Learning to Access Computation: Accessibility Plasticity as a Principle of Adaptive Intelligence

# Accessibility Plasticity as a Principle of Adaptive Intelligence
Source: [https://arxiv.org/html/2607.22748](https://arxiv.org/html/2607.22748)
## Learning to Access Computation: Accessibility Plasticity as a Principle of Adaptive Intelligence

###### Abstract

Modern neural networks primarily adapt through parameter modification within predefined computational structures\. While recent methods introduce modularity, conditional computation, and parameter\-efficient adaptation, they generally do not distinguish computational capability from computational accessibility as separate adaptive variables\. This work introduces Accessibility Plasticity, a principle of adaptive computation in which systems adapt not only by changing what computation exists, but also by reorganizing which existing computations can interact and participate\. We formalize Accessibility Plasticity through a relationship\-based operational realization and establish a reuse\-first hierarchy of adaptation, where accessibility modification precedes more costly capability and structural changes\. A proof\-of\-concept evaluation on sequential learning tasks shows that accessibility adaptation can reduce capability modification while maintaining comparable task performance\. These results suggest accessibility as a distinct adaptive dimension and provide a foundation for future dynamic neural systems whose computational relationships evolve with changing environments\.

## Keywords

Accessibility Plasticity; adaptive computation; continual learning; neural plasticity; conditional computation; dynamic neural systems

## 1Introduction

Most contemporary artificial neural systems are optimized under a parameter\-centric learning paradigm: a computational architecture is specified before deployment, and adaptation is primarily achieved by modifying numerical parameters within that fixed computational organization\[[13](https://arxiv.org/html/2607.22748#bib.bib1)\]\. This paradigm has enabled remarkable progress in large\-scale perception, language modeling, and decision\-making, with modern foundation models achieving unprecedented capabilities through large\-scale pretraining and parameter optimization\[[22](https://arxiv.org/html/2607.22748#bib.bib2),[5](https://arxiv.org/html/2607.22748#bib.bib3),[16](https://arxiv.org/html/2607.22748#bib.bib4),[4](https://arxiv.org/html/2607.22748#bib.bib5)\]\. However, when deployed in dynamic environments with continuously evolving data distributions, tasks, and operational conditions, parameter\-centric adaptation remains costly and prone to catastrophic forgetting, limiting the ability to preserve and efficiently reuse previously acquired capabilities\[[17](https://arxiv.org/html/2607.22748#bib.bib6)\]\.

Recent advances have explored alternatives by introducing modularity,\[[18](https://arxiv.org/html/2607.22748#bib.bib7)\]conditional computation\[[3](https://arxiv.org/html/2607.22748#bib.bib8)\], and parameter\-efficient adaptation\[[6](https://arxiv.org/html/2607.22748#bib.bib9)\]\. Residual architectures such as ResNet\[[8](https://arxiv.org/html/2607.22748#bib.bib10)\]demonstrate the value of preserving existing computational pathways, while graph neural networks\[[12](https://arxiv.org/html/2607.22748#bib.bib11),[2](https://arxiv.org/html/2607.22748#bib.bib12)\]highlight the role of relationships among computational units in information propagation\. Adapters\[[10](https://arxiv.org/html/2607.22748#bib.bib13)\]and low\-rank adaptation\[[11](https://arxiv.org/html/2607.22748#bib.bib14)\]reduce modification cost by restricting parameter updates, whereas mixture\-of\-experts\[[21](https://arxiv.org/html/2607.22748#bib.bib15)\], attention mechanisms\[[22](https://arxiv.org/html/2607.22748#bib.bib2)\], and routing strategies\[[20](https://arxiv.org/html/2607.22748#bib.bib16)\]dynamically regulate information flow and component selection\. Nevertheless, these approaches are generally developed as architecture\-specific mechanisms rather than as a unified adaptive principle\. They manipulate connectivity, parameter subsets, expert selection, or information routing, but do not explicitly distinguish computational capability from computational accessibility or treat the evolving relationships among computations as a first\-class adaptive object\.

Biological intelligence suggests that such a separation may be fundamental\.\[[7](https://arxiv.org/html/2607.22748#bib.bib17)\]Organisms rarely respond to environmental changes by immediately reconstructing their entire computational machinery; instead, adaptation occurs across multiple timescales\[[19](https://arxiv.org/html/2607.22748#bib.bib18)\]\. Existing pathways are reused whenever possible\[[1](https://arxiv.org/html/2607.22748#bib.bib19)\], functional relationships and activity patterns are reorganized, synaptic strengths are modified\[[14](https://arxiv.org/html/2607.22748#bib.bib20)\], and only over longer timescales does large\-scale structural reorganization occur\[[9](https://arxiv.org/html/2607.22748#bib.bib21)\]\. This ordering suggests that efficient adaptation may depend not only on learning new computations, but also on dynamically controlling access to existing computational resources\[[15](https://arxiv.org/html/2607.22748#bib.bib22)\], motivating the concept of Accessibility Plasticity introduced in this work\.

This paper investigates the following question:

Can artificial systems adapt more efficiently by modifying how existing computation is accessed before modifying what computation exists?

We introduce Accessibility Plasticity as a distinct adaptive degree of freedom that separates computational capability from computational accessibility: the former describes what transformations a system can perform, while the latter describes which computational components can interact during adaptation\. Under this perspective, learning is not only a process of changing computational operators, but also a process of reorganizing relationships among existing computations\.

We formalize this principle through a relationship\-based computational system in which capability and accessibility evolve as separate states\. The proposed reuse\-first principle prioritizes accessibility adaptation before more costly capability or structural modifications\. We show through a proof\-of\-concept evaluation that accessibility adaptation can reduce capability modification while maintaining comparable task performance in sequential learning scenarios\. The operational mechanism studied in this work is one realization of Accessibility Plasticity, providing a foundation for future adaptive systems in which computational relationships evolve continuously with changing environments\.

## 2Conceptual Framework

### 2\.1Capability, Accessibility, and Scope

Standard feedforward descriptions of neural computation can be summarized as

Architecture→Parameters→Computation\.\\text\{Architecture\}\\rightarrow\\text\{Parameters\}\\rightarrow\\text\{Computation\}\.
In that view, the architecture determines which transformations may interact, while the learned parameters determine the specific behavior realized along those fixed routes\.

The proposed perspective introduces an additional dimension\. Architecture does not fully determine realized computation; it provides only potential computation\. Accessible computation depends on the relationships that determine whether existing capabilities can interact under current conditions\.

The adaptive computational substrate is the formal object used here to represent this idea\. It is not the claim itself\. The claim is that accessibility should be treated as a distinct computational object, alongside capability, and that its adaptation can precede modification of computational capability\.

At the most compact level, the manuscript distinguishes two fundamental computational objects:

W\\displaystyle Wdetermines what computation exists,𝒜\\displaystyle\\mathcal\{A\}determines what computation is accessible\.
The theory concerns the second object without reducing it to the first\.

This manuscript does not claim to provide a complete theory of intelligence\. It proposes a missing adaptive degree of freedom: the ability of a computational system to modify accessibility independently from capability\. The purpose of the paper is therefore to isolate and formalize that degree of freedom, not to claim that all adaptation reduces to this single mechanism\.

### 2\.2Reuse Before Modification

The conceptual principle is:

> *An intelligent adaptive system should exhaust cheaper and more reversible forms of modification before invoking more expensive and more persistent ones\.*

This principle changes the optimization target\. Traditional optimization primarily focuses on maximizing task performance\. The proposed paradigm instead seeks performance\-efficient adaptation:

max⁡P​\(𝒯\)⋅R​\(𝒮\)Cadapt\\max\\;\\frac\{P\(\\mathcal\{T\}\)\\cdot R\(\\mathcal\{S\}\)\}\{C\_\{\\mathrm\{adapt\}\}\}\(1\)
whereP​\(𝒯\)P\(\\mathcal\{T\}\)denotes task performance,R​\(𝒮\)R\(\\mathcal\{S\}\)denotes computational reuse of the substrate, andCadaptC\_\{\\mathrm\{adapt\}\}denotes the cost of changing the system\.

The shift is conceptual as well as technical: intelligence is not only the ability to achieve a goal, but the ability to achieve goals by efficiently reusing existing computational resources\. This formulation is particularly relevant to continual learning, where repeated parameter overwriting can become a liability\.

### 2\.3Accessibility Plasticity versus Selection

Selection answers which already accessible path should be used now\. Accessibility plasticity answers how the future structure of accessible computation should change through experience\. The first is an inference\-time choice inside a given accessibility state; the second is a learning\-time modification of that accessibility state itself\.

This distinction matters because a selection mechanism can choose among already available possibilities without changing the substrate that makes those possibilities available\. Accessibility plasticity instead changes the accessibility landscape so that future computations are shaped by past experience\. Thus accessibility is not only a parameter to be optimized at a single endpoint\. It can be treated as a dynamically evolving computational state whose trajectory reflects interaction with a changing environment\.

## 3Formalization

### 3\.1Adaptive Computational Substrate

We represent the substrate as an undirected graph

Each nodevi∈Vv\_\{i\}\\in Vis a computational unit

whereWiW\_\{i\}denotes the local transition operator and no persistent node state is stored inside the vertex itself\. For a transient input signalxitx\_\{i\}^\{t\}, the node computes

x~it=Wi​xit,\\tilde\{x\}\_\{i\}^\{\\,t\}=W\_\{i\}x\_\{i\}^\{t\},\(4\)
so the node contributes only its transition matrix and does not introduce an additional nonlinear transformation at this stage\.

Each undirected relation indexei​j=ej​i∈Ee\_\{ij\}=e\_\{ji\}\\in Emarks a potential computational relationship\. The adaptive computational object associated with that potential relationship is the relationship state:

Ri​j=\(ℱi​j,di​j\),R\_\{ij\}=\(\\mathcal\{F\}\_\{ij\},d\_\{ij\}\),\(5\)
whereℱi​j\\mathcal\{F\}\_\{ij\}is a learned compatibility function anddi​j≥0d\_\{ij\}\\geq 0denotes computational resistance\. Given an information flow, the relationship state evaluates the compatibility of the interaction and modifies the future accessibility of this computational relationship\. The evolving relationship state already encodes the history of previous interactions, so no separate relation\-memory variable is required\.

### 3\.2Relationship State and Accessibility

Computation in an adaptive computational substrate is not determined solely by the existence of computational units or by fixed connections between them\. Instead, relationships between computational units define an adaptive accessibility structure that determines which transformations can participate in the current computation\.

Crucially, accessibility is not identical to the relation setEE\. The setEEspecifies potential relationships in the substrate, whereas accessibility specifies which relationships become computationally available under the current adaptive state\. Relationship states are therefore one realization of accessibility, not accessibility itself\.

For a potential relationship between computational unitsiiandjj, the relationship state evaluates an interaction tendency:

si​jt=ℱi​j​\(xit,xjt\),s\_\{ij\}^\{t\}=\\mathcal\{F\}\_\{ij\}\(x\_\{i\}^\{t\},x\_\{j\}^\{t\}\),\(6\)
whereℱi​j\\mathcal\{F\}\_\{ij\}represents a discrimination mechanism that evaluates whether interaction between the two computational capabilities is computationally meaningful\.

The tendency is modulated by a resistance term:

zi​jt=si​jt−β​di​j,z\_\{ij\}^\{t\}=s\_\{ij\}^\{t\}\-\\beta d\_\{ij\},\(7\)
wheredi​j≥0d\_\{ij\}\\geq 0represents the intrinsic difficulty of establishing the relationship andβ\\betacontrols the influence of resistance\.

The accessibility of the relationship is then determined by

ai​jt=g​\(zi​jt\),a\_\{ij\}^\{t\}=g\(z\_\{ij\}^\{t\}\),\(8\)
whereg​\(⋅\)g\(\\cdot\)maps the evaluated tendency into an accessibility state\. The resulting accessibility does not represent a message weight\. Instead, it defines whether and to what degree the computational relationship becomes available within the current substrate configuration\.

The effective computational substrate at timettis therefore induced by the set of accessible relationships:

Et∗=\{\(i,j\)∈E∣ai​jt\>θ\},E\_\{t\}^\{\*\}=\\\{\(i,j\)\\in E\\mid a\_\{ij\}^\{t\}\>\\theta\\\},\(9\)
which forms a dynamically accessible substrate:

Gt=\(V,Et∗\)\.G\_\{t\}=\(V,E\_\{t\}^\{\*\}\)\.\(10\)
Multiple adaptive relationships may become simultaneously accessible, producing concurrent computational pathways within the induced substrateGtG\_\{t\}\. Accordingly, the system does not rely on a single predetermined execution trajectory\. Instead, computation emerges from the collective configuration of active relationships\.

The central distinction is that relationships are not passive communication channels\. Their states are adaptive computational structures that evaluate, enable, suppress, and reshape future accessibility between existing capabilities\.

At the principle level, accessibility evolves according to an abstract update operator:

𝒜t\+1=𝒫A​\(𝒜t,𝒳t\)\.\\mathcal\{A\}\_\{t\+1\}=\\mathcal\{P\}\_\{A\}\(\\mathcal\{A\}\_\{t\},\\mathcal\{X\}\_\{t\}\)\.\(11\)
This equation is intentionally more general than the particular relationship\-state implementation used in the proof\-of\-concept experiments\. It states that accessibility is a time\-indexed computational object whose future state may depend on its present configuration and on the encountered environment𝒳t\\mathcal\{X\}\_\{t\}\. Updates toℱi​j\\mathcal\{F\}\_\{ij\}ordi​jd\_\{ij\}are possible realizations of this principle, not definitions of Accessibility Plasticity itself\.

### 3\.3Computational Interpretation

The model separates two usually entangled concepts:

- •node operators determine*what*local computation can be performed;
- •accessibility states determine*whether and how*existing computation can be reached\.

This separation is the core design move of the paradigm\. Learning is therefore not only the acquisition or modification of computational capability\. It is also the reorganization of access to capabilities that already exist in the substrate\. The system can respond to new tasks by reshaping relationships to existing operators before rewriting the operators themselves\.

Unlike conventional neural networks, where learning is primarily stored in node parameters, the proposed substrate allows learning to emerge from the evolution of relationships between computational units\. Adaptation occurs through the evolution of computational relationships, not through explicit storage of interaction history\.

In compact form, the interpretation is:

W\\displaystyle W⇒what computation exists,\\displaystyle\\Rightarrow\\text\{what computation exists\},𝒜\\displaystyle\\mathcal\{A\}⇒what computation is accessible\.\\displaystyle\\Rightarrow\\text\{what computation is accessible\}\.
The contribution of the paper is Accessibility Plasticity as a first\-class object of learning, not a new family of network architectures\.

Reuseℛ\\mathcal\{R\}Exploit existing computationAccessibility PlasticityΔ​𝒜\\Delta\\mathcal\{A\}Reorganize what existing computation becomes accessibleCapability PlasticityΔ​W\\Delta WModify computational operatorsSubstrate PlasticityΔ​\(D,G\)\\Delta\(D,G\)Reorganize computational organizationFigure 1:Adaptive systems possess multiple degrees of adaptive freedom\. The proposed hierarchy orders forms of adaptation by increasing depth: systems should preferentially reuse existing computation, then modify computational accessibility, then modify computational capability, and only at the deepest level reorganize computational organization itself\. Lower levels preserve more of the current computational identity of the system, whereas higher levels incur greater modification cost and structural persistence\. The hierarchy denotes an ordering of adaptive depth rather than a mandatory optimization schedule\.
### 3\.4Hierarchy of Adaptive Depth

Adaptive systems possess multiple degrees of adaptive freedom\. These degrees of freedom differ in persistence, reversibility, and modification cost\. Adaptive freedom refers to the hierarchy of internal degrees of freedom through which a system can respond to environmental change\. We propose a reuse\-first ordering in which a system first exploits existing computational capability, then reorganizes computational accessibility, then modifies computational capability itself, and only finally reconfigures the organization of computation\.

The hierarchy can be summarized as:

ℛ≺Δ​𝒜≺Δ​W≺Δ​\(D,G\)\\mathcal\{R\}\\prec\\Delta\\mathcal\{A\}\\prec\\Delta W\\prec\\Delta\(D,G\)
whereℛ\\mathcal\{R\}denotes pure computational reuse without modification of accessibility, capability, or organization;Δ​𝒜\\Delta\\mathcal\{A\}denotes changes in computational accessibility;Δ​W\\Delta Wdenotes modifications of computational capability; andΔ​\(D,G\)\\Delta\(D,G\)denotes reorganization of the computational substrate\.

The ordering does not represent a fixed algorithmic procedure or a mandatory optimization sequence\. It is an ordering of adaptation depth\. Lower levels preserve more of the existing computational identity of the system, whereas higher levels introduce increasingly fundamental changes to what the system can compute and how computation is organized\.

##### Reuse

The first adaptive response is to exploit existing computational capability without modification\. Given a new task or a shift in input distribution, the system first evaluates whether its current computational organization already contains sufficient capability to solve the problem\.

Successful reuse preserves existing knowledge and incurs minimal adaptation cost because neither accessibility relations nor computational operators are altered\.

##### Accessibility plasticity

When the required computational capability already exists but is not effectively reachable under the current configuration, adaptation occurs through changes in computational accessibility\. Accessibility is therefore not an additional computational capability; it is a property describing whether existing capabilities can participate in computation\.

We refer to this process as accessibility plasticity\. In the adaptive computational substrate studied here, relationship\-state evolution provides one substrate\-level realization of this principle\. Unlike mechanisms that merely select among existing pathways at inference time, accessibility plasticity modifies the underlying relationship landscape through which future computational pathways emerge\.

Let the accessibility configuration of the computational substrate be

𝒜t=\{ai​jt\},\\mathcal\{A\}\_\{t\}=\\\{a\_\{ij\}^\{t\}\\\},\(12\)
whereai​jta\_\{ij\}^\{t\}represents the accessibility of the computational relationship between unitsiiandjjunder the current substrate state\.

For the adaptive computational substrate, accessibility is induced by the relationship stateRi​jt=\(ℱi​jt,di​jt\)R\_\{ij\}^\{t\}=\(\\mathcal\{F\}\_\{ij\}^\{t\},d\_\{ij\}^\{t\}\):

ai​jt=g​\(ℱi​jt​\(xit,xjt\)−β​di​jt\),a\_\{ij\}^\{t\}=g\\left\(\\mathcal\{F\}\_\{ij\}^\{t\}\(x\_\{i\}^\{t\},x\_\{j\}^\{t\}\)\-\\beta d\_\{ij\}^\{t\}\\right\),\(13\)
whereℱi​jt\\mathcal\{F\}\_\{ij\}^\{t\}evaluates relational compatibility anddi​jtd\_\{ij\}^\{t\}represents computational distance between units\. The mapping from relationship state to accessibility is not unique; the purpose of Eq\.[13](https://arxiv.org/html/2607.22748#S3.E13)is to provide one realizable coordinate system for an otherwise abstract adaptive variable\.

The evolution of accessibility is therefore described at an abstract level as:

𝒜t\+1=𝒫A​\(𝒜t,𝒳t\),\\mathcal\{A\}\_\{t\+1\}=\\mathcal\{P\}\_\{A\}\(\\mathcal\{A\}\_\{t\},\\mathcal\{X\}\_\{t\}\),\(14\)
where𝒫A\\mathcal\{P\}\_\{A\}denotes an accessibility plasticity operator and𝒳t\\mathcal\{X\}\_\{t\}represents the computational experience accumulated by the system at timett, including interaction outcomes, task feedback, and environmental signals\. This formulation emphasizes that accessibility is itself an adaptive state variable whose evolution is governed by experience, rather than a fixed property of the computational substrate\. The abstract update𝒜t\+1=𝒫A​\(𝒜t,𝒳t\)\\mathcal\{A\}\_\{t\+1\}=\\mathcal\{P\}\_\{A\}\(\\mathcal\{A\}\_\{t\},\\mathcal\{X\}\_\{t\}\)is therefore the protected theoretical statement; any concrete distance\-based update or relationship\-state update is only one possible realization, not the definition of Accessibility Plasticity\.

A concrete realization of this principle can be obtained by adapting the underlying relationship geometry\. For example, computational distance may evolve according to:

di​jt\+1=di​jt−ηd​si​jt,d\_\{ij\}^\{t\+1\}=d\_\{ij\}^\{t\}\-\\eta\_\{d\}s\_\{ij\}^\{t\},\(15\)
wheresi​jts\_\{ij\}^\{t\}denotes the interaction outcome between computational unitsiiandjj\. Successful interactions reduce computational distance and increase future accessibility, whereas unsuccessful interactions weaken the corresponding relationship\. In this realization, the history of interaction is implicitly stored in the evolving relationship state rather than through an external memory mechanism\.

Therefore, adaptation occurs first by reshaping access to existing computation rather than modifying the computation itself\.

##### Capability plasticity

When accessibility adaptation is insufficient because the existing computational capability cannot adequately represent the required transformation within the current substrate, the system modifies its local computational capabilities\.

This corresponds to conventional parameter adaptation, but with a stronger interpretation: capability plasticity changes what computation is available within the substrate, whereas accessibility plasticity changes whether existing computation can be reached\.

Wi←Wi\+Δ​Wi\.W\_\{i\}\\leftarrow W\_\{i\}\+\\Delta W\_\{i\}\.\(16\)
Because modifying operators can overwrite previously acquired competence, it is considered a deeper and more costly form of adaptation than accessibility plasticity\.

##### Substrate plasticity

The highest level of adaptation occurs when both accessibility and capability modification become insufficient\. At this level, the organization of computation itself changes\.

The learned computational distance matrixD=\[di​j\]D=\[d\_\{ij\}\]defines the relational geometry of the substrate\. Persistent low\-distance regions indicate strong computational affinity, while high\-distance regions indicate weak relationships\.

Through this learned geometry, the substrate may reorganize itself by:

- •forming computational modules with persistent relational affinity;
- •dissolving obsolete structures when their internal relationships become incompatible;
- •redistributing computational boundaries according to learned relational geometry\.

Therefore, substrate plasticity is not presented here as a search procedure over architectures\. It is the deepest adaptive level at which computational organization itself changes\.

A generic substrate adaptation objective can be written as:

minD,G⁡Ltask\+λs​Cs​\(D,G\)\\min\_\{D,G\}L\_\{\\mathrm\{task\}\}\+\\lambda\_\{s\}C\_\{s\}\(D,G\)\(17\)
whereCs​\(D,G\)C\_\{s\}\(D,G\)measures the cost of reorganizing computational organization under the learned relational geometry\.

At this highest level, adaptation no longer changes only information flow or individual computational operators\. Instead, it transforms the computational landscape in which future computation becomes possible\.

## 4Operational Realization \(Experimental Setup\)

The experiments are designed as proof\-of\-concept validation of the principle, not as a benchmark campaign for state\-of\-the\-art continual learning\. Their role is to test whether accessibility behaves as a distinct adaptive variable and whether reuse\-first adaptation can reduce shared capability modification under sequential tasks\. Concretely, the experimental design evaluates the following hypotheses:

- •accessibility plasticity constitutes a meaningful adaptive degree of freedom;
- •adaptive systems can reduce capability modification by first modifying accessibility;
- •accessibility adaptation is not equivalent to merely adding extra adaptive parameters;
- •accessibility alone is insufficient for continual adaptation, consistent with the proposed hierarchyℛ≺Δ​𝒜≺Δ​W≺Δ​\(D,G\)\\mathcal\{R\}\\prec\\Delta\\mathcal\{A\}\\prec\\Delta W\\prec\\Delta\(D,G\)\.

### 4\.1Proof\-of\-Concept Realization and Training Protocol

The reuse\-first hierarchy defines a general preference over modification depth: adaptation should first exploit existing computation, then reorganize accessibility, and only afterwards rewrite computational capability\. At the principle level, the objective is not only low task loss, but low task loss with minimal internal transformation\. One practical realization therefore augments the task objective with separate costs for accessibility and capability change:

ℒ=Ltask\+λA​CA\+λW​CW\.\\mathcal\{L\}=L\_\{\\mathrm\{task\}\}\+\\lambda\_\{A\}C\_\{A\}\+\\lambda\_\{W\}C\_\{W\}\.\(18\)
The key point is not regularization by itself\. The point is that the optimization distinguishes modification depths by assigning different costs to changes in accessibility and changes in capability\. In the present instantiation,

CA\\displaystyle C\_\{A\}=‖Δ​ℱ‖1\+‖Δ​D‖1,\\displaystyle=\\\|\\Delta\\mathcal\{F\}\\\|\_\{1\}\+\\\|\\Delta D\\\|\_\{1\},\(19\)CW\\displaystyle C\_\{W\}=∑i‖Δ​Wi‖F\.\\displaystyle=\\sum\_\{i\}\\\|\\Delta W\_\{i\}\\\|\_\{F\}\.
The first term measures reorganization of relationship state, while the second measures changes to shared computational operators\. The intended inductive preference is

λA≤λW,\\lambda\_\{A\}\\leq\\lambda\_\{W\},
so that capability plasticity remains available but is invoked only when shallower adaptation is insufficient\.

Algorithm[1](https://arxiv.org/html/2607.22748#alg1)summarizes one operational realization of the principle\. It should be read as an instantiation rather than as the contribution itself\. The experiments implement the hierarchy using a performance\-based controller: at each task, the system attempts the shallowest adaptation depth and avoids deeper modification if the current depth satisfies a fixed training criterion\. Operationally,

s∗=mins⁡\{s:Acc​\(s\)≥τ\},s∈\{reuse,Δ​𝒜,Δ​W\}\.s^\{\\ast\}=\\min\_\{s\}\\\{s:\\mathrm\{Acc\}\(s\)\\geq\\tau\\\},\\qquad s\\in\\\{\\mathrm\{reuse\},\\Delta\\mathcal\{A\},\\Delta W\\\}\.\(20\)
Hereτ=0\.9\\tau=0\.9is the task\-sequential experimental performance constraint, not the theoretical definition of Accessibility Plasticity\. The dynamic datastream demonstration uses a slightly stricter target\-environment controller threshold \(τ=0\.92\\tau=0\.92\) because it tracks progress toward the hardest stream endpoint rather than per\-task adaptation alone\. The task\-sequential experiments contain three controlled stages for each task after the first:

1. 1\.Reuse:adapt only the task\-specific readout head while freezing shared capability and accessibility;
2. 2\.Accessibility plasticity:freeze shared capability and update only the relationship state that induces accessibility;
3. 3\.Capability plasticity:freeze the learned relationship state and update only the shared computational operators if the previous stages do not achieve the task\-accuracy threshold\.

The first task is used to initialize the shared capability bank, so it necessarily invokes capability plasticity\. Thereafter, adaptation\-stage decisions are made on the current task’s training split, while the reported continual\-learning metrics are measured on held\-out test data\. This design avoids using test performance to decide when deeper modification stages are activated\. In the dynamic datastream demonstration, the same staged preference is preserved, but reuse corresponds to evaluating the current model state on the incoming stream slice rather than to head\-only adaptation\.

Environment and task inputxt,𝒳tx\_\{t\},\\mathcal\{X\}\_\{t\}Existing computational capabilityW1,W2,…,WnW\_\{1\},W\_\{2\},\\dots,W\_\{n\}Relationship stateRi​j=\(ℱi​j,di​j\)R\_\{ij\}=\(\\mathcal\{F\}\_\{ij\},d\_\{ij\}\)Accessibility state𝒜t\\mathcal\{A\}\_\{t\}Task computation and outputyty\_\{t\}Satisfied with the output?Organizational plasticityUpdate organizationΔ​\(D,G\)\\Delta\(D,G\)Capability plasticityUpdate computationΔ​W\\Delta WAccessibility plasticityUpdate relationship stateRt\+1R\_\{t\+1\}𝒜t\+1=𝒫A​\(𝒜t,𝒳t\)\\mathcal\{A\}\_\{t\+1\}=\\mathcal\{P\}\_\{A\}\(\\mathcal\{A\}\_\{t\},\\mathcal\{X\}\_\{t\}\)Figure 2:Operational realization of the adaptive transformation hierarchy\. The system first evaluates output satisfaction\. If adaptation is required, it proceeds through a hierarchical routing structure: first modifying accessibility state via relationship updates \(𝒜t\+1=𝒫A​\(𝒜t,𝒳t\)\\mathcal\{A\}\_\{t\+1\}=\\mathcal\{P\}\_\{A\}\(\\mathcal\{A\}\_\{t\},\\mathcal\{X\}\_\{t\}\)\), then invoking capability plasticity \(Δ​W\\Delta W\) if needed, and finally engaging theoretical organizational plasticity \(Δ​\(D,G\)\\Delta\(D,G\)\) as a deeper evolutionary layer\.Algorithm 1One Reuse\-First Instantiation in the Operational Realization1:computational graph

G=\(V,E\)G=\(V,E\), task batch

ℬ\\mathcal\{B\}, adaptation thresholds

ϵr,ϵA,ϵW\\epsilon\_\{r\},\\epsilon\_\{A\},\\epsilon\_\{W\}
2:Evaluate current configuration on

ℬ\\mathcal\{B\}
3:iftask loss

≤ϵr\\leq\\epsilon\_\{r\}then

4:return without modification

5:endif

6:Update accessibility state

𝒜\\mathcal\{A\}
7:Realize accessibility adaptation through relationship updates

8:iftask loss

≤ϵA\\leq\\epsilon\_\{A\}then

9:return after accessibility adaptation

10:endif

11:Freeze accessibility state

𝒜\\mathcal\{A\}
12:Update computational operators

WW
13:iftask loss

≤ϵW\\leq\\epsilon\_\{W\}then

14:return after capability adaptation

15:endif

16:Trigger deeper organizational reconfiguration if required

### 4\.2Datasets, Baselines, and Evaluation Metrics

All experiments are CPU\-only and use a single fixed random seed\. Two controlled continual\-learning settings are evaluated\.

##### Split MNIST\.

Five sequential binary tasks are constructed from MNIST:0versus11,22versus33,44versus55,66versus77, and88versus99\.

##### Permuted MNIST\.

The same binary task sequence is retained, but each task receives a fixed task\-specific pixel permutation\. This benchmark preserves the simple continual\-learning protocol while introducing a stronger distribution shift\.

For both datasets, each class contributes250250training examples and120120test examples per task\. The baseline and EWC models are two\-layer multilayer perceptrons with hidden dimension6464and task\-specific binary heads\. The operational realization of Accessibility Plasticity uses a shared bank of88experts, hidden dimension6464, and a task\-conditioned relationship stateR=\(ℱ,d\)R=\(\\mathcal\{F\},d\)that induces accessibility over the experts\. The experimental comparisons include:

- •Baseline MLP:direct capability modification of a shared trunk;
- •Accessibility Plasticity Realization:reuse\-first accessibility plasticity with capability updates when necessary;
- •Fixed Relationships:the same capability bank with accessibility adaptation disabled;
- •Accessibility Only:accessibility adaptation allowed, later capability plasticity disabled;
- •Random Accessibility Control:the same accessibility\-state budget as the operational realization, but accessibility updates are random rather than relationship\-driven;
- •EWC:a classical weight\-preservation baseline\.

#### 4\.2\.1Dynamic Accessibility Evolution

In addition to the two task\-sequential demonstrations, we include a lightweight streaming distribution\-shift experiment\. Its purpose is not benchmark comparison, but to test whether accessibility behaves as a dynamically evolving adaptive state\. A single binary MNIST classifier is first trained on an easy stationary slice of digits0versus11to establish an initial computational state\. The same classifier and readout are then exposed to an eight\-step datastream in which permutation strength and noise level increase gradually over time\. At each stream step, the system first evaluates the current model state, then updates the accessibility\-inducing relationship state, and only then updates shared capability parameters if accessibility adaptation remains insufficient\. The main readout is a learning\-progress curve on the fixed hardest target distribution at the endpoint of the stream, together with the measured accessibility movementΔ​At\\Delta A\_\{t\}and shared capability movementΔ​Wt\\Delta W\_\{t\}at each step\.

The primary reported metrics are final average accuracy, average forgetting, capability modification costCWC\_\{W\}, accessibility modification costCAC\_\{A\}, and modification\-efficiency score

MES=PerformanceCA\+CW\.\\mathrm\{MES\}=\\frac\{\\mathrm\{Performance\}\}\{C\_\{A\}\+C\_\{W\}\}\.\(21\)
In the experiments,CWC\_\{W\}is measured as the accumulated movement of the shared capability parameters only\. For the baseline and EWC models, these parameters are the shared MLP trunk\. For the operational realization of Accessibility Plasticity, they are the shared expert bank and shared post layer\. Task\-specific heads are excluded fromCWC\_\{W\}, and relationship\-state parameters are excluded fromCWC\_\{W\}and counted instead inCAC\_\{A\}\. This distinction is important because the experimental claim concerns modification of shared computational capability, not all trainable parameters indiscriminately\.

## 5Results & Discussion

Table[1](https://arxiv.org/html/2607.22748#S5.T1)reports the results on Split MNIST, and Table[2](https://arxiv.org/html/2607.22748#S5.T2)reports the results on Permuted MNIST\. The results should be interpreted as proof\-of\-concept evidence for the proposed principle rather than as benchmark rankings\.

Table 1:Proof\-of\-concept results on Split MNIST\. The central comparison is not raw accuracy alone, but the relationship between performance and shared capability modification cost\.Table 2:Proof\-of\-concept results on Permuted MNIST\. The qualitative pattern observed on Split MNIST remains visible under stronger distribution shift\.![Refer to caption](https://arxiv.org/html/2607.22748v1/x1.png)Figure 3:Capability modification cost across methods on Split MNIST and Permuted MNIST\. The operational realization of Accessibility Plasticity occupies a markedly lower capability\-modification regime than the direct weight\-updating baselines while remaining meaningfully above zero, indicating reduced but not eliminated capability plasticity\.![Refer to caption](https://arxiv.org/html/2607.22748v1/x2.png)Figure 4:Final average accuracy on Split MNIST and Permuted MNIST\. The purpose of the comparison is not to identify the highest\-accuracy method in isolation, but to show that reduced capability modification under Accessibility Plasticity does not come from collapse of task performance\.### 5\.1Experimental Observations

The first empirical observation is that the operational realization of Accessibility Plasticity does not achieve the highest raw accuracy\. The strongest raw accuracies are obtained by the baseline MLP and EWC\. This is consistent with the purpose of the experiments: they are not intended to establish state\-of\-the\-art continual learning, but to test whether adaptation can move into a lower shared\-capability\-modification regime\. Figures[3](https://arxiv.org/html/2607.22748#S5.F3)and[4](https://arxiv.org/html/2607.22748#S5.F4)summarize this empirical trade\-off directly\.

##### Split MNIST\.

On Split MNIST, the operational realization of Accessibility Plasticity reaches accuracy0\.91830\.9183with capability cost2\.86742\.8674, compared with baseline accuracy0\.95830\.9583and capability cost8\.44608\.4460\. The same model attains lower raw accuracy than Fixed Relationships \(0\.93500\.9350\), but requires much less capability modification \(2\.86742\.8674versus6\.82096\.8209\)\. The Random Accessibility Control reaches0\.88580\.8858accuracy while incurring accessibility cost2\.79262\.7926, substantially higher than the accessibility cost of the learned operational realization \(1\.41311\.4131\)\. The Accessibility Only ablation yields final accuracy0\.66250\.6625, indicating that accessibility adaptation alone does not carry the full sequential\-learning burden\.

##### Permuted MNIST\.

On Permuted MNIST, the same qualitative pattern remains visible under stronger distribution shift\. The operational realization reaches accuracy0\.92420\.9242with capability cost2\.24842\.2484, compared with baseline accuracy0\.97000\.9700and capability cost9\.50169\.5016\. Fixed Relationships attains accuracy0\.94080\.9408, but again with much larger capability cost \(6\.23896\.2389\)\. The Random Accessibility Control falls to0\.86080\.8608accuracy while spending accessibility cost2\.95992\.9599, compared with0\.55970\.5597for the learned operational realization\. Accessibility Only remains insufficient, with final accuracy0\.63750\.6375\.

![Refer to caption](https://arxiv.org/html/2607.22748v1/x3.png)Figure 5:Accuracy\-capability trade\-off space for all methods on both datasets\. Colors identify methods and marker shapes identify datasets, allowing the figure to compare adaptation regimes without crowding the plot with direct point labels\. Dashed and dash\-dotted curves show smooth objective\-front fits to the empirical non\-dominated trends within each dataset, not theoretical Pareto fronts over the broader model class\. The operational realization of Accessibility Plasticity occupies a region with competitive accuracy and substantially lower shared capability modification than the direct weight\-updating baselines\.
##### Accuracy\-capability trade\-off\.

Figure[5](https://arxiv.org/html/2607.22748#S5.F5)summarizes the same empirical pattern in a single view\. The operational realization of Accessibility Plasticity remains well below the baseline and EWC in capability modification cost while avoiding the severe performance collapse of the Accessibility Only ablation\. Fixed Relationships and Random Accessibility Control occupy distinct intermediate regimes, reinforcing that the central effect is not merely the presence of additional adaptive state, but the learned use of accessibility as a separate adaptive degree of freedom\.

![Refer to caption](https://arxiv.org/html/2607.22748v1/x4.png)Figure 6:Online adaptation in a gradually shifting datastream\. A modest initial state is established first, after which the same binary MNIST classifier is exposed to an eight\-step stream with increasing permutation mix and noise level\. The top panel shows the controlled shift schedule, the middle panel reports accessibility and capability modification at each step, and the bottom panel tracks accuracy on the fixed hardest target environment before adaptation, after accessibility adaptation, and after the final model state\. The trajectory shows continuous accessibility evolution throughout the stream, with capability plasticity appearing only at the latest and hardest steps\.
#### 5\.1\.1Dynamic Accessibility Evolution

Figure[6](https://arxiv.org/html/2607.22748#S5.F6)tests the temporal interpretation of Accessibility Plasticity\. Before the stream begins, the initialized model state reaches0\.77920\.7792accuracy on the hardest target environment\. As the datastream progressively approaches that environment, target accuracy rises from0\.80830\.8083at the first stream step to0\.92500\.9250at the last\. Accessibility changes at every step, withΔ​At\\Delta A\_\{t\}remaining nonzero throughout the stream, while shared capability modification is withheld until the final two and hardest steps \(Δ​Wt=0\.0556\\Delta W\_\{t\}=0\.0556and0\.06200\.0620\)\. The stagewise curves show that accessibility adaptation already improves target accuracy during the stream, from0\.77920\.7792to0\.89580\.8958before the late capability updates, after which the final target accuracy reaches0\.92500\.9250\. This experiment is intentionally small, but it provides a clearer proof\-of\-concept for the claim that accessibility is not only an optimization variable at an endpoint; it can function as a continuously evolving adaptive state under feedback from a changing datastream\.

### 5\.2Interpretation Relative to the Central Claims

The experiments support this claim\. Removing accessibility adaptation while keeping the shared capability bank produces a materially different regime\. Compared with Fixed Relationships, the operational realization reduces capability modification by approximately58\.0%58\.0\\%on Split MNIST and64\.0%64\.0\\%on Permuted MNIST\. This is the most direct evidence in the current experiments that accessibility is not a decorative auxiliary variable, but a meaningful adaptive degree of freedom\.

The support for this claim is positive but appropriately qualified\. After the first task, the operational realization follows the trace reuse→\\rightarrowaccessibility→\\rightarrowcapability on every subsequent task in both datasets\. Accessibility adaptation often improves the current\-task training signal before capability plasticity is enabled, and the relationship state is frozen once capability plasticity begins\. Across the eight post\-initial tasks, accessibility adaptation improves current\-task training accuracy in seven cases\. The effect is especially visible on Permuted MNIST, where the accessibility stage raises current\-task training accuracy from0\.5200\.520to0\.5440\.544, from0\.6180\.618to0\.6500\.650, from0\.4940\.494to0\.5760\.576, and from0\.5640\.564to0\.7920\.792before shared capability is updated\. However, accessibility adaptation alone is usually not sufficient to reach the target threshold, so capability plasticity is still invoked\. The experiments therefore support a reduction\-before\-rewriting interpretation rather than a claim that accessibility generally eliminates the need for capability change\.

The random accessibility control is designed precisely for this question\. It matches the operational realization at the level of accessibility\-state budget, but replaces relationship\-driven updates with random perturbations\. If the effect were only a consequence of adding extra adaptable state, the random control should behave similarly to the learned realization\. It does not\. On Split MNIST, the random control attains lower accuracy \(0\.88580\.8858versus0\.91830\.9183\) while spending much more accessibility cost \(2\.79262\.7926versus1\.41311\.4131\)\. On Permuted MNIST, the gap is even clearer:0\.86080\.8608versus0\.92420\.9242in accuracy, with2\.95992\.9599versus0\.55970\.5597in accessibility cost\. These comparisons support the claim that structured relationship adaptation matters, not merely the presence of extra adaptive parameters\.

The Accessibility Only variant strongly supports this claim\. Once later capability plasticity is disabled, final accuracy drops to0\.66250\.6625on Split MNIST and0\.63750\.6375on Permuted MNIST\. Forgetting is low in this condition, but that low forgetting is inseparable from the model’s limited ability to absorb the full task sequence\. In other words, accessibility plasticity can carry part of the adaptation burden, but not the whole burden\. This is consistent with the proposed hierarchy: reuse and accessibility plasticity are meaningful shallower responses, but deeper capability plasticity remains necessary when the required computation does not become sufficiently available through accessibility alone\.

### 5\.3Relationship to Existing Adaptive Mechanisms

These experiments do not establish state\-of\-the\-art continual learning, nor do they show superiority over all continual\-learning baselines\. They also do not constitute empirical comparisons against attention, routing, gating, mixture\-of\-experts systems, dynamic networks, or deeper organizational plasticity\. That is intentional\. The present paper proposes Accessibility Plasticity as a higher\-level adaptive abstraction rather than as a competing architectural mechanism\. Existing mechanisms such as attention, routing, gating, and mixture\-of\-experts may be viewed as possible realizations of accessibility modulation at different levels of description; direct empirical comparisons with those mechanisms are left for future work\.

### 5\.4Limitations and Future Work

The current empirical evidence should therefore be interpreted narrowly and carefully\. It provides proof\-of\-concept support for the claim that accessibility is a distinct computational object whose adaptation can precede and reduce shared capability modification\. It does not yet validate the deepest level of the hierarchy,Δ​\(D,G\)\\Delta\(D,G\), and it does not yet provide the scale of evidence that would be required for a mature benchmark paper\. Natural next steps include multiple random seeds, confidence intervals, larger continual\-learning benchmarks, stronger ablation studies, larger\-scale online environments, embodied agents, and lifelong\-learning settings in which environmental change is not organized into hand\-designed phases\. These extensions would broaden the empirical case; they are not prerequisites for the narrower proof\-of\-concept conclusions drawn here\.

## 6Conclusion

This paper develops Accessibility Plasticity as a paradigm for reuse\-first adaptation and presents one graph\-based operational realization\. The key move is to separate computational capability from computational accessibility and to treat accessibility as a fundamental computational object\. In this view,WWdetermines what computation exists, whereas𝒜\\mathcal\{A\}determines what computation is accessible\. Learning is therefore not only changing what computation exists; it is changing how existing computation becomes accessible\. The resulting framework is mathematically simple enough to instantiate, yet conceptually broad enough to connect continual learning and adaptive computation under a shared principle\.

If validated empirically, the paradigm would support a shift from architecture\-centric learning toward relationship\-centric adaptation\. Even if future experiments reveal limitations, the formulation provides a rigorous starting point for studying whether intelligent systems can adapt by reorganizing computation before rebuilding it\.

## References

- \[1\]M\. L\. Anderson\(2010\)Neural reuse: a fundamental organizational principle of the brain\.Behavioral and brain sciences33\(4\),pp\. 245–266\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[2\]P\. W\. Battaglia, J\. B\. Hamrick, V\. Bapst, A\. Sanchez\-Gonzalez, V\. Zambaldi, M\. Malinowski, A\. Tacchetti, D\. Raposo, A\. Santoro, R\. Faulkner,et al\.\(2018\)Relational inductive biases, deep learning, and graph networks\.arXiv preprint arXiv:1806\.01261\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[3\]Y\. Bengio, N\. Léonard, and A\. Courville\(2013\)Estimating or propagating gradients through stochastic neurons for conditional computation\.arXiv preprint arXiv:1308\.3432\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[4\]R\. Bommasani, D\. A\. Hudson, E\. Adeli, R\. Altman, S\. Arora, S\. von Arx, M\. S\. Bernstein, J\. Bohg, A\. Bosselut, E\. Brunskill,et al\.\(2021\)On the opportunities and risks of foundation models\.arXiv preprint arXiv:2108\.07258\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1)\.
- \[5\]T\. Brown, B\. Mann, N\. Ryder, M\. Subbiah, J\. D\. Kaplan, P\. Dhariwal, A\. Neelakantan, P\. Shyam, G\. Sastry, A\. Askell,et al\.\(2020\)Language models are few\-shot learners\.Advances in neural information processing systems33,pp\. 1877–1901\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1)\.
- \[6\]N\. Ding, Y\. Qin, G\. Yang, F\. Wei, Z\. Yang, Y\. Su, S\. Hu, Y\. Chen, C\. Chan, W\. Chen,et al\.\(2023\)Parameter\-efficient fine\-tuning of large\-scale pre\-trained language models\.Nature machine intelligence5\(3\),pp\. 220–235\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[7\]D\. Hassabis, D\. Kumaran, C\. Summerfield, and M\. Botvinick\(2017\)Neuroscience\-inspired artificial intelligence\.Neuron95\(2\),pp\. 245–258\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[8\]K\. He, X\. Zhang, S\. Ren, and J\. Sun\(2016\)Deep residual learning for image recognition\.InProceedings of the IEEE conference on computer vision and pattern recognition,pp\. 770–778\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[9\]A\. Holtmaat and K\. Svoboda\(2009\)Experience\-dependent structural synaptic plasticity in the mammalian brain\.Nature Reviews Neuroscience10\(9\),pp\. 647–658\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[10\]N\. Houlsby, A\. Giurgiu, S\. Jastrzebski, B\. Morrone, Q\. De Laroussilhe, A\. Gesmundo, M\. Attariyan, and S\. Gelly\(2019\)Parameter\-efficient transfer learning for nlp\.InInternational conference on machine learning,pp\. 2790–2799\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[11\]E\. J\. Hu, Y\. Shen, P\. Wallis, Z\. Allen\-Zhu, Y\. Li, S\. Wang, L\. Wang, W\. Chen,et al\.\(2022\)Lora: low\-rank adaptation of large language models\.\.Iclr1\(2\),pp\. 3\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[12\]T\. N\. Kipf and M\. Welling\(2016\)Semi\-supervised classification with graph convolutional networks\.arXiv preprint arXiv:1609\.02907\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[13\]Y\. LeCun, Y\. Bengio, and G\. Hinton\(2015\)Deep learning\.nature521\(7553\),pp\. 436–444\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1)\.
- \[14\]J\. C\. Magee and C\. Grienberger\(2020\)Synaptic plasticity forms and functions\.Annual review of neuroscience43\(1\),pp\. 95–117\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[15\]E\. Marder and V\. Thirumalai\(2002\)Cellular, synaptic and network effects of neuromodulation\.Neural Networks15\(4\-6\),pp\. 479–493\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[16\]V\. Mnih, K\. Kavukcuoglu, D\. Silver, A\. A\. Rusu, J\. Veness, M\. G\. Bellemare, A\. Graves, M\. Riedmiller, A\. K\. Fidjeland, G\. Ostrovski,et al\.\(2015\)Human\-level control through deep reinforcement learning\.nature518\(7540\),pp\. 529–533\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1)\.
- \[17\]G\. I\. Parisi, R\. Kemker, J\. L\. Part, C\. Kanan, and S\. Wermter\(2019\)Continual lifelong learning with neural networks: a review\.Neural networks113,pp\. 54–71\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1)\.
- \[18\]J\. Pfeiffer, S\. Ruder, I\. Vulić, and E\. M\. Ponti\(2023\)Modular deep learning\.arXiv preprint arXiv:2302\.11529\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[19\]B\. A\. Richards, T\. P\. Lillicrap, P\. Beaudoin, Y\. Bengio, R\. Bogacz, A\. Christensen, C\. Clopath, R\. P\. Costa, A\. de Berker, S\. Ganguli,et al\.\(2019\)A deep learning framework for neuroscience\.Nature neuroscience22\(11\),pp\. 1761–1770\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p3.1)\.
- \[20\]C\. Rosenbaum, T\. Klinger, and M\. Riemer\(2017\)Routing networks: adaptive selection of non\-linear functions for multi\-task learning\.arXiv preprint arXiv:1711\.01239\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[21\]N\. Shazeer, A\. Mirhoseini, K\. Maziarz, A\. Davis, Q\. Le, G\. Hinton, and J\. Dean\(2017\)Outrageously large neural networks: the sparsely\-gated mixture\-of\-experts layer\.arXiv preprint arXiv:1701\.06538\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.
- \[22\]A\. Vaswani, N\. Shazeer, N\. Parmar, J\. Uszkoreit, L\. Jones, A\. N\. Gomez, Ł\. Kaiser, and I\. Polosukhin\(2017\)Attention is all you need\.Advances in neural information processing systems30\.Cited by:[§1](https://arxiv.org/html/2607.22748#S1.p1.1),[§1](https://arxiv.org/html/2607.22748#S1.p2.1)\.