ\\gammaincreases \(Figure[7](https://arxiv.org/html/2605.24585#S3.F7)a\), regardless of clustering algorithm orKK\. This pattern is consistent with the interpretation that low\-γ\\gammaSRsweight immediate successors heavily, preserving local syntactic signal, whereas high\-γ\\gammaSRsintegrate over longer contextual windows, blending the distributional signatures of different syntactic categories and thereby reducing cluster coherence\. Notably, both metrics remain substantially above zero across all configurations, indicating that syntactic structure is recoverable from SRgeometry even at longer horizons\.

At fixedγ=0\.2\\gamma=0\.2, ARIand NMIboth peak sharply atK=3K=3\(Figure[7](https://arxiv.org/html/2605.24585#S3.F7)b\), with ARIreaching0\.660\.66, and NMIreaching0\.590\.59for both cluster methods, before declining steeply as cluster count increases\. This is consistent with the ground\-truth label structure: whenKKmatches the number of POScategories in the NVA subset, the clustering solution aligns most closely with the syntactic partition\. NMIdeclines more gradually than ARIand plateaus around0\.320\.32–0\.330\.33for largeKK, reflecting that finer partitions still capture some residual syntactic organization even as exact label recovery degrades\. KMeans and BGM perform near\-identically across all configurations, suggesting that the geometric signal in SRembeddings, rather than the clustering algorithm, drives performance\.

Having established the robustness of SR\-based category recovery for the three\-category NVA case, we now ask whether the same geometric organization extends to a broader and more heterogeneous vocabulary\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x8.png)Figure 8:Clustering of Successor Representations \(full,k=13k=13\)\.SRsforγ=0\.2\\gamma=0\.2were extracted for up to 200 of the most frequent tokens per part\-of\-speech category across 13 categories, yielding a dataset of 1377 tokens in total\.\(a\)UMAP projections of full vocabulary token embeddings, colored by KMeans cluster assignment \(left\) and POStags \(right\)\.\(b\)Cluster purity heatmaps evaluating the alignment between the 13 KMeans clusters and POS categories\.
### 3\.5Extended Vocabulary Clustering: Cross\-Category Structure atk=13k=13

Expanding the analysis to the extended set of POStags \(1377 tokens across 13 POScategories,γ=0\.2\\gamma=0\.2,k=13k=13\) tests whether SRgeometry captures syntactic structure beyond the relatively clean NVA case\. The UMAPprojections in Figure[8](https://arxiv.org/html/2605.24585#S3.F8)a demonstrate that the embedding space retains a broadly organized topology, with several clusters occupying distinct spatial regions that correspond well to ground\-truth POSlabels\.

The purity heatmaps in Figure[8](https://arxiv.org/html/2605.24585#S3.F8)b verify that several high\-purity clusters persist\. C1 is dominated by adverbs \(0\.83\), C6 by adjectives \(0\.71\), and C11 by proper nouns \(0\.77\)\. The two numeral clusters, C7 and C12, both achieve high purity \(0\.86 and 0\.87 respectively\) while capturing a meaningful internal distinction within the numeral category\. Specifically, C7 groups bare cardinals and measurement units \(56, 35, km, ft, million, hundred\), while C12 groups calendar years and month names \(1960, 1975, April, November\) together with temporal boundary markers \(since, until, late\)\.

Furthermore, several mixed clusters are themselves linguistically interpretable\. C2 groups subordinating conjunctions and complementizers \(that, because, although, whether, when\) with reporting verbs \(said, believed, claimed, stated\)\. This effectively captures the syntagmatic relationship between the verbs that select for propositional complements and the functional items that introduce them\. C4 groups prepositions with a large set of past participles \(created, followed, removed, included, found\), a pairing consistent with the shared syntactic environments of passive and prepositional phrases in English\. C5 groups quantificational determiners \(several, many, some, most, various\) with a subset of string numerals \(two, three, five, four, six\), reflecting their shared paradigmatic function as pre\-nominal quantity expressions\. C8 conflates nouns \(0\.37\) and proper nouns \(0\.49\) to capture geographically and institutionally grounded entities \(area, city, company, force, England, France\)\. C9 forms a temporally coherent cluster that blends duration and interval nouns \(days, months, weeks, years, night, summer\), aspectual and transitional verbs \(began, started, ended, completed, died, spent\), and temporal prepositions \(before, after, till\)\. This broad grouping suggests that the geometry organises around semantic\-functional domains rather than syntactic categories alone\. Finally, C10 and C11 both group common nouns with proper names but reflect distinct registers of Wikitext\-103\. C10 pairs event and cultural nouns with performer and athlete surnames, while C11 clusters institutional titles with the first names that follow them in biographical prose\.

C3 is a small cluster of five tokens \(become, became, becoming, formerly, newly\), whose composition suggests convergent successor profiles across inchoative copular verbs and state\-boundary adverbs\. C0 is the least pure cluster overall \(majority PRON at 0\.33\), aggregating pronouns, adverbs, and modal auxiliaries \(they, often, must, should, never\)\.

Together, these results confirm that SRgeometry captures linguistic structure well beyond surface syntactic categories, reflecting the constructional organization of language across a heterogeneous extended token set \(see AppendixLABEL:app:full\_k13for full token listings\)\.

Whereas the inter\-cluster transition structure of the NVA case revealed broad grammatical asymmetries at the level of major word classes, the following subsection examines whether the same transition logic extends to finer\-grained constructional distinctions\. Specifically, it focuses on the numerical and temporal subnetwork recoverable atk=120k=120\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x9.png)Figure 9:Successor representation connectivity within numerical and temporal cluster subnetworks\.\(a\)Directed SR subnetwork restricted to a selection of numerical and temporal clusters\. Nodes represent individual KMeans clusters colored by their majority POS tag; directed edges represent inter\-cluster transition strengths\.\(b\)SR connectivity matrix corresponding to the subnetwork in \(a\)\. The final column \(Max External\) reports the maximum connectivity from each source cluster to any cluster outside the restricted subset\.
### 3\.6SR Transition Structure at High Cluster Resolution

Figure[9](https://arxiv.org/html/2605.24585#S3.F9)presents a directed SRsubnetwork of seven clusters from thek=120k=120solution: one adpositional \(C37\), one nominal \(C67\), four numeral \(C65, C66, C118, C119\), and one proper nominal cluster encoding month names \(C117\)\.

The connectivity pattern reveals that transitions within the subnetwork broadly exceed theMax Externalbaseline, indicating that these tokens preferentially succeed one another in context rather than transitioning into the broader vocabulary\. However, the source clusters differ substantially in their target connections and transition strengths\.

Mid\-range numerals \(C65:Numbers Mid\) comprise integers spanning roughly 32 to 110\. Their outflow is sharply focused, with dominant flow toward units \(C67: 0\.26\) and a secondary transition toward relational prepositions \(C37: 0\.13\), both well exceeding the Max External baseline \(0\.07\)\. Outflow toward months and all year clusters is uniformly zero\.

Date\-range cardinals \(C66:Numbers Date\) comprise integers from 0 to 31\. Their outflow contrasts sharply with C65: the dominant transition is toward months \(C117: 0\.27\), well above the Max External baseline \(0\.05\), with moderate self\-connectivity \(0\.05\) and secondary flow toward units \(C67: 0\.10\) and relational prepositions \(C37: 0\.09\)\.

Unit expressions \(C67:km, ft, mph, mm\) exhibit the most focused outflow pattern, with transitions concentrated on date\-range cardinals \(C66: 0\.28\), relational prepositions \(C37: 0\.10\), and mid\-range numerals \(C65: 0\.07\), all exceeding the Max External baseline \(0\.05\)\. Outflow toward months and year clusters is effectively zero\.

Month names \(C117\) display the richest outflow profile, with strong transitions toward date\-range cardinals \(C66: 0\.30\), post\-1960 years \(C118: 0\.26\), and pre\-1960 years \(C119: 0\.13\), all well above the Max External baseline \(0\.06\)\. The year\-directed transitions show an asymmetry between C118 and C119, with stronger flow toward the more recent cluster\.

Beyond the numerical subnetwork, several furtherk=120k=120clusters illustrate the distributional specialization recoverable from SRgeometry\. Modal auxiliaries \(C0:would, should, could, might, must\) form a coherent pre\-verbal cluster, distinct from copular and aspectual auxiliaries \(C7:was, is, were, had, been\)\. Temporal sequence adverbs \(C12:then, eventually, finally, subsequently\) form a distinct, isolated cluster\. Personal given names \(C115\) and person\-role titles \(C116\) occupy adjacent but distinct regions, with C116 showing its strongest outflow toward the relational preposition cluster \(C37: 0\.31\) and its second strongest toward C115 \(0\.11\)\.

Taken together, these transition patterns demonstrate that at high cluster resolution, SRgeometry encodes not only the categorical identity of tokens but their sequential and constructional relationships, capturing the internal structure of complex expressions such as date phrases, measurement constructions, and biographical naming conventions without explicit supervision\. As in the NVA case, it now remains to assess how the broader cross\-category structure varies as a function of the SRhorizon parameterγ\\gammaand cluster countkk\.

![Refer to caption](https://arxiv.org/html/2605.24585v1/x10.png)Figure 10:Clustering quality metrics \(ARIand NMI\) across SR configurations for the extended set of POStags\.\(a\)ARI\(left\) and NMI\(right\) as a function of the SRdecay parameterγ\\gamma, evaluated on the extended POStag set\. Trends are shown for varying cluster granularities \(KK\), comparing KMeans \(solid lines\) and BGM \(dashed lines\)\.\(b\)ARIand NMIas a function of cluster countKKat fixedγ=0\.2\\gamma=0\.2, illustrating how cluster resolution affects the recovery of syntactic structure across the extended vocabulary\.
### 3\.7Clustering Quality Across SR Configurations: Extended Vocabulary

As in the NVA case, we assess how cross\-category structure varies as a function of the SRhorizon parameterγ\\gammaand cluster countKK\. Applying the same ARIand NMIanalysis to the extended vocabulary illustrated in Figure[10](https://arxiv.org/html/2605.24585#S3.F10)replicates the qualitative trends observed in the NVA subset, while revealing that syntactic structure is harder to recover for the broader token set\. As shown in Table[2](https://arxiv.org/html/2605.24585#S2.T2), the vocabulary is heavily imbalanced: six categories each contribute 200 tokens and together account for approximately 87% of the total, while the remaining seven categories are sparsely represented\.

Both ARIand NMIdecrease monotonically withγ\\gammaacross all values ofKKand both clustering algorithms \(Figure[10](https://arxiv.org/html/2605.24585#S3.F10)a\), mirroring the pattern observed in the NVA case\. Both metrics remain substantially above zero across all configurations, confirming that the embedding geometry captures genuine syntactic structure well beyond chance\.

At fixedγ=0\.2\\gamma=0\.2, ARIand NMIexhibit distinct behaviors as a function ofKK\(Figure[10](https://arxiv.org/html/2605.24585#S3.F10)b\)\. ARIpeaks sharply nearK=12K=12–1414, reaching0\.400\.40\(KMeans,K=14K=14\) and0\.410\.41\(BGM,K=12K=12\), close to the number of POScategories in the extended set, before declining steadily as over\-segmentation degrades label recovery\. NMIalso shows a local peak in the same range, at0\.490\.49\(KMeans,K=14K=14\) and0\.500\.50\(BGM,K=14K=14\), but the two methods diverge from there\. For BGM, this early peak constitutes the global maximum, after which NMIremains essentially flat, never dropping below0\.470\.47across the full range ofKK\. For KMeans,K=14K=14is only a local peak; NMIdips only modestly before climbing gradually through a secondary peak atK=18K=18\(0\.490\.49\) and reaching its global maximum of0\.50\.5atK=62K=62, after which it too stabilizes\. In both cases, the relative stability of NMIacross a wide range ofKKsuggests that the SRembedding space preserves substantial syntactic information regardless of cluster resolution\.

Together, these results confirm that the SRembedding space encodes syntactic category information across the extended vocabulary\. The theoretical implications of this emergent structure, and its relationship to constructionist accounts of word classes and grammatical knowledge, are taken up in the Discussion\.

## 4Discussion

### 4\.1Summary of Main Findings

The central result of this work is that SRs, trained as multi\-horizon predictive representations over a large naturalistic text corpus, spontaneously organise into a geometry that mirrors the hierarchical linguistic structure of language, namely its constructional organisation, without any explicit supervision\.

Focusing first on the three major categories of nouns, verbs, and adjectives, unsupervised clustering of SRembeddings atγ=0\.2\\gamma=0\.2recovers these categories with per\-cluster POSpurities of 0\.89, 0\.91, and 0\.85 respectively \(k=3k=3\)\. The inter\-cluster transition network further replicates well\-motivated grammatical asymmetries: strong ADJ→\\toNOUN flow \(67%\) reflects the modifier–head construction; dominant NOUN→\\toVERB connectivity \(52%\) encodes the subject–predicate template; and minor VERB→\\toVERB self\-connectivity \(13%\) mirrors the rarity of bare main\-verb serialisation in English\. Extending tok=30k=30reveals semantically coherent sub\-classes—ordinal modifiers, scalar adjectives, epistemic verbs, temporal nouns—interpretable as distributional signatures of the constructional slots these items habitually occupy\.

Extending the analysis to the full vocabulary of 1377 tokens across 13 POScategories shows that this structure generalises well beyond the clean three\-way NVA case, albeit with greater between\-category blurring\. Atk=13k=13, high\-purity clusters persist for adverbs \(C1: 0\.83\), adjectives \(C6: 0\.71\), and proper nouns \(C11: 0\.77\), while the mixed clusters that do arise are largely interpretable through a constructional lens\. C2 is a particularly striking case: rather than following any single syntactic category boundary, it groups subordinating conjunctions and complementizers with reporting verbs\. This captures the syntagmatic relationship of the clause\-embedding construction, linking the verbs that select for propositional complements with the functional items that introduce them\. C9 cuts across POScategories entirely, grouping temporal nouns, aspectual verbs, and temporal prepositions into a single coherent cluster, suggesting the geometry organises around semantic\-functional domains rather than syntactic categories alone\. C10 and C11 further reveal sensitivity to register and discourse context, distinguishing event and cultural nouns paired with performer surnames from institutional titles paired with the first names that follow them in biographical prose\. Particularly striking is the spontaneous separation of numerals into two distinct clusters despite their shared POStag: C7 groups bare cardinals and measurement units \(56, 35, km, ft, million, hundred\), while C12 groups calendar years and month names \(1960, 1975, April, November\) alongside temporal boundary markers \(since, until, late\), both achieving high purity \(0\.86 and 0\.87 respectively\)\. The SRhas thus implicitly distinguished between bare quantity expressions and temporal reference expressions, a distinction that standard POStagging collapses entirely\.

Notably, the organisational principles underlying these clusters vary freely between traditionally syntactic and semantic criteria\. The geometry recovers formal category boundaries where they are distributionally sharp, and semantic\-functional domains where they are not, reflecting no commitment to the autonomy of syntax that standard POStaxonomies presuppose\.

This separation sharpens atk=120k=120, where the numerical subnetwork decomposes into date\-range cardinals \(C66, integers 0–31\), mid\-range numerals \(C65, roughly 32–110\), month names \(C117\), and two historically stratified year clusters \(C118, C119\)\. Reciprocal month–day transitions \(C66↔\\leftrightarrowC117: 0\.27/0\.30\) and asymmetric month–year flow \(C117→\\toC118: 0\.26 vs\. C117→\\toC119: 0\.13\) reveal a coherent date\-formation subsystem\. Within this subsystem, the boundary between date\-relevant and date\-irrelevant numerals is drawn precisely at 31, the maximum day\-of\-month value\. The stronger flow toward the more recent year cluster \(C118: 0\.26 vs\. C119: 0\.13\) further reflects the higher frequency with which modern events are cited at full date resolution\.

Taken across all clustering resolutions, ARIand NMIatγ=0\.2\\gamma=0\.2confirm this pattern quantitatively\. For the NVA subset, both metrics peak sharply atK=3K=3, with ARIreaching0\.660\.66and NMI0\.590\.59, reflecting a clean three\-way partition that closely matches the ground\-truth category structure\. For the extended vocabulary, ARIpeaks nearK=12K=12–1414at0\.400\.40–0\.410\.41, while NMIplateaus across a broad range ofKKat approximately0\.470\.47–0\.500\.50\. This gap reflects not only the greater challenge of separating thirteen categories rather than three, but also the inherently fuzzy boundaries between them\. At the same time, the broad NMI plateau and the continued emergence of interpretable clusters at higherKKsuggest that the SRssupport additional, finer\-grained semantic and constructional substructure that is not captured by standard POSannotations, and therefore not reflected in these metrics\.

### 4\.2Constructions as Lossy Clusters of Memory Traces

The cluster purity results have a theoretical implication that extends beyond methodological validation\. Together with the ARIand NMIpeaks atK=3K=3, the recovery of groupings closely corresponding to ADJ, NOUN, and VERB indicates that these categories possess a coherent distributional signature implicit in sequential co\-occurrence statistics\. This is consistent with a constructionist view of word classes, in which category membership is not an intrinsic lexical property but an emergent consequence of the positional and combinatorial privileges a form repeatedly occupies across constructions\[cf\.croft2001radical,bybee2010language,hopper1987emergent,goldberg1995constructions,goldberg2006constructions,hoffmann2013oxford\]\. Crucially, the model spontaneously encodes both dimensions of linguistic organization\. It captures the sequential links that bind elements together into constructions \(syntagmatic relations\) as well as the equivalence classes of items that can substitute into the same structural slots \(paradigmatic relations\)\. On this view, the clusters recovered atk=3k=3are not merely taxonomic groupings, but reflect distinct distributional niches defined jointly by the positions an item occupies and the transitions it licenses\.

This interpretation is reinforced by the directional asymmetries in inter\-cluster connectivity\. The strong ADJ→\\toNOUN flow \(60%\) aligns with the canonical modifier–head construction, in which adjectives are licensed as dependents but not as heads\. The dominant NOUN→\\toVERB transition \(56%\) reflects the subject–predicate construction, the most productive clause\-level template in English\. Conversely, the near absence of VERB→\\toVERB transitions \(1%\) corresponds to the lack of a construction in which bare main verbs license a second main verb as their immediate successor\. That these typologically well\-motivated constraints emerge from sequential statistics alone indicates that the SRsencode not just category structure, but the constructional skeleton of the language\[cf\.bybee2002word,bybee2010language,diessel2019grammar,diessel2019usage\]\.

The geometry underlying these patterns supports a stronger claim\. Goldberg’s recent formulation defines constructions as emergent clusters of lossy memory traces that align in a high\-dimensional space on the basis of shared form, function, and contextual dimensions\[goldberg2019explain\]\. The SRspace instantiates precisely such a space, and the clusters that emerge from it can be understood as such compressions: each cluster summarises a family of partially overlapping usage traces whose shared successor profile reflects the combinatorial privileges conferred by repeated participation in similar contexts\. Under this view, the SRdoes not merely approximate a pre\-existing constructional taxonomy; it provides a computational substrate for the emergence of constructions from usage\.

Within this framework, the cluster resolutionkkhas a natural interpretation as a compression threshold over memory traces\. Thek=3k=3solution applies the coarsest compression, capturing broad distinctions between nominal, verbal, and adjectival slots\. Increasingkklowers this threshold and reveals finer\-grained structure: the sub\-class distinctions observed atk=30k=30, such as ordinal adjectives in ranked\-list constructions, scalar adjectives in degree constructions, and epistemic verbs in complement\-clause constructions, correspond to increasingly specific constructional slots\. The embedding space thus encodes not only category membership, but the constructional contexts items inhabit, consistent with usage\-based accounts in which lexical representations are stored together with their distributional histories\. Each increase inkkreveals a deeper layer of this hierarchy, from abstract slot types to item\-specific construction families, supporting the view that constructional knowledge emerges from general predictive memory mechanisms applied to sequential structure\.

### 4\.3Construction\-Specific Successor Profiles

If the preceding subsection establishes that SRgeometry encodes constructional organization in principle, the mixed clusters in the extended vocabulary analysis \(k=13k=13\) demonstrate this more directly\. Several clusters are best understood not as approximations of POScategories, but as traces of specific construction families, where grouping is determined by shared successor environments rather than surface category membership\. Crucially, the organizational principles these clusters reflect vary freely between traditionally syntactic and semantic criteria: the geometry recovers formal category boundaries where they are distributionally sharp, and semantic\-functional domains where they are not, reflecting no commitment to the autonomy of syntax that standard POStaxonomies presuppose\. This is precisely what usage\-based accounts predict: a system abstracting structure from sequential experience should arrive at representations organized around the constructions that unite form and meaning in actual use, rather than the formal categories imposed on top of them\. In this view, the mixed clusters are not categorization errors, but precise representations of the slot\-and\-filler architecture that defines the constructicon\. By grouping items according to their shared transitional profiles, the model captures both the horizontal, syntagmatic templates that dictate how elements are combined into larger symbolic assemblies, and the vertical, paradigmatic classes of lexical items licensed to fill those specific semantic\-functional slots\.

Cluster C2, which groups subordinating conjunctions and complementizers with reporting verbs, aligns with the complement\-clause construction, encoding the syntagmatic relationship where these verbs select precisely these items as successors\. C5, grouping quantificational determiners with certain numerals, reflects their shared paradigmatic function as nominal pre\-modifiers\. C9, blending temporal nouns, aspectual verbs, and temporal prepositions, captures a semantic\-functional domain defined by temporality rather than any syntactic category\. In each case, the grouping is opaque from a categorical perspective but coherent in constructional terms\.

The division of the numeral category illustrates this particularly clearly\. Bare cardinals and measurement units \(C7\) and calendar years with month names \(C12\) occupy distinct constructional slots and are accordingly separated in the SRspace\. At higher resolution \(k=120k=120\), this distinction develops into a structured subsystem: reciprocal month–day transitions encode the bidirectional\[DD MONTH\]/\[MONTH DD\]construction; transitions from months to years encode the\[MONTH YEAR\]construction; and the boundary between date\-relevant and irrelevant numerals aligns precisely with the maximum day\-of\-month value, without any explicit supervision\. The isolation of measurement expressions from this subsystem further confirms that the geometry tracks constructional function rather than surface category\.

A similar pattern appears in the distinction between person\-role titles \(C116\) and given names \(C115\)\. The dominant transitions from titles to relational prepositions relates to the\[TITLE of NP\]construction, while transitions to name clusters encode the appositive\[TITLE NAME\]construction\. That these patterns emerge from successor statistics alone indicates that the SRspace captures fine\-grained slot distinctions within lexical domains\. Ultimately, these results confirm that the SRspace encodes the full slot\-and\-filler architecture predicted by usage\-based accounts\. By abstracting both syntagmatic combinatorial rules and paradigmatic equivalence classes from sequential experience, the model provides a concrete computational substrate for the emergence of grammar\.

### 4\.4Neurally Plausible Acquisition of Constructional Knowledge

The preceding subsections establish that SRgeometry encodes constructional organization across multiple levels of resolution, from the broad privileges of major word classes down to the internal structure of specific constructions\. The theoretical framework used to interpret these results—constructions as emergent clusters of lossy memory traces—carries an implicit claim about the biological substrate of this process\. If constructions are memory traces, then the system responsible for their formation is, in the first instance, a memory system, and a remaining question is whether the learning mechanism proposed here is consistent with what is known about such systems\.

The hippocampus is precisely the structure implicated in the formation, consolidation, and organisation of episodic and semantic memory traces\[eichenbaum2000cortical\], and is known to build cognitive maps of the environment\[tolman1948cognitive\]\. The SRframework was originally proposed as a model of these hippocampal maps, extending the cognitive map concept by proposing that place cells encode not current location but anticipated future states\[stachenfeld2017hippocampus\]\. Empirical support for SR\-like representations in the brain has since been reported in neuroimaging studies\[ekman2023successor,garvert2017map,brunec2022predictive\], strengthening the case that the computational principles formalised here have a genuine neural realization\.

Understanding how the SRis acquired in the brain is an important open question, and temporal difference learning with eligibility traces, or TD\(λ\\lambda\), offers a plausible mechanism\. Computationally, TD algorithms efficiently learn SRs\[russek2017predictive\]\. Biologically, spike\-timing\-dependent plasticity in spiking neural networks corresponds algorithmically to TD\(λ\\lambda\) learning to form predictive maps\[bono2023learning\]\. Behaviorally, TD\(λ\\lambda\) updating rule helps explain trial\-by\-trial sequence learning in humans\[kahn2025trial\]\. Thus, modelling SRlearning via TD\(λ\\lambda\) is well supported by computational, biological, and behavioral evidence\.

Token\-level SRscan then be understood as an analogous predictive map of linguistic space: just as place cells compress trajectories of spatial experience into a predictive map of the environment, SRscompress trajectories of linguistic experience into a geometry that reflects the constructional structure of the language\. The clusters that emerge from this compression are, in Goldberg’s terms, precisely the lossy memory traces that constructions are\. The resulting representations are not purely syntactic or semantic, but organized around constructions that integrate both, consistent with usage\-based accounts of grammar\.

Crucially, this structure is acquired with striking efficiency\. Training loss declines sharply within the first epoch, with only marginal gains thereafter, indicating that the dominant constructional regularities are extracted after minimal exposure\. This pattern aligns with usage\-based theories of rapid generalization from limited input\[tomasello2003constructing\], and is consistent with neuro\-scientific accounts of rapid unsupervised structure learning in the hippocampal\-entorhinal system\[kumaran2016learning\], standing in stark contrast to the prolonged training regimes typical of contemporary large language models\.

Taken together, these findings support a unifying hypothesis: constructional knowledge is not a specialized linguistic module, but an instance of a more general predictive memory system operating over structured sequences\. If constructions are lossy compressions of usage traces stored in memory, the SRmay serve as a computational bridge between the constructional organization of language and the neuro\-scientific accounts of the memory system in which that organization is grounded\.

### 4\.5The Problem of Clustering Resolution and Temporal Horizon

A practical limitation of the current framework is the absence of a principled criterion for selecting the appropriate clustering resolutionkkor the temporal horizonγ\\gamma\. Both parameters govern fundamentally different aspects of representational granularity, and their interaction has substantial consequences for what structure is recovered\.

Theγ\\gammaparameter controls the temporal depth of the SR: low values weight immediate successors heavily and preserve local syntactic signal, yielding high POSpurity; high values integrate over longer contextual windows, blending the distributional signatures of different categories and reducing cluster coherence, though potentially encoding discourse\-level or semantic structure that local representations obscure\. This monotonic decrease in POSpurity withγ\\gammais observed consistently across all cluster counts and both algorithms, suggesting that higherγ\\gammadoes not simply encode different structure but encodes structure at a coarser syntactic grain which could relate to higher\-level features such as thematic roles or information structure, but at the cost of categorical distinctiveness\. Whether the blurring of distributional signatures at highγ\\gammareflects genuine structural overlap between categories or simply a loss of representational resolution is an open question that future work with richer evaluation tasks would need to address\.

The cluster countkksimilarly lacks a theoretically motivated stopping criterion\. The current analysis relies on qualitative interpretability at selected values \(k=3,13,30,120k=3,13,30,120\) and quantitative purity metrics as proxies for structural validity\. A more principled approach might employ information\-theoretic model selection, the Bayesian evidence computed by BGM, or held\-out prediction tasks that measure whether a given clustering level supports downstream generalization\. The observation that BGM and KMeans converge at lowkkbut diverge at higher granularities, with KMeans achieving marginally higher purity at largekk, is itself informative: it suggests that the coarse structure of the SRspace is robust to algorithmic choice, while finer subdivisions are more sensitive to the clustering objective\. A systematic model selection framework capable of simultaneously optimizingkk,γ\\gamma, and the clustering criterion would constitute a significant methodological advance and a possible direction for future work\.

### 4\.6Polysemy, Context\-Sensitivity, and the Limits of Type\-Level Representations

A fundamental limitation shared by SRanalyses reported here is the inability to distinguish between distinct senses of a surface form\. The SRof a token is estimated by averaging across all its corpus occurrences\. This collapses multiple distinct usage patterns, and with them potentially multiple distinct constructional roles, into a single point in embedding space\. This conflation of polysemy with distributional centrality is a known issue in distributional semantics more broadly\[camacho2018word,erk2008structured,fonteyn2021varying\], but it is particularly consequential for the constructional interpretation advanced here, where the claim is that distinct positional privileges should occupy distinct regions of the representational space\.

The practical implications are visible in several of the mixed clusters described above\. Past participles and prepositions are co\-assigned in cluster C4 of thek=13k=13extended vocabulary analysis, plausibly because their type\-level SRslikely conflate passive, relative clause, and adjectival participial contexts that differ structurally but share enough surface successors to appear similar in aggregate\. More pointedly, case\-collapsed forms likemay\(modal vs\. proper noun\) orsince\(temporal vs\. causal\) cannot be disambiguated without access to the local context\. This is not merely a tokenisation problem: it reflects a principled limitation of type\-level representations for a goal that ultimately requires token\-level, contextualised inference\.

Addressing this limitation will require a shift to contextualised SRestimation, in which the successor representation of a token is conditioned on the preceding context rather than averaged across contexts\. Several architectures are natural candidates for this extension, including transformer\-based models, recurrent networks, sliding window approaches, and accumulating the predecessors in a similar way to our SRstargets, each offering different trade\-offs between computational efficiency and the depth of contextual conditioning\. Crucially, contextualised estimation may also rehabilitate the higherγ\\gammaconfigurations that underperformed in the type\-level setting: where averaging across contexts blurs distinct constructional roles, conditioning on local context may instead allow high\-γ\\gammarepresentations to capture genuine long\-range structural dependencies that are simply invisible to context\-insensitive averaging\.

### 4\.7Emergent Niches and a Distributional Methodology for Typology

The recovery of broad word\-class structure from SRgeometry carries a methodological implication that extends well beyond the present English\-language model\. Typological linguistics has long recognized the danger of imposing traditional, often Eurocentric grammatical conventions onto diverse languages\[wierzbicka2013imprisoned,haspelmath2010comparative\]\. Because our unsupervised approach demonstrates that structural categories can be discovered directly from sequential statistics, it offers a powerful alternative: a data\-driven tool for cross\-linguistic analysis that organically maps a language’s true emergent categories without requiring any prior commitment to traditional taxonomies\.

This data\-driven potential is consistent with a strand of thinking in both typological linguistics and computational cognitive science that treats linguistic structure not as an innate constraint but as a convergent outcome of the same learning pressures applied to structurally similar statistical environments\[christiansen2008language,kirby2014iterated,christiansen2015language\]\. Under this view, the fact that ADJ, NOUN, and VERB emerge from SRclustering without any prior commitment to these categories is not surprising: they correspond to the most stable and productive distributional niches in the structure of English\. Rather than treating these specific classes as universal templates, the present results provide a concrete computational demonstration of this convergence mechanism\. They raise the broader conjecture that the spontaneous formation of structural categories is a stable phenomenon that emerges independently of the specific architecture, training regime, or substrate in which prediction is implemented, whether biological or artificial\.

When restricted to the specific statistical environment of English, the emergence of NOUN, VERB, and ADJ takes on a particularly striking character\. Because the model recovers these categories so robustly without explicit supervision, they can be understood as Platonic attractors within the language’s specific distributional space\. That is, for a language with English’s particular typological profile, these three categories represent mathematically optimal, highly stable representational states\. Any sufficiently powerful predictive system—whether biological or artificial—navigating this specific linguistic environment is inevitably drawn to these structural solutions\. They emerge not because they are universal constraints on all human language, but because they are the inescapable topological attractors of this particular grammar’s sequential dynamics\.

HERE we can tell more about the other evidence from your previous studies and elaborate on platonic attractors

### 4\.8Relation to Predictive Coding and Towards Multiscale Planning

The theoretical framing of the present work connects naturally to the predictive coding account of cortical function and the free\-energy principle\[friston2010free,clark2013whatever\]\. Under this framework, the brain is understood as a hierarchical inference engine that continuously generates and updates predictions about incoming sensory data, with higher cortical levels encoding increasingly abstract and temporally extended predictions\. The multi\-head SRarchitecture shares the core commitment to prediction as the organising principle of representation: eachγ\\gammahead encodes expected future context at a different temporal horizon, together spanning multiple timescales of sequential structure\. The present work has examined these heads independently, however, and makes no claim about how their representations should be integrated and weighted across timescales, a question that future work would need to address before a closer architectural parallel to predictive coding can be drawn\.

This open question points toward a broader possibility: that the hierarchical structure of the SRembedding space could serve as a substrate for multiscale planning in language production\. Under predictive coding, action is not merely reactive but anticipatory, the motor system fulfils top\-down predictions rather than responding to bottom\-up error signals alone\. In psycholinguistics, it is well established that an analogous principle governs language production: speakers do not select words sequentially in isolation\[lashley1951problem\], but rather pre\-activate hierarchical plans in which abstract frames constrain slot\-level lexical choice before articulation begins\[garrett1975analysis,bock1986syntactic,dell1986spreading,levelt1989speaking\]\.

However, formalizing this dynamic, anticipatory process within the theoretical framework of Construction Grammar has remained a challenge\. The SRtransition structure provides a concrete, mathematical mechanism to bridge this gap\. It is well\-suited to support exactly this kind of planning: it encodes not merely which clusters follow which, but the full probability mass over expected successors at multiple levels of granularity simultaneously\. The date\-formation subnetwork atk=120k=120illustrates this concretely, a production system operating over this space could commit to a\[MONTH YEAR\]frame at the coarse level and then use the fine\-grained transition probabilities to constrain the selection of a specific month name and year token in sequence, propagating structural commitments downward from abstract template to concrete lexical instantiation\.

Realizing this vision in full requires several advances beyond the scope of the present work\. The representations must be made contextualised rather than type\-level, so that production plans are sensitive to the specific discourse context rather than averaged distributional profiles\. A mechanism for the bidirectional use of the SRmust be specified — not only predicting what follows, but using predicted successors to actively constrain what should be produced next\. And a principled account of how multipleγ\\gammaheads are weighted and coordinated in real\-time sequential production remains to be developed\. These are substantive open problems, but the present results provide an encouraging demonstration that the representational substrate required for such a system is, in principle, learnable from corpus statistics alone and that the same predictive objective that gives rise to interpretable constructional structure may also be sufficient to support its productive use\.

### 4\.9Predicting Creativity

Beyond showing how syntax emerges, SR\-based cognitive maps provide a rigorous framework to model linguistic creativity\. In usage\-based linguistics, creativity is not random deviation, but the structured extension of established patterns\. While F\-creativity covers conventional productivity, E\-creativity involves stretching the constructicon through mechanisms like conceptual blending\[sampson2016two,fauconnier2003conceptual\]\. Herbst’s collo\-creativity\[herbst2018collo\]highlights a specific instance of this, where speakers insert highly unexpected lexical fillers into familiar constructional slots\.

The theoretical challenge in analyzing these extensions lies in distinguishing deliberate, creative deviations from unintelligible errors\. As recent usage\-based models emphasize, successful creativity relies on violating local conventions while maintaining enough global structural coherence for the listener to infer the speaker’s creative intent\[uhrig2020creative,uhrig2018don,hoffmann20245c\]\.

The SR framework operationalizes this exact dynamic by modeling creativity as a scale\-dependent violation\. In our model, a collo\-creative utterance—such as an unexpected lexical filler—corresponds to a drop in SR transition weights to near\-zero at a fine\-grained, item\-specific level \(such as k=120\)\. However, the utterance remains structurally coherent because the transition still aligns with the robust, higher\-order expectations of a coarse\-grained constructional supercluster \(such as k=13\)\.

The numerical and temporal subnetwork illustrates this clearly\. A conventional phrase like ”on the 28th of March” carries high SR probability mass at fine\-grained resolutions because it respects the established boundaries of a 31\-day month\. Conversely, an anomalous phrase like ”on the 32nd of March” exhibits near\-zero probability at the fine\-grained level, violating the local lexical constraint\. Yet, because ”32” is part of the same expected supercluster of numerals at coarser resolutions, the overarching syntactic and constructional frame is preserved\.

This multi\-granular alignment provides a topological metric for the theoretical distinction between errors and innovation\. The SR space maps the structural expectation landscape, quantifying exactly how and where a rule is broken\. Ultimately, while the transition geometry captures the precise structural nature of the deviation, it is the pragmatic context and communicative intent that determine whether a mathematically low\-probability transition is processed as a mistake or a deliberate act of creativity\.

### 4\.10Limitations and Future Directions

Several limitations of the current study should be noted explicitly\. The training corpus \(Wikitext\-103\) is a relatively homogeneous, encyclopaedic text collection, and it remains to be seen whether the same structural regularities emerge from more typologically or register\-diverse corpora, or from child\-directed speech more directly relevant to acquisition\. The model architecture and vocabulary size are modest by contemporary standards, and while this motivates the biological plausibility argument for efficiency, it also limits the depth of sub\-class structure that can be recovered\. Future work should examine whether SR\-based representations trained on richer or more diverse corpora yield a correspondingly richer constructional hierarchy, and whether the date\-formation and title–name subnetworks described here generalize across genres\.

The conflation of polysemous forms under type\-level representations has been noted above as methodological priority\. A further important direction is the direct validation of SR\-based constructional clusters against neural data: if these representations provide a genuine model of hippocampal cognitive maps for linguistic sequences, the cluster structure and transition connectivity should make testable predictions about representational similarity in the brain during language processing, which fMRI and electrophysiology studies can evaluate\. Grounding the computational model described here in such empirical evidence is the most direct path toward a fully validated neuro\-computational theory of constructional knowledge\. A further important direction is the direct validation of SR\-based representations against neural data: if the SRsthemselves provide a genuine model of hippocampal cognitive maps for linguistic sequences, both the raw representational geometry encoded in the SR vectors and the constructional cluster structure and transition connectivity derived from them should make testable predictions about neural representational structure during language processing\. Representational similarity analysis\[kriegeskorte2008representational\]offers one principled method for this comparison, aligning the pairwise similarity structure of SR\-based representations with that of neural responses measured by fMRI or electrophysiology\. Grounding the computational model described here in such empirical evidence is the most direct path toward a fully validated neuro\-computational theory of constructional knowledge\.

## References

## Appendix ACluster Token Assignments:γ=0\.2\\gamma=0\.2, NVA,k=3k=3

Cluster 0: same, new, use, own, particular, other, s, known, separate, such, form, individual, level, associated, similar, current, first, possible, key, important, related, limited, whole, previous, larger, additional, real, original, different, single, standard, active, available, common, future, minor, remaining, successful, traditional, independent, create, certain, regular, full, subsequent, notable, potential, popular, third, complete, main, specific, range, local, unknown, recent, various, number, true, major, strong, powerful, clear, significant, entire, wide, special, second, modern, poor, overall, multiple, numerous, primary, prominent, several, high, american, mixed, official, complex, open, european, smaller, contemporary, century, last, commercial, fourth, older, critical, using, free, many, early, difficult, international, top, initial, famous, direct, national, chinese, small, living, good, great, final, greatest, next, secret, large, right, best, long, higher, fifth, canadian, better, few, indian, largest, provide, historical, russian, white, german, professional, japanese, french, daily, body, opening, 20th, increased, private, heavy, short, dead, low, italian, soviet, light, seventh, total, annual, female, highest, sixth, foreign, black, military, double, average, polish, bad, natural, 19th, hard, big, positive, roman, central, federal, greater, latin, western, personal, cultural, ancient, middle, public, native, male, anti, human, dark, armed, social, civil, political, legal, economic, medical, physical, nuclear, senior, lower, severe, imperial, yellow, southern, religious, naval, electric, maximum, estimated, upper, financial, 1st

Cluster 1: created, removed, followed, addition, worked, included, made, taken, put, done, introduced, given, found, seen, allowed, added, used, see, revealed, saw, involved, including, making, return, served, claimed, performed, returned, held, suggested, support, offered, appeared, reported, brought, called, said, recorded, established, led, way, compared, wanted, stated, take, described, noted, turned, came, placed, discovered, believed, formed, produced, leave, shows, ran, released, raised, took, developed, leaving, wrote, run, changed, carried, taking, announced, make, give, present, gave, opened, following, supported, designed, saying, selected, moved, order, ordered, replaced, inspired, keep, find, allow, thought, based, required, lost, pass, takes, sent, left, awarded, provided, signed, include, working, featured, come, running, includes, launched, composed, intended, played, passed, appear, built, playing, considered, planned, issued, went, directed, appears, lead, hit, met, going, caused, proposed, leading, published, fell, responsible, decided, go, sold, features, member, forced, moving, get, do, destroyed, arrived, received, joined, failed, named, know, captured, extended, agreed, won, written, killed, help, according, able, felt, win, told, runs, entered, asked, old, helped, winning, former, became, become, appointed, praised, got, reached, damaged, remains, unable, prime, ranked, becoming, nearby, located, remained, scored, defeated, born, t, suffered, fellow, married

Cluster 2: time, work, place, events, days, position, part, event, group, result, life, line, history, years, day, end, site, company, games, success, role, development, period, project, list, set, case, months, example, release, show, hours, area, weeks, series, point, performance, works, rest, center, times, region, version, year, beginning, office, house, members, play, studio, men, production, start, game, man, stage, country, town, force, action, track, system, field, story, band, campaign, latter, month, power, scene, building, side, film, station, team, post, book, shot, career, war, base, island, record, week, season, service, minutes, tour, control, others, half, death, match, world, party, points, school, bridge, design, children, song, crew, score, command, magazine, home, cast, attack, people, title, head, players, review, night, women, album, construction, fire, division, style, songs, started, ended, name, characters, episode, ground, areas, completed, battle, writing, victory, family, coast, age, forces, ship, front, cut, training, recording, state, damage, music, broadcast, fight, sound, road, player, class, having, art, chart, close, m, ships, live, father, offensive, likely, c, began, radio, government, guns, football, college, land, summer, love, character, square, operation, finished, continued, population, h, league, aircraft, air, least, fighting, media, law, feet, video, son, mother, much, police, fleet, sea, championship, television, species, troops, re, died, northwest, storm, km, late, wife, miles, route, president, spent, ft, water, critics, comic, rear, mm, mph, musical, hurricane

## Appendix BCluster Token Assignments:γ=0\.2\\gamma=0\.2, NVA,k=30k=30

Cluster 0: fourth, third, fifth, second, seventh, sixth, first, next, last, final, 20th, 19th, opening, 1st

Cluster 1: russian, french, german, italian, chinese, polish, american, soviet, canadian, indian, japanese, european, local, independent, national, international, foreign, military, roman, civil, federal, imperial, professional, naval, private, senior, armed

Cluster 2: known, modern, prominent, century, traditional, contemporary, older, popular, famous, native, unknown, ancient, powerful, living, western, latin, central, southern, anti

Cluster 3: higher, high, low, average, increased, total, lower, highest, overall, maximum, greater, estimated, middle, upper

Cluster 4: white, black, dead, male, female, yellow, dark

Cluster 5: larger, large, small, smaller, largest, entire, whole

Cluster 6: level, single, s, standard, wide, long, range, open, full, short, complete, right, light, double, body, hard, top, free, heavy, big, electric

Cluster 7: political, economic, social, cultural, legal, religious, historical, financial, personal, public, medical

Cluster 8: previous, subsequent, recent, new, future, current, original, successful, official, regular, initial, early, annual, daily

Cluster 9: use, using, create, form, such, associated, provide, available

Cluster 10: other, several, various, numerous, many, multiple, few, certain, individual, different, separate, additional, remaining, number

Cluster 11: particular, similar, same, possible, important, specific, related, key, own, significant, real, common, potential, limited, minor, primary, strong, critical, poor, difficult, true, clear, good, active, notable, main, complex, major, direct, special, greatest, better, mixed, commercial, positive, great, best, bad, natural, secret, physical, human, severe, nuclear

Cluster 12: won, win, winning, scored

Cluster 13: removed, ran, moved, held, returned, formed, opened, came, carried, raised, served, return, run, built, left, leave, destroyed, leaving, placed, fell, turned, reported, arrived, established, passed, went, lost, pass, launched, come, running, captured, sold, hit, moving, going, runs, issued, located, reached, go, damaged, extended, entered, caused, killed, nearby, suffered

Cluster 14: intended, decided, wanted, able, order, allowed, unable, failed, required, agreed, planned, forced, help, helped, proposed

Cluster 15: led, joined, replaced, named, met, selected, signed, sent, appointed, supported, member, awarded, according, told, asked, ordered, former, defeated, leading, fellow, old, born, married, ranked

Cluster 16: become, became, becoming, remained, remains

Cluster 17: get, got, t, way, do

Cluster 18: said, stated, revealed, believed, thought, saying, found, shows, suggested, noted, seen, done, see, appeared, claimed, discovered, appears, felt, considered, know, appear, announced

Cluster 19: addition, support, involved, responsible, present, lead, prime

Cluster 20: take, give, making, given, put, taking, made, offered, make, took, gave, taken, takes, brought, find, saw, provided, allow, keep, received

Cluster 21: created, included, introduced, followed, performed, produced, including, described, featured, worked, added, used, recorded, inspired, compared, composed, includes, wrote, called, developed, include, released, based, designed, features, published, directed, following, changed, working, playing, written, played, praised

Cluster 22: work, members, life, case, result, role, group, example, history, others, children, works, men, times, period, man, project, list, people, characters, women, development, death, latter, party, players, father, name, family, war, world, son, mother, likely, age, having, fight, player, law, wife, much, critics, president, re

Cluster 23: event, games, match, season, events, team, success, tour, career, campaign, championship, victory, points, league, football, action

Cluster 24: performance, show, film, release, series, game, book, version, song, story, album, play, writing, music, songs, studio, episode, scene, production, band, magazine, video, recording, stage, track, cast, style, design, title, record, review, shot, score, sound, broadcast, character, art, television, love, live, comic, radio, media, chart, musical

Cluster 25: days, months, weeks, beginning, years, hours, month, time, day, year, start, started, week, ended, minutes, completed, began, night, finished, continued, summer, died, spent, late

Cluster 26: end, place, part, point, set, position, half, post, head, cut, close

Cluster 27: line, area, site, company, force, region, island, center, rest, building, station, town, base, field, bridge, system, service, ground, house, ship, forces, power, areas, construction, office, command, division, control, coast, fire, attack, side, country, front, crew, ships, land, training, battle, damage, road, aircraft, home, state, school, air, fleet, guns, government, sea, troops, class, population, offensive, square, operation, police, northwest, college, fighting, water, species, storm, rear, hurricane

Cluster 28: feet, km, ft, mph, m, h, miles, c, mm, route

Cluster 29: least

## Appendix CCluster Token Assignments:γ=0\.2\\gamma=0\.2, Extended,k=13k=13

Cluster 0: them, else, him, myself, you, ourselves, t, should, ’d, here, yourself, people, everything, will, we, forever, characters, not, would, anything, me, herself, might, someone, men, shall, man, do, there, does, something, did, anyone, i, players, children, must, could, just, whoever, ’ll, appears, nothing, ’re, women, get, can, everyone, got, appear, really, ve, somebody, ll, god, am, able, love, exactly, anybody, may, ta, everybody, ago, hasn, unable

Cluster 1: also, actually, itself, themselves, indeed, therefore, apparently, even, sometimes, yet, be, nevertheless, nonetheless, likewise, consequently, often, initially, occasionally, it, simultaneously, otherwise, instead, already, probably, merely, others, possibly, simply, rather, himself, frequently, thus, been, still, well, being, certainly, once, were, rarely, have, then, had, essentially, either, again, partly, reportedly, is, previously, always, usually, they, perhaps, similarly, was, likely, are, having, subsequently, ultimately, he, who, mostly, traditionally, commonly, eventually, regularly, never, has, generally, soon, solely, easily, normally, typically, now, entirely, largely, specifically, effectively, consistently, quickly, she, increasingly, finally, originally, naturally, properly, remains, equally, literally, clearly, ever, potentially, truly, recently, primarily, mainly, longer, directly, personally, deliberately, immediately, suddenly, partially, completely, rapidly, extensively, briefly, constantly, successfully, permanently, currently, historically, too, fully, virtually, quite, somewhat, significantly, seriously, much, physically, almost, widely, temporarily, repeatedly, far, closely, heavily, poorly, badly, slowly, officially, gradually, slightly, considerably, exclusively, critically, thereby, species, strongly, greatly, more, severely, less, unusually, remained, re, publicly, locally, politically, commercially, fairly, nearly, predominantly, formally, very, positively, highly, actively, extremely, steadily, deeply, accidentally, relatively, unsuccessfully, pretty

Cluster 2: that, though, however, because, but, although, furthermore, where, if, said, and, believed, whether, when, why, wherein, thought, saying, hence, which, additionally, whenever, notably, neither, nor, unless, stated, while, afterwards, how, both, so, what, whilst, whom, meanwhile, afterward, claimed, felt, name, especially, know, particularly, young

Cluster 3: become, became, becoming, formerly, newly

Cluster 4: out, up, apart, of, for, created, followed, down, removed, as, on, included, aside, with, addition, from, including, introduced, to, put, except, part, place, over, found, involved, made, used, seen, than, called, see, added, making, allowed, given, saw, taken, through, back, off, behind, worked, return, compared, away, result, support, suggested, done, established, revealed, returned, described, example, recorded, brought, held, into, discovered, reported, led, formed, placed, in, whereas, served, include, performed, developed, raised, leave, take, by, known, leaving, produced, noted, offered, following, about, supported, turned, includes, along, present, upon, taking, carried, make, based, give, took, appeared, allow, replaced, keep, opened, ran, released, towards, gave, wanted, came, around, like, besides, alongside, changed, moved, inspired, designed, onto, beyond, find, left, ordered, unlike, lost, selected, toward, wrote, required, running, provided, featured, e\.g\., at, outside, awarded, within, sent, takes, launched, built, due, working, caused, above, composed, signed, intended, considered, proposed, between, planned, responsible, passed, notwithstanding, under, amongst, inside, come, issued, using, moving, destroyed, prior, played, during, playing, among, hit, leading, against, closer, directed, despite, forced, captured, published, across, extended, joined, via, features, went, versus, fell, named, arrived, entered, close, sold, going, received, go, old, according, failed, below, decided, killed, help, former, reached, written, continued, throughout, agreed, nearby, damaged, near, helped, praised, aboard, without, located, ranked, amidst, defeated, opposite, suffered, amid, fellow, vs\.

Cluster 5: two, three, five, four, six, seven, several, eight, nine, few, twelve, ten, many, other, twenty, all, numerous, thirty, number, various, remaining, some, multiple, these, those, most

Cluster 6: ’s, same, new, own, s, use, the, particular, or, form, whose, such, one, earlier, first, their, individual, separate, level, any, current, similar, associated, possible, kind, another, whole, key, only, single, real, previous, limited, no, original, important, its, plus, related, standard, his, additional, larger, successful, future, active, full, third, common, available, create, different, complete, our, regular, minor, independent, traditional, subsequent, popular, true, clear, second, enough, potential, unknown, strong, certain, powerful, cut, special, notable, range, recent, entire, poor, local, main, overall, her, specific, wide, this, whatever, american, official, last, major, open, fourth, high, significant, modern, century, primary, mixed, complex, every, european, prominent, free, good, english, contemporary, critical, regardless, commercial, difficult, older, worldwide, famous, final, international, great, early, initial, next, top, chinese, direct, each, right, national, smaller, secret, living, long, greatest, fifth, best, small, australian, better, canadian, british, a, white, large, russian, french, african, german, japanese, higher, body, indian, non, dead, provide, professional, opening, 20th, daily, spanish, chief, short, historical, largest, italian, private, increased, little, seventh, low, heavy, soviet, prime, female, black, light, sixth, pre, annual, greek, double, per, bad, total, highest, my, your, military, polish, further, average, overseas, big, an, hard, foreign, 19th, green, grand, positive, roman, personal, natural, latin, federal, greater, public, male, dark, anti, cultural, ancient, human, native, blue, civil, red, armed, deep, musical, legal, political, social, allied, christian, medical, economic, brown, senior, physical, imperial, nuclear, severe, yellow, lower, super, religious, royal, naval, electric, hot, maximum, financial, 1st

Cluster 7: 56, 35, 44, 57, 39, 32, 20, 62, 85, 15, 33, 65, 16, 22, 48, 25, 43, 13, 58, 42, 66, 9, 14, 6, 12, 45, 8, 41, 46, 70, 26, 60, 10, 53, 80, 28, 30, 23, 75, 51, 17, 27, 24, 55, 54, 36, 7, 37, 76, 5, 90, 52, 21, 95, 34, 38, 40, 50, 11, 19, 18, 47, 29, 4, 110, 31, 49, 3, 2, 120, 250, 64, 150, 1, 400, 200, 300, 100, 800, 700, 600, 500, 0, 000, approximately, c, million, hundred, feet, thousand, km, least, ft, billion, m, h, mm, mi, °, miles, mph, estimated, roughly

Cluster 8: area, city, africa, line, canada, company, region, island, europe, town, india, site, wales, australia, america, center, britain, position, territory, england, scotland, china, france, rest, park, group, hall, force, islands, coast, station, country, germany, house, service, kingdom, mexico, run, society, bridge, bank, elsewhere, building, states, cross, point, empire, office, hill, field, division, japan, base, association, ii, army, areas, florida, airport, republic, west, system, command, forces, bay, state, side, district, war, united, north, department, corps, south, london, texas, abroad, school, york, set, union, pass, construction, forth, power, drive, east, council, party, california, museum, street, home, virginia, control, ship, ground, campaign, road, club, county, attack, front, iii, river, university, washington, academy, railway, land, training, battle, fire, church, government, half, head, annually, crew, manchester, congress, pacific, college, uk, brigade, regiment, damage, infantry, runs, ships, northwest, navy, chicago, family, creek, atlantic, angeles, court, michigan, battalion, ocean, squadron, class, boston, st\., fleet, sea, parliament, air, machine, troops, square, population, act, lake, aircraft, northeast, oxford, guns, forward, us, police, operation, eastward, los, lead, offensive, northward, studios, ashore, law, fighting, san, depression, route, mountain, highway, water, storm, southern, western, central, offshore, eastern, middle, northern, rear, aft, upper, hurricane

Cluster 9: days, months, weeks, years, day, beginning, hours, time, month, year, start, ended, end, week, started, before, after, minutes, completed, ahead, announced, began, night, shortly, till, finished, summer, died, spent, mid, en

Cluster 10: work, games, together, event, performance, events, show, series, release, success, version, life, history, play, game, role, list, alone, records, film, respectively, times, works, project, case, book, shows, studio, development, story, hers, band, jones, way, song, scene, smith, production, stage, magazine, songs, period, cast, episode, album, record, action, track, career, tour, title, members, season, writing, order, onwards, match, team, review, score, u\.s\., music, shot, soundtrack, race, award, awards, design, post, johnson, recording, latter, world, williams, style, twice, death, jackson, broadcast, points, d, later, star, grant, video, character, box, player, art, sound, fight, victory, thereafter, win, x, chart, media, screen, live, football, radio, age, television, league, entertainment, cup, conference, rock, b, championship, winning, comic, won, critics, co, yard, scored

Cluster 11: son, captain, paul, thomas, father, john, george, manager, director, michael, david, edward, c\., richard, james, charles, peter, william, scott, robert, martin, henry, president, a\., lieutenant, mary, j\., governor, mark, secretary, king, met, tom, wife, minister, member, sir, chris, prince, don, jack, lord, queen, al, van, mother, asked, saint, o, st, told, v\., general, married, appointed, fort, de, born, la, und

Cluster 12: 1960, 1955, 1959, 1957, 1968, 1971, 1972, 1975, 1965, 1962, 1963, 1958, 1961, 1949, 1986, 1950, 1974, 1977, 1990, 1954, 1970, 1989, 1969, 1966, 1964, 1982, 1951, 1979, 1976, 1952, 1946, 1983, 1973, 1992, 1967, 1956, 1978, 1987, 1937, 1947, 1936, 1991, 1981, 1994, 1995, 1932, 1999, 1988, 1933, 1938, 1984, 1993, 1980, 1996, 1953, 1934, 1985, 1926, 1997, 1945, 2002, 1998, 1940, 1921, 1920, 2001, 1930, 2004, 1939, 2005, 1915, 1927, 2003, 1910, 1913, 2006, 1944, 2007, 1917, 1941, 1919, 1948, 1914, 1942, 2014, 1912, 2008, 2000, 2009, 1943, 1916, 2012, 2010, 2011, 2013, 2015, 1918, 2016, april, june, november, october, july, february, january, december, march, september, august, since, until, late

## Appendix DCluster Token Assignments:γ=0\.2\\gamma=0\.2, Extended,k=120k=120

Cluster 0: would, should, could, might, shall, will, must, can, did, not, does, able, unable, do, may

Cluster 1: here, appears, appear, there, ago, exactly

Cluster 2: men, people, women, children, players, man

Cluster 3: myself, else, them, you, everything, ourselves, yourself, him, someone, me, ’d, anything, forever, t, herself, we, something, somebody, characters, anyone, whoever, ’re, really, everyone, nothing, just, ve, i, everybody, got, anybody, ’ll, get, love, god, am, ll, hasn, ta

Cluster 4: mostly, solely, primarily, partly, mainly, largely, entirely, similarly, essentially, exclusively, specifically, extensively, partially, heavily, predominantly, historically, poorly, widely, completely, fully, strongly, closely, critically, commercially, locally, positively

Cluster 5: significantly, considerably, slightly, greatly, much, severely

Cluster 6: very, extremely, quite, too, equally, unusually, fairly, rather, somewhat, less, more, increasingly, truly, highly, relatively, pretty, politically, deeply

Cluster 7: be, been, were, being, was, is, had, previously, already, are, have, having, has, once, originally, now, recently, remains, currently, remained

Cluster 8: almost, either, well, virtually, nearly, far, species

Cluster 9: often, occasionally, sometimes, frequently, rarely, usually, always, normally, typically, merely, commonly, still, otherwise, regularly, generally, consistently, traditionally, easily, naturally, clearly, constantly, properly, longer, potentially, deliberately, physically, actively

Cluster 10: actually, indeed, also, therefore, nonetheless, nevertheless, consequently, probably, itself, apparently, likewise, himself, yet, themselves, certainly, it, others, even, thus, who, he, simply, initially, possibly, reportedly, they, perhaps, she, likely, never, literally, ever

Cluster 11: seriously, badly

Cluster 12: eventually, subsequently, again, then, finally, quickly, soon, simultaneously, instead, ultimately, immediately, effectively, briefly, suddenly, successfully, temporarily, rapidly, gradually, repeatedly, personally, slowly, permanently, officially, thereby, directly, formally, publicly, steadily, re, accidentally, unsuccessfully

Cluster 13: afterwards, afterward, meanwhile, whom, name

Cluster 14: young

Cluster 15: particularly, especially

Cluster 16: that, though, because, however, although, but, furthermore, if, where, whether, believed, said, and, why, wherein, when, thought, hence, saying, which, whenever, unless, nor, neither, additionally, how, stated, while, notably, so, both, what, whilst, felt

Cluster 17: know

Cluster 18: claimed

Cluster 19: became, become, becoming

Cluster 20: newly, formerly

Cluster 21: continued, planned

Cluster 22: following, during, prior

Cluster 23: used, created, added, made, making, given, make, provided, required, offered, developed, using, designed, based, proposed, received

Cluster 24: apart, involved, aside, reported, seen, found, upon, than, due, about, discovered, caused, support, responsible, amidst, without, amid, suffered

Cluster 25: result, suggested, addition, example, noted, revealed, notwithstanding, considered, despite, find, keep

Cluster 26: known

Cluster 27: performed, produced, worked, recorded, featured, wrote, appeared, composed, released, done, played, published, features, written, playing

Cluster 28: present, part

Cluster 29: arrived, leaving, moved, returned, captured, destroyed, left, formed, leave, built, placed, located, reached, damaged, killed, aboard

Cluster 30: going, go, come

Cluster 31: up, out, down, taken, place, back, removed, put, ran, away, held, off, take, took, came, taking, return, opened, carried, served, raised, turned, lost, running, established, changed, fell, went, takes, launched, passed, moving, working, extended, issued, sold, hit, close, closer

Cluster 32: sent, signed, selected, ordered, awarded

Cluster 33: to, wanted, allowed, decided, intended, helped, help, forced, agreed, failed

Cluster 34: former, fellow, old, leading

Cluster 35: with, including, included, as, alongside, for, called, behind, by, whereas, described, followed, include, compared, introduced, saw, replaced, see, except, unlike, like, led, besides, supported, gave, inspired, give, against, named, includes, brought, allow, e\.g\., directed, amongst, versus, joined, among, according, under, praised, defeated, opposite, ranked, vs\.

Cluster 36: below, above

Cluster 37: from, of, through, into, on, in, over, towards, around, along, toward, within, across, onto, outside, at, between, near, via, beyond, entered, inside, nearby, throughout

Cluster 38: six, five, eight, four, three, seven, nine, twelve, two, ten, twenty, thirty, number, remaining

Cluster 39: many, several, other, few, numerous, various, some, these, all, multiple, most, those

Cluster 40: chief

Cluster 41: prime

Cluster 42: french, british, russian, german, spanish, italian, chinese, polish, american, english, australian, indian, canadian, japanese, african, european, soviet, local, independent, greek, roman, foreign, national, international, overseas, military, allied, imperial, professional, civil, federal, private, native, naval, christian, royal, senior, latin, armed

Cluster 43: grand

Cluster 44: 20th, 19th, 1st

Cluster 45: third, fourth, second, fifth, one, first, next, seventh, sixth, last, another, single, every, final, each, per, opening, top, pre

Cluster 46: only

Cluster 47: cut, long, short, open, double, hard, right, light, big, electric, super

Cluster 48: white, blue, red, black, green, yellow, brown, dead, dark, hot

Cluster 49: body

Cluster 50: large, larger, smaller, small, largest

Cluster 51: use, form, or, create, available, plus, provide

Cluster 52: high, level, higher, low, limited, increased, average, wide, overall, range, total, standard, highest, maximum, greater, heavy, lower, daily, free, deep

Cluster 53: previous, new, earlier, the, original, subsequent, current, future, recent, successful, early, official, regular, entire, traditional, annual

Cluster 54: female, male, unknown, living, powerful

Cluster 55: contemporary, modern, century, famous, prominent, older, popular, ancient, anti

Cluster 56: political, economic, social, cultural, legal, religious, historical, financial, public, medical

Cluster 57: musical

Cluster 58: associated, such, mixed

Cluster 59: similar, specific, particular, same, possible, any, related, important, significant, certain, key, different, individual, separate, potential, common, additional, no, minor, primary, main, critical, complex, active, strong, major, notable, initial, direct, special, commercial, positive, physical, natural, further, non, human, severe, nuclear

Cluster 60: this, whole, complete, full, a, an

Cluster 61: ’s, own, whose, his, their, our, s, her, my, your, real, its, true, personal, great, greatest, secret

Cluster 62: good, kind, better, whatever, poor, difficult, enough, clear, bad, regardless, best, little

Cluster 63: worldwide

Cluster 64: 400, 300, 500, 800, 600, 250, 700, 200, 150, 000, 100, 120, thousand, hundred, million, billion

Cluster 65: 56, 44, 57, 46, 62, 43, 33, 39, 58, 66, 55, 42, 41, 35, 54, 53, 51, 32, 37, 48, 85, 45, 76, 65, 38, 70, 36, 34, 47, 80, 75, 52, 60, 40, 90, 95, 50, 110, 49, 64

Cluster 66: 22, 14, 16, 15, 17, 13, 26, 8, 27, 28, 12, 23, 9, 21, 19, 6, 24, 20, 7, 11, 25, 29, 10, 18, 5, 4, 30, 31, 3, 2, 1, 0

Cluster 67: feet, km, ft, mi, mph, m, h, c, miles, °, approximately, mm, roughly

Cluster 68: least

Cluster 69: estimated

Cluster 70: st\., machine

Cluster 71: control

Cluster 72: base, front, ground, drive, side, field, fire, power, cross, forward, air, square, rear, water, aft

Cluster 73: training, offensive

Cluster 74: class

Cluster 75: set, forth, lead

Cluster 76: head, half

Cluster 77: run, pass, runs, point

Cluster 78: attack, battle, rest, fighting, operation

Cluster 79: line, bridge, station, road, building, park, airport, site, railway, center, street, hill, construction, highway, route

Cluster 80: system

Cluster 81: storm, hurricane, depression

Cluster 82: island, area, islands, region, areas, coast, bay, river, creek, ocean, sea, pacific, land, atlantic, damage, lake, ashore, offshore, mountain, population

Cluster 83: upper, middle

Cluster 84: south, east, north, northwest, west, northeast, eastern, southern, northern, western, northward, eastward, central

Cluster 85: corps, forces, brigade, force, army, battalion, infantry, regiment, squadron, division, troops, fleet, ships, command, ship, navy, aircraft, crew, guns, police

Cluster 86: ii, war, campaign, group, abroad, position, iii

Cluster 87: europe, africa, britain, canada, india, australia, france, germany, china, america, scotland, japan, kingdom, england, states, wales, territory, mexico, united, republic, country, elsewhere, empire, annually, uk, us

Cluster 88: council, society, government, congress, company, party, association, office, parliament, department, court, service, union, act, law, family

Cluster 89: city, town, hall, york, london, university, school, academy, college, house, chicago, county, angeles, district, boston, florida, virginia, california, texas, washington, state, michigan, bank, manchester, club, museum, church, home, oxford, los, studios

Cluster 90: san

Cluster 91: days, months, weeks, years, hours, beginning, month, day, time, year, start, ended, week, started, end, before, after, minutes, completed, announced, began, shortly, night, till, finished, died, summer, spent

Cluster 92: ahead

Cluster 93: mid

Cluster 94: en

Cluster 95: smith, jones, johnson, williams, jackson, hers, grant, members

Cluster 96: thereafter, later, twice

Cluster 97: won, winning, scored

Cluster 98: event, games, season, match, team, career, championship, win, cup, race, tour, league, points, awards, conference, award, victory, football, record, score, chart, yard

Cluster 99: player

Cluster 100: d, b, x

Cluster 101: co, post

Cluster 102: performance, film, show, release, game, series, book, version, story, song, music, album, studio, play, soundtrack, writing, songs, production, scene, band, episode, magazine, video, track, stage, style, recording, cast, design, action, title, sound, review, broadcast, character, screen, art, television, box, live, star, comic, radio, media, rock, entertainment

Cluster 103: work, events, history, works, success, life, development, records, list, project, times

Cluster 104: world

Cluster 105: critics

Cluster 106: u\.s\., alone, latter

Cluster 107: age

Cluster 108: order

Cluster 109: period, death

Cluster 110: onwards, respectively, role, case

Cluster 111: together, way

Cluster 112: shot, fight

Cluster 113: shows

Cluster 114: met, asked, told, appointed, born

Cluster 115: john, thomas, richard, george, james, william, david, paul, robert, edward, michael, peter, charles, henry, c\., scott, j\., a\., martin, mary, mark, tom, chris, jack, don, sir, lord, van

Cluster 116: son, father, director, president, manager, captain, member, secretary, minister, governor, king, lieutenant, wife, prince, queen, saint, mother, al, st, o, general, married, de, v\., fort, la, und

Cluster 117: october, june, july, december, april, november, january, september, february, august, march, until, since, late

Cluster 118: 1986, 1997, 1995, 1996, 1999, 1990, 1994, 1989, 2002, 1983, 1998, 1992, 2004, 1993, 1988, 1987, 2005, 2003, 1984, 2006, 2007, 2001, 1982, 1991, 1979, 1985, 1977, 1975, 2009, 1972, 1971, 1978, 1981, 2008, 1976, 1968, 2014, 1980, 2011, 1974, 2010, 1970, 2013, 1969, 2012, 1973, 1966, 1958, 1967, 2015, 2000, 2016

Cluster 119: 1937, 1936, 1946, 1949, 1938, 1932, 1947, 1955, 1933, 1934, 1940, 1957, 1926, 1951, 1921, 1952, 1950, 1961, 1956, 1939, 1915, 1913, 1959, 1963, 1930, 1919, 1945, 1920, 1914, 1965, 1960, 1912, 1917, 1944, 1916, 1953, 1910, 1941, 1962, 1964, 1954, 1942, 1943, 1927, 1948, 1918