Evidence-Informed LLM Beliefs for Continual Scientific Discovery

# Evidence-Informed LLM Beliefs for Continual Scientific Discovery
Source: [https://arxiv.org/html/2606.29182](https://arxiv.org/html/2606.29182)
![[Uncaptioned image]](https://arxiv.org/html/2606.29182v1/figs/ai2.png)

Dhruv AgarwalαβReece AdamsonβAndrew McCallumα

Peter ClarkβAshish SabharwalβBodhisattwa Prasad Majumderβ

αUniversity of Massachusetts AmherstβAllen Institute for AI dagarwal@cs\.umass\.edu, bodhisattwam@allenai\.org22[https://github\.com/allenai/autodiscovery\-continual\-beliefs](https://github.com/allenai/autodiscovery-continual-beliefs)

###### Abstract

Open\-ended scientific discovery with large language models \(LLMs\) increasingly operates as a long\-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next\. A notable recent example is AutoDiscovery\(Agarwal et al\.,[2025b](https://arxiv.org/html/2606.29182#bib.bib2)\), which uses “Bayesian surprise”—the belief shift an LLM undergoes after observing evidence for a hypothesis—as both a discovery metric and a reward for search\. We first observe that AutoDiscovery treats surprisal as a*static*quantity, while surprisal in human reasoning is*non\-stationary*—it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery\. We address this mismatch with*evidence\-informed LLM beliefs*: priors updated with evidence from previous hypotheses to compute*non\-stationary surprisal*for new hypotheses\. We compare in\-context belief\-updating mechanisms and find that embedding\-based retrieval\-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37\.5% of static surprisals as spurious\. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non\-stationary beliefs\. Concretely, we introduce two complementary changes to the original search procedure: belief\-update filtering and diversity maximization\. Across five discovery domains, our method increases accumulated non\-stationary surprisal by 30\.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity\.

## 1Introduction

Scientific discovery is inherently*continual*––each observation alters what should be considered novel, informative, or surprising going forward\. This view is central to formal accounts of scientific inquiry, where evidence goes beyond isolated hypothesis verification to also revise the epistemic state of a discovery agent, thus changing the space of plausible future hypotheses\(Alchourrón et al\.,[1985](https://arxiv.org/html/2606.29182#bib.bib4); Gärdenfors,[1988](https://arxiv.org/html/2606.29182#bib.bib11); Martin and Osherson,[1997](https://arxiv.org/html/2606.29182#bib.bib28)\)\. In Bayesian accounts of scientific reasoning, this revision is captured by conditioning, where evidence transforms a prior set of beliefs into a posterior set of beliefs, and subsequent inference proceeds from the updated posterior rather than the original prior\(Earman,[1992](https://arxiv.org/html/2606.29182#bib.bib10); Howson and Urbach,[2006](https://arxiv.org/html/2606.29182#bib.bib15)\)\. Similarly, computational accounts of how scientific theories evolve emphasize that hypotheses are accepted or rejected not independently, but through their coherence with accumulated explanations and observations\(Thagard,[1989](https://arxiv.org/html/2606.29182#bib.bib35),[1992](https://arxiv.org/html/2606.29182#bib.bib36); Jansen et al\.,[2026](https://arxiv.org/html/2606.29182#bib.bib18)\)\. Thus, in a continual discovery setting, the belief state should be*non\-stationary*and evolve in light of previous results\. For instance, when assessing novelty, once a finding is observed, other hypotheses entailed or strongly suggested by this finding should be considered*less*novel\.

![Refer to caption](https://arxiv.org/html/2606.29182v1/x1.png)Figure 1:Static vs\. non\-stationary beliefs\.Belief distributions for 7500 hypotheses found by AutoDiscovery across five discovery domains\. AutoDiscovery uses*static*beliefs to score hypotheses using an unchanged LLM prior, which causes discoveries already implied by past evidence from search to spuriously appear novel\. Evidence\-informed LLM priors move the reference belief state towards the eventual posterior and allow for*non\-stationary*surprisal to be computed instead, lowering surprisal count by 37\.43% compared to what was found by the original search\.Automated scientific discovery with large language models \(LLMs\) has begun showing promise in such continual settings, alternating between proposing hypotheses \(“search”\) and evaluating their support \(“verification”\) over long horizons\(Lu et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib24); Yamada et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib38); Gottweis et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib13)\)\. A notable recent example of such a system is AutoDiscovery\(Agarwal et al\.,[2025b](https://arxiv.org/html/2606.29182#bib.bib2)\), which uses “Bayesian surprise”\(Itti and Baldi,[2005](https://arxiv.org/html/2606.29182#bib.bib17)\)as a reward for hypothesis search—given a hypothesisHH, the system elicits a prior beliefP​\(θH\)P\(\\theta\_\{H\}\)about the support forHHaccording to an LLM, evaluatesHHusing a verification procedure𝒱D\\mathcal\{V\}\_\{D\}over available dataDD, then elicits a posterior beliefP​\(θH∣𝒱D\)P\(\\theta\_\{H\}\\mid\\mathcal\{V\}\_\{D\}\)to compute a reward according to the resulting belief shift\. This reward is then used to steer search towards candidate hypotheses that are likely to surprise the LLM as a proxy signal for discovery\.

However, we observe that in both the surprisal reward and evaluation metric, AutoDiscovery treats the LLM prior as*static*—each hypothesis is evaluated against the model’s parametric beliefs in isolation, without conditioning on discoveries made earlier in the search trajectory\. This static treatment creates a mismatch between LLM\-driven discovery and human scientific reasoning—as an evaluation metric, static surprisal overestimates progress by counting derivative hypotheses as successful discoveries; as a search reward, it wastes budget by repeatedly steering the agent toward saturated regions of the hypothesis space\. Through a human expert study in neuroscience and social science, we find that 29\.54% and 25% of hypotheses found surprising by AutoDiscovery in each domain, respectively, are substantially implied by its previous discoveries rather than being genuinely novel\.

Akin to Bayesian models of cognition that treat human learning as probabilistic inference over hypotheses, where observations update beliefs that support further prediction and exploration\(Tenenbaum et al\.,[2006](https://arxiv.org/html/2606.29182#bib.bib33); L Griffiths et al\.,[2008](https://arxiv.org/html/2606.29182#bib.bib22); Tenenbaum et al\.,[2011](https://arxiv.org/html/2606.29182#bib.bib34)\), we argue that LLM\-driven discovery must instead utilize*non\-stationary*surprisal using prior beliefs that are continually updated with evidence from previous hypotheses\. We compare different mechanisms for updating beliefs using in\-context learning, including a structured memory baseline\(Chhikara et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib7)\), and find that simple top\-kkembedding\-based retrieval\-augmented generation \(RAG\) best integrates prior evidence to anticipate the eventual posterior, lowering total surprisal by 37\.43%111Hypotheses where evidence\-informed priors match the posteriors after verification\.on average\. As shown in Figure[1](https://arxiv.org/html/2606.29182#S1.F1), the distribution of non\-stationary prior beliefs is able to move closer to the experimental posterior\.

We then investigate whether the search budget lost to spurious surprisal can be reallocated to finding hypotheses that remain surprising under non\-stationary beliefs\. To do so, we present evidence\-informed search in AutoDiscovery introducing two complementary mechanisms: \(a\) belief\-update filtering, to sample hypotheses that cannot be derived in\-context using prior discoveries, and \(b\) diversity maximization, which explicitly prioritizes exploration by selecting hypotheses with the least embedding\-based similarity to previous discoveries\. Across five discovery domains\(Majumder et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib27); Gu et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib14)\), these modifications increase accumulated non\-stationary surprisal by 30\.62% on average over the original search procedure, showing that continual discovery requires search policies that explicitly manage redundancy, belief saturation, and diversity\.

In summary, our contributions are:

- •We identify a failure mode of*static surprisal*in continual LLM\-driven discovery: hypotheses are scored against unchanged priors despite accumulating evidence during search\. We validate this failure mode with human experts in neuroscience and social science, showing that 29\.54% and 25% of hypotheses considered surprising using static beliefs, respectively, are derivable from prior discoveries\.
- •We introduce*non\-stationary surprisal*, which evaluates hypotheses relative to LLM beliefs updated with evidence from previously tested hypotheses\. We compare ICL\-based belief\-updating mechanisms and find that embedding\-based RAG best anticipates posterior beliefs, lowering total surprisal count by 37\.5% of the number of static surprisals\.
- •We present evidence\-informed search for AutoDiscovery with belief\-update filtering and diversity maximization, yielding a 30\.62% average increase in accumulated non\-stationary surprisal across five discovery domains\.

## 2Background

##### Data\-driven discovery\.

FollowingMajumder et al\. \([2025](https://arxiv.org/html/2606.29182#bib.bib27)\), we define a*data\-driven hypothesis*H∈ℋH\\in\\mathcal\{H\}as a natural language statement\. Given a datasetDD, the truth value ofHHis determined by a verification procedure𝒱D:ℋ→\{supported,unsupported\}\\mathcal\{V\}\_\{D\}:\\mathcal\{H\}\\to\\\{\\mathrm\{supported\},\\mathrm\{unsupported\}\\\}, where𝒱D\\mathcal\{V\}\_\{D\}may be any executable Python program\.

##### AutoDiscovery\.

Our focus in this work is on a recent open\-ended discovery system called AutoDiscovery\(Agarwal et al\.,[2025b](https://arxiv.org/html/2606.29182#bib.bib2)\), where, given a datasetDDand a search budget, a discovery agent iteratively searches for promising hypotheses driven by “Bayesian surprise” as a reward using MCTS with Progressive Widening\(Coulom,[2006](https://arxiv.org/html/2606.29182#bib.bib9); Couëtoux et al\.,[2011](https://arxiv.org/html/2606.29182#bib.bib8)\)\. Here, we use a variation of MCTS, UCB1 Recursive, which greedily selects the next state for expansion among a node and its children in a recursive manner until either the parent node or a leaf is selected\. FollowingAgarwal et al\. \([2025b](https://arxiv.org/html/2606.29182#bib.bib2)\), we measure Bayesian surpriseB​SBSfor a hypothesis by the change in its expected belief before and after results from its verification procedure are observed\. To elicit beliefs, multiple responses are sampled from an LLM based on five categories:*“definitely false”*,*“maybe false”*,*“uncertain”*,*“maybe true”*, and*“definitely true”*, which are then mapped to pseudo\-Bernoulli counts by assigning scores of0,0\.250\.25,0\.50\.5,0\.750\.75, and1\.01\.0\. These counts can then converted into a Beta distribution using the Beta\-Bernoulli conjugacy\. For simplicity and interpretability, we evaluate belief change using empirical surprisal, defined as the difference between the posterior and prior empirical means\. Each empirical mean is simply the average numerical score assigned to the sampled categorical responses, so the resulting quantity directly reflects the shift in the model’s elicited belief on the\[0,1\]\[0,1\]scale\.

## 3From Static to Non\-Stationary Surprisal

Consider an agent at timestepttof the continual discovery process in AutoDiscovery after observing hypotheses\{H\(i\)\}i=1t−1\\\{H^\{\(i\)\}\\\}\_\{i=1\}^\{t\-1\}and their verification outcomes\{𝒱D\(i\)\}i=1t−1\\\{\\mathcal\{V\}\_\{D\}^\{\(i\)\}\\\}\_\{i=1\}^\{t\-1\}\. To evaluate a new hypothesisH\(t\)H^\{\(t\)\}, a prior beliefP​\(θH\(t\)\)P\(\\theta\_\{H^\{\(t\)\}\}\)is elicited from an LLM, which is then standardly used when measuring surprisal with respect to a posterior beliefP​\(θH\(t\)∣𝒱D\(t\)\)P\(\\theta\_\{H^\{\(t\)\}\}\\mid\\mathcal\{V\}\_\{D\}^\{\(t\)\}\)\. However, previous work elicits the prior independently for each new hypothesis from the same*static*222Encoded within LLM parameters during various stages of model training\.belief distribution\.

##### Failure mode with static priors\.

We first observe that using static beliefs in continual discovery results in a systematic failure mode\. Hypotheses that are implied—partially or completely—by earlier discoveries may still elicit a significant prior\-to\-posterior shift, thereby incorrectly registering as surprising\. Consequently, the discovery agent may repeatedly propose derivative hypotheses with low information gain or even “rediscover” previous hypotheses, spuriously inflating reward for saturated regions of the search space \(i\.e\., nodes in the search tree\), which results in a wastage of search budget\. Thus, the relevant prior for evaluating a new hypothesisH\(t\)H^\{\(t\)\}is not a*static*, unconditional beliefP​\(θH\(t\)\)P\(\\theta\_\{H^\{\(t\)\}\}\), but a belief state updated with previous discoveries as evidence,

P​\(θH\(t\)∣\{\(H\(i\),𝒱D\(i\)\)\}i=1t−1\)\.P\\\!\\left\(\\theta\_\{H^\{\(t\)\}\}\\mid\\\{\(H^\{\(i\)\},\\mathcal\{V\}\_\{D\}^\{\(i\)\}\)\\\}\_\{i=1\}^\{t\-1\}\\right\)\.We define the above expression as anon\-stationary prior, which allows us to formally definenon\-stationary surprisalas,

SNS​\(H\(t\),𝒱D\):=𝟙​\[\|𝔼P​\(θH\(t\)∣𝒱D\)​\[θH\(t\)\]−𝔼P​\(θH\(t\)∣\{\(H\(i\),𝒱D\(i\)\)\}i=1t−1\)​\[θH\(t\)\]\|≥τ\],S\_\{\\mathrm\{NS\}\}\(H^\{\(t\)\},\\mathcal\{V\}\_\{D\}\):=\\mathbbm\{1\}\\left\[\\left\|\\mathbb\{E\}\_\{P\(\\theta\_\{H^\{\(t\)\}\}\\mid\\mathcal\{V\}\_\{D\}\)\}\[\\theta\_\{H^\{\(t\)\}\}\]\-\\mathbb\{E\}\_\{P\(\\theta\_\{H^\{\(t\)\}\}\\mid\\\{\(H^\{\(i\)\},\\mathcal\{V\}\_\{D\}^\{\(i\)\}\)\\\}\_\{i=1\}^\{t\-1\}\)\}\[\\theta\_\{H^\{\(t\)\}\}\]\\right\|\\geq\\tau\\right\],whereτ\\tauis a threshold used to determine if a belief shift should be marked as a surprisal or not333We set this value to0\.30\.3throughout this paper\.\. This non\-stationary view is consistent with formal and Bayesian accounts of scientific reasoning, where evidence revises an agent’s epistemic state and changes which future hypotheses should be considered plausible, informative, or surprising\(Alchourrón et al\.,[1985](https://arxiv.org/html/2606.29182#bib.bib4); Gärdenfors,[1988](https://arxiv.org/html/2606.29182#bib.bib11); Martin and Osherson,[1997](https://arxiv.org/html/2606.29182#bib.bib28); Earman,[1992](https://arxiv.org/html/2606.29182#bib.bib10); Howson and Urbach,[2006](https://arxiv.org/html/2606.29182#bib.bib15); Thagard,[1989](https://arxiv.org/html/2606.29182#bib.bib35),[1992](https://arxiv.org/html/2606.29182#bib.bib36); Jansen et al\.,[2026](https://arxiv.org/html/2606.29182#bib.bib18); Tenenbaum et al\.,[2006](https://arxiv.org/html/2606.29182#bib.bib33); L Griffiths et al\.,[2008](https://arxiv.org/html/2606.29182#bib.bib22); Tenenbaum et al\.,[2011](https://arxiv.org/html/2606.29182#bib.bib34)\)\.

##### Non\-stationarity in human beliefs\.

We validate this premise with human experts in neuroscience and social science on hypotheses generated by AutoDiscovery\. In each domain, we ask experts to annotate their prior belief for 50 hypotheses when the top\-5 most similar previous hypotheses and their verification outcomes are made available to them\. First, we find that experts indeed*update*their beliefs from the stated prior based on past discoveries in 48\.07% and 52% cases, respectively\. Further, in 29\.54% \(of 44\) and 25% \(of 32\) hypotheses considered surprising by AutoDiscovery, experts agree that evidence from past discoveries would be informative, hence may not be truly surprising discovery\. This confirms that the*static*treatment of beliefs in AutoDiscovery may be misaligned with human judgements in continual discovery\. We provide additional details on the study in Appendix[B](https://arxiv.org/html/2606.29182#A2)\.

### 3\.1Continually Updating LLM Priors

#### 3\.1\.1In\-Context Memory

A natural way to incorporate evidence from previous discoveries is via in\-context learning444Our study focuses on nonparametric methods to capture the discovery context, given the use of proprietary LLMs with only black\-box access\. Investigating parametric methods represents an important future direction\.\(Brown et al\.,[2020](https://arxiv.org/html/2606.29182#bib.bib6)\)\. Indeed, recent work shows that accumulating interaction history in\-context can substantially change the stated beliefs and downstream behavior in LLMs\(Geng et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib12)\), though this malleability is often framed as a reliability concern\. Instead in this work, we use it constructively as a trajectory\-specific nonparametric memory to continually update beliefs as relevant evidence accumulates\.

##### Context Representations\.

We define𝒞​\(\{\(H\(i\),𝒱D\(i\)\)\}i=1t−1\)\\mathcal\{C\}\(\\\{\(H^\{\(i\)\},\\mathcal\{V\}\_\{D\}^\{\(i\)\}\)\\\}\_\{i=1\}^\{t\-1\}\)as an in\-context representation of evidence from previous discoveries in the search trajectory\. The simplest approach𝒞full\\mathcal\{C\}\_\{\\text\{full\}\}injects all previous discoveries and their verification outcomes in the context, providing complete information to the LLM but incurring a rapidly growing context length\. Next, we evaluate imposing some structure via top\-kkembedding\-based retrieval𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}, which selects thekkpreviously verified hypotheses most semantically similar toH\(t\)H^\{\(t\)\}\. Finally, we also compare against a structured long\-term memory baseline, Mem0\(Chhikara et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib7)\)\(𝒞mem0\\mathcal\{C\}\_\{\\text\{mem0\}\}\), which dynamically extracts, consolidates, and retrieves salient information from prior interactions jointly via text embeddings and a graph structure\.

#### 3\.1\.2Evaluation: Reducing Surprisal Under Non\-Stationary Beliefs

Our evaluation focuses on the ability of each context representation𝒞​\(⋅\)\\mathcal\{C\}\(\\cdot\)to reduce the total surprisal𝒯:=∑t=1BS​\(H\(t\),𝒱D\)\\mathcal\{T\}:=\\sum\_\{t=1\}^\{B\}S\(H^\{\(t\)\},\\mathcal\{V\}\_\{D\}\)accumulated in a discovery run under a given search budgetBB\. When using evidence\-informed priors, we replaceSSwithSNSS\_\{\\mathrm\{NS\}\}in𝒯\\mathcal\{T\}and aim to align evidence\-informed prior beliefs with their eventual posteriors\. Operationally, for each hypothesisH\(t\)H^\{\(t\)\}, we elicit three beliefs: the static priorP​\(H\(t\)\)P\(H^\{\(t\)\}\), the evidence\-informed priorP​\(H\(t\)∣𝒞​\(\{\(H\(i\),𝒱D\(i\)\)\}i=1t−1\)\)P\(H^\{\(t\)\}\\mid\\mathcal\{C\}\(\\\{\(H^\{\(i\)\},\\mathcal\{V\}\_\{D\}^\{\(i\)\}\)\\\}\_\{i=1\}^\{t\-1\}\)\), and the posterior after verificationP​\(H\(t\)∣𝒱D\)P\(H^\{\(t\)\}\\mid\\mathcal\{V\}\_\{D\}\)\. A belief\-update mechanism may result in the surprise of a hypothesis either decreasing \(identified spurious surprisal\), increasing \(misaligned evidence\), or remaining the same\. A method is considered performant if, in aggregate, it is able to reduce a larger number of surprisals than it causes, i\.e\., if𝒯\\mathcal\{T\}is kept low\.

##### Experiment setup\.

We run belief elicitation on hypotheses generated by AutoDiscovery over 5 real\-world domains from DiscoveryBench \(NLS\-SES,Archaeology,Evolution Freshwater Fish;Majumder et al\. \([2025](https://arxiv.org/html/2606.29182#bib.bib27)\)\) and BLADE \(Fertility,Mortgage;Gu et al\. \([2024](https://arxiv.org/html/2606.29182#bib.bib14)\)\) using 3 repeat runs with a search budget ofn=200n=200each using GPT\-5\-mini as the belief model\.

![Refer to caption](https://arxiv.org/html/2606.29182v1/x2.png)\(a\)Comparing context representations𝒞\\mathcal\{C\}
![Refer to caption](https://arxiv.org/html/2606.29182v1/x3.png)\(b\)Effect on static surprisals with𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}

Figure 2:Evidence\-informed priors reduce total surprisal\.\(a\)Comparing context\-construction methods, ICL with top\-kkretrieval yields the lowest total surprisal𝒯\\mathcal\{T\}, indicating that retrieved evidence helps align the prior with the eventual posterior\.\(b\)Decomposing the effect of𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}relative to the static prior shows the proportion of surprising hypotheses from static priors that were reduced \(53\.5%\) or newly introduced \(increased; 16%\) by evidence\-informed priors\. Surprisal decision for 70\.35% hypotheses of the total search budget \(n=200n=200\) remain unchanged\.
##### Top\-kkrepresentation performs best\.

As shown in Figure[2](https://arxiv.org/html/2606.29182#S3.F2), embedding\-based retrieval𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}\(atk=25k=25\) is the most effective context representation for evidence\-informed belief updates, showing the most reduction in𝒯\\mathcal\{T\}by 31\.8 surprisals on average across repeat runs with respect to 85\.1 static surprisals\. In comparison,𝒞full\\mathcal\{C\}\_\{\\text\{full\}\}has 28\.2 fewer surprisals and𝒞mem0\\mathcal\{C\}\_\{\\text\{mem0\}\}has 23\.5\.

##### Effect ofkkand reasoning effort\.

To assess the effect of the number of retrievalskk, we show in Figure[6](https://arxiv.org/html/2606.29182#A1.F6)a comparison of𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}atk=\{1,5,25,50,all\}k=\\\{1,5,25,50,\\text\{all\}\\\}in a longer\-horizon setting ofn=800n=800experiments\. Our results show that full context𝒞full\\mathcal\{C\}\_\{\\text\{full\}\}has 6\.1 percentage points greater total surprisal \(≈23\\approx 23hypotheses\) than𝒞top\-25\\mathcal\{C\}\_\{\\text\{top\-25\}\}, while costing8\.45×8\.45\\timesthe number of tokens on average \(≈12​k\\approx 12kmore\)\. We also find that total surprisal is similar atk=5k=5, while increasing atk=1k=1andk=50k=50\. Balancing cost and performance, we choose𝒞top\-25\\mathcal\{C\}\_\{\\text\{top\-25\}\}as the context representation to compute non\-stationary surprisal in the rest of the paper, and also use this as the new metric to report in §[4](https://arxiv.org/html/2606.29182#S4)\. Additionally, in Figure[7](https://arxiv.org/html/2606.29182#A1.F7), we show the cost\-performance tradeoff when using different levels of LLMreasoning effort, and use the “elbow” as the point of diminishing returns to selectlowas our default setting for all subsequent evaluations\.

## 4Improving Search for Continual Discovery

The previous section shows that static surprisal overestimates discovery progress by rewarding hypotheses already implied by earlier discoveries\. This raises a complementary optimization question: how can we modify the search process so as to maximize the number of hypotheses produced with high non\-stationary surprisal?

The most direct intervention is to replace AutoDiscovery’s static surprisal reward with non\-stationary surprisal\. However, as shown in Figure[3](https://arxiv.org/html/2606.29182#S4.F3), this substitution alone has no effect on discovery yield—static\- and non\-stationary reward runs, although exploring different hypotheses, in the end produce a nearly identical number of non\-stationary surprisals\. This suggests that changing the scalar reward is insufficient to redirect exploration toward hypotheses that remain novel under updated beliefs\.

![Refer to caption](https://arxiv.org/html/2606.29182v1/x4.png)Figure 3:Discovery with static vs\. non\-stationary beliefs\.The trajectories are nearly identical, indicating that replacing the reward alone is insufficient to make the original search respond to non\-stationary beliefs\.To address this, we consider ways to make the search more sensitive to evidence\-informed prior, specifically via two mechanisms that directly guide the search during the hypothesis selection step\. We recall that during search in AutoDiscovery, once a node is selected for expansion by MCTS based on a UCB1 selection policy, the system randomly samples one of a pre\-generated set of untried hypotheses to verify next\. Instead, we propose to replace this random hypothesis selection with two complementary mechanisms—*belief\-update filtering*and*diversity maximization*\. These mechanisms help in two distinct ways: by disregarding hypotheses that are influenced strongly by some prior evidence, and by pushing the search towards semantic regions away from everything that has already been explored\. We refer to our combination of the two mechanisms asevidence\-informed search\. Next, we discuss these mechanisms in more detail\.

##### Belief\-update filtering\.

First, we filter hypotheses whose static surprisal is likely to be explained well by prior discoveries, making the non\-stationary surprisal low\. To this end, for each candidate hypothesisHH, we construct an evidence\-informed context using𝒞top\-25​\(⋅\)\\mathcal\{C\}\_\{\\text\{top\-25\}\}\(\\cdot\)and elicit an updated prior conditioned on this context\. If the absolute shift between the static prior and the evidence\-informed prior exceeds a thresholdκ\\kappa, i\.e\.,

\|𝔼P​\(θH∣𝒞top\-25​\(⋅\)\)​\[θH\]−𝔼P​\(θH\)​\[θH\]\|\>κ,\\left\|\\mathbb\{E\}\_\{P\(\\theta\_\{H\}\\mid\\mathcal\{C\}\_\{\\text\{top\-25\}\}\(\\cdot\)\)\}\[\\theta\_\{H\}\]\-\\mathbb\{E\}\_\{P\(\\theta\_\{H\}\)\}\[\\theta\_\{H\}\]\\right\|\>\\kappa,thenHHis unlikely to yield non\-stationary surprisal since previous discoveries already provide enough evidence for the LLM to have a significant impact on its belief inHH, and hence likely anticipate the posterior ofHH\. Figure[8](https://arxiv.org/html/2606.29182#A1.F8)supports this criterion: as the magnitude of the shift between the static and evidence\-informed priors increases, the proportion of hypotheses that remain surprising under non\-stationary beliefs decreases \(we setκ=0\.2\\kappa=0\.2based on this analysis\)\.

We note that absolute belief shift, which can be computed without knowing the posterior, is identical to absolute surprisal shift when both the static prior and the non\-stationary prior are on the same side of the posterior \(i\.e\., both are less or both are more\)\. In general, absolute belief shift is at least as large as the absolute surprisal shift, approaching equality as either prior gets close to the posterior\. This implies that regions with relatively low belief shift given prior evidence are guaranteed to have relatively low surprisal shift as well, making them promising candidates to explore\.

##### Diversity maximization\.

Second, we encourage search to explore semantically diverse regions of the hypothesis space\. We embed each candidate hypothesis and compare it to its top\-kkmost similar previously verified hypotheses\. For a candidateHH, we define its local similarity score as the average distance to these previously verified hypotheses:

sk​\(H\)=1k​∑H′∈topk​\(H;ℋ<t\)simϕ​\(H,H′\),s\_\{k\}\(H\)=\\frac\{1\}\{k\}\\sum\_\{H^\{\\prime\}\\in\\mathrm\{topk\}\(H;\\mathcal\{H\}\_\{<t\}\)\}\\mathrm\{sim\}\_\{\\phi\}\(H,H^\{\\prime\}\),whereϕ​\(⋅\)\\phi\(\\cdot\)is the embedding function,ℋ<t\\mathcal\{H\}\_\{<t\}is the set of previously verified hypotheses, andtopk​\(H;ℋ<t\)\\mathrm\{topk\}\(H;\\mathcal\{H\}\_\{<t\}\)denotes thekk\-nearest previous hypotheses toHH\. We then select the candidate with the lowestsk​\(H\)s\_\{k\}\(H\), prioritizing hypotheses that are relatively far, and thus less likely to be redundant or derivable under evidence\-informed beliefs\.

We note that this mechanism is distinct from belief\-update filtering introduced earlier; neither subsumes the other\. For instance, if a selected hypothesisHHis relatively far from prior hypotheses, then a closely related next candidate hypothesisH′H^\{\\prime\}\(e\.g\., the negation ofHH\) will also be relatively far \(on average\) from prior hypotheses includingHH—and thus desirable according to this mechanism\. However,H′H^\{\\prime\}would be strongly implied by a prior hypothesisHH, resulting in it being filtered out due to a large belief shift\.

In addition to the above modifications, we find that including anonline de\-duplicationprocedure that removes hypotheses that are semantically redundant with previously verified hypotheses or with other candidates proposed for the current node improves search performance when measured via both static \(as in original AutoDiscovery\) as well as non\-stationary surprisal\. We use the LLM\-based hierarchical agglomerative clustering \(HAC\) procedure\(Zhang et al\.,[2023](https://arxiv.org/html/2606.29182#bib.bib40)\)from AutoDiscovery, but apply it*online*during each search iteration rather than only as a post\-hoc step after the discovery run\. Candidates that cluster with an already verified hypothesis are discarded, thus preventing search from spending budget on near\-duplicate past discoveries\.

Note that online de\-duplication is not subsumed by either of the first two mechanisms\. For instance, a near\-duplicate candidate hypothesisH′H^\{\\prime\}of a prior hypothesisHHwould not be filtered out by belief\-update filtering ifHHwas not surprising to begin with—its static prior, non\-stationary prior, and posterior would all be roughly equal, resulting in no or little belief shift\. Similarly, as mentioned earlier, ifHHis far on average from other prior hypotheses, then so would candidateH′H^\{\\prime\}be\. It would thus be prioritized by the diversity maximization objective \(which looks at the*average*distance from the top 25 closest matches\)\. Online de\-duplication, however, will correctly discardH′H^\{\\prime\}\.

### 4\.1Experiments

![Refer to caption](https://arxiv.org/html/2606.29182v1/x5.png)\(a\)Comparison between variants of standard AutoDiscovery search and evidence\-informed search\.
![Refer to caption](https://arxiv.org/html/2606.29182v1/x6.png)\(b\)Ablation showing the effect of each component in evidence\-informed search\.

Figure 4:Evidence\-informed search improves non\-stationary discovery\.Search performance over 5 datasets and 3 repeat runs withn=500n=500experiments\.\(a\)Evidence\-informed search, which combines belief\-update filtering with diversity maximization, outperforms standard AutoDiscovery search across reward and deduplication variants\. Our method with non\-stationary beliefs and online de\-duplication performs best overall, yielding a 30\.63% gain \(≈41\\approx 41surprisals\) over standard static search and a 13\.37% gain \(≈21\\approx 21surprisals\) over standard search with online de\-duplication\. Online de\-duplication consistently improves performance across methods, while simply replacing static surprisal rewards with non\-stationary surprisal has an inconsistent effect\.\(b\)Ablations on the evidence\-informed search components show that the full method performs best, and switching to static rewards shows similar performance\. Removing each of the other components—diversity maximization, belief\-update filtering, and online\-deduplication— degrades performance \(from lowest to highest effect\), validating the complementary strengths of each of our modifications\.##### Setup\.

We use the same evaluation setting as §[3](https://arxiv.org/html/2606.29182#S3)and run experiments across five discovery domains from DiscoveryBench and BLADE using 3 repeat runs, each with a search budget ofn=500n=500experiments\. We use GPT\-5\-mini as the belief model and GPT\-4o as the discovery agent\. We measure performance using accumulated*non\-stationary surprisal*, computed with𝒞top\-25\\mathcal\{C\}\_\{\\text\{top\-25\}\}as the evidence\-informed context representation and GPT\-5\-mini as the belief model\.

##### Methods compared\.

We evaluate our proposed search modifications against a set of ablations to isolate the contribution of each component\. As a baseline, we include the standard AutoDiscovery search\. We then add each hypothesis selection mechanism, belief\-update filtering and diversity maximization, independently\. Finally, our full method combines belief\-update filtering and diversity maximization\. For each method, we also run variants with static as well as non\-stationary rewards\. Additionally, we also run each variant with and without online\-deduplication\.

##### Main results\.

Figure[4](https://arxiv.org/html/2606.29182#S4.F4)\(a\) compares standard AutoDiscovery search against our proposed evidence\-informed search under accumulated non\-stationary surprisal𝒯NS\\mathcal\{T\}\_\{\\text\{NS\}\}\. Evidence\-informed search, which combines belief\-update filtering with diversity maximization, consistently outperforms standard search across reward and de\-duplication variants\. The strongest variant uses non\-stationary beliefs with online de\-duplication, achieving a 30\.63% gain over standard static\-reward search \(≈41\\approx 41additional surprisals\) and a 13\.37% gain over standard search with online de\-duplication \(≈21\\approx 21additional surprisals\)\. This shows that the proposed hypothesis\-selection mechanisms provide gains beyond de\-duplication alone\. We also find that online de\-duplication improves performance across methods, confirming that near\-duplicate hypotheses are a persistent source of wasted budget\. In contrast, simply replacing the static search reward with non\-stationary rewards has an inconsistent effect, reinforcing the need for explicit mechanisms to avoid redundancy and encourage diversity\. In Figure[9](https://arxiv.org/html/2606.29182#A1.F9), we also show the cumulative surprisal over the full search trajectory for each search variant\.

![Refer to caption](https://arxiv.org/html/2606.29182v1/x7.png)Figure 5:Evidence\-informed search improves semantic diversity\.Our method produces hypotheses with lower average pairwise cosine similarity than standard search, indicating broader semantic coverage\. Switching from static to non\-stationary beliefs alone does not change semantic diversity\.
##### Analyzing diversity\.

Next, we analyze the semantic diversity of hypotheses found by each search variant555See the full plot in Figure[10](https://arxiv.org/html/2606.29182#A1.F10)\.\. First, we see that online de\-duplication increases the count of unique hypotheses across both standard and evidence\-informed variants, as expected\. However, as shown in Figure[5](https://arxiv.org/html/2606.29182#S4.F5), evidence\-informed search also produces hypotheses with greater semantic diversity, reflected in*lower*average pairwise cosine similarity than standard search\. By contrast, switching from static to non\-stationary beliefs alone does not substantially change diversity, suggesting that the broader coverage comes primarily from the experiment\-selection modifications we introduce in evidence\-informed search rather than the choice of beliefs\.

##### Ablations\.

The ablations in Figure[4](https://arxiv.org/html/2606.29182#S4.F4)\(b\) show that all components of evidence\-informed search, except the choice of surprisal reward, contribute to performance\. The full method performs best, while removing diversity maximization, belief\-update filtering, and online de\-duplication each degrades cumulative surprisal, showing that each of our introduced modifications provides complementary gains by respectively avoiding already\-implied hypotheses, encouraging broader coverage, and suppressing redundant discoveries\.

## 5Related Work

##### LLM\-based scientific discovery\.

Most existing AI\-scientists treat discovery as an episodic problem\. When applied in an open\-ended setting, they typically expect a dataset, objective, literature context, or a prompt, and optimize for an output conditioned on the fixed input\(Bran et al\.,[2023](https://arxiv.org/html/2606.29182#bib.bib5); Majumder et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib26)\)\. While AI\-scientist\(Yamada et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib38); Lu et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib24)\)uses search\-trees for optimized agentic actions, such as managing experiments, refining figures, and producing full manuscripts, it does not use intermediate results to update the frame of reference for novelty detection\. Google AI co\-scientist666[https://research\.google/blog/accelerating\-scientific\-breakthroughs\-with\-an\-ai\-co\-scientist/](https://research.google/blog/accelerating-scientific-breakthroughs-with-an-ai-co-scientist/)operates on a goal\-driven setup, where it formulates hypotheses based on the literature related to the given objective; however, it does not accumulate evidence to update its cumulative world model, which could be used to inform newer sub\-discoveries\. Finally, Kosmos\(Mitchener et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib29)\), while working in a goal\-driven setup, internally develops a world model to inform literature search or the next data analysis task\. While Kosmos presents the closest system that uses intermediate findings to inform subsequent hypothesis generation, it does not use these findings to update inference over the world model to reflect a non\-stationary belief\. Evidence\-informed next action selection approaches akin to those presented here could be used to similarly augment these systems for their native objectives and to elicit non\-stationary beliefs representing the cumulative scientific discovery knowledge uncovered\.

##### Non\-parametric LLM memory\.

Recent work on memory\-augmented LLMs has explored external memory mechanisms for coherent, consistent, and efficient reasoning\. These systems may provide memory capabilities that merely augment an LLM’s reasoning capabilities via context manipulation or provide their own native reasoning capabilities\. BeliefBank\(Kassner et al\.,[2021](https://arxiv.org/html/2606.29182#bib.bib20)\)treats the language model as a subcomponent as part of a larger system, which maintains a symbolic memory of beliefs and constraint\-based reasoning to improve language model belief consistency without requiring retraining the underlying model\. Dealing with the finite nature of LLM context windows presents an additional challenge in determining which context to provide to the LLM, and how to do so efficiently\. InfLLM\(Xiao et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib37)\)explores a training\-free method that stores distant context, which can then be efficiently retrieved based on their relevance to enable effective processing of extremely long sequences\. Finding ideal ways to store, organize, and consolidate information is also an active area of research that includes tree\(Rezazadeh et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib31)\), graph\(Chhikara et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib7)\), and operating systems like hierarchical\-based\(Kang et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib19)\)structures\.

##### Parametric Memory\.

Recent work on parametric and semi\-parametric memory studies how models can internalize information beyond the transient prompt, either by writing new information into compact trainable states or by retrieving parameter\-like updates at inference time\. GradMem learns to compress a context into a small set of writable prefix\-memory tokens through test\-time gradient descent, providing a loss\-driven mechanism for storing contextual information while keeping the base model fixed\(Kuratov et al\.,[2026](https://arxiv.org/html/2606.29182#bib.bib21)\)\. Similarly, MIRA augments a shared backbone with Hopfield\-style associative memories that retrieve adapter\-weight updates, enabling per\-sample modulation across task and domain shifts\(Agrawal et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib3)\)\. These approaches are closely related to our goal of making models adapt to newly observed evidence, but they primarily treat memory as a mechanism for storing or retrieving task\-relevant information\. In contrast, our work focuses on the epistemic role of memory: evidence is not merely retained, but used to update an LLM’s in\-context beliefs so that future hypotheses are evaluated relative to a non\-stationary belief state\.

##### Test\-time adaptation and LLM\-based Bayesian optimization\.

A growing body of work treats inference not as a one\-shot prediction problem, but as an adaptive process in which model behavior changes in response to test\-time feedback\. Test\-time training methods update model parameters using self\-supervised objectives at inference time to improve robustness under distribution shift\(Sun et al\.,[2020](https://arxiv.org/html/2606.29182#bib.bib32)\); recent LLM\-oriented variants extend this idea to language models by adapting them to unlabeled test inputs or by optimizing policies online\(Hu et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib16); Phan et al\.,[2025](https://arxiv.org/html/2606.29182#bib.bib30)\)\. Other work adapts LLM outputs without parameter updates through iterative feedback and refinement, as in Self\-Refine\(Madaan et al\.,[2023](https://arxiv.org/html/2606.29182#bib.bib25)\)\. A complementary line uses LLMs as black\-box optimizers, where previously evaluated candidates and their rewards are placed in context to guide future proposals\. OPRO casts optimization itself as prompting, using an LLM to iteratively generate improved solutions conditioned on past solution–score pairs\(Yang et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib39)\), while LLAMBO integrates LLMs into Bayesian optimization for warm\-starting, surrogate modeling, and candidate generation\(Liu et al\.,[2024](https://arxiv.org/html/2606.29182#bib.bib23)\)\. More directly, Bayesian\-OPRO combines LLM proposal generation with Bayesian optimization to search over candidate solutions using evolving uncertainty estimates\(Agarwal et al\.,[2025a](https://arxiv.org/html/2606.29182#bib.bib1)\)\. Our work shares this sequential, evidence\-conditioned view of inference, but shifts the object of adaptation from parameters, prompts, or candidate solutions to the model’s*belief state*in context\. By explicitly updating LLM beliefs with observed evidence, our method induces a non\-stationary discovery objective: evidence that was initially surprising should cease to be surprising once incorporated, allowing search to prioritize hypotheses that remain informative under the current epistemic state\.

## 6Limitations

First, our belief estimates are elicited from LLM samples and therefore depend on prompting choices, sampling variance, calibration quality, and the model’s ability to faithfully express uncertainty\. Second, while our non\-stationary objective reduces redundant rediscovery, it may also suppress hypotheses that are legitimately worth revisiting under stronger or conflicting evidence\. Third, our experiments focus on controlled discovery settings with finite search budgets; scaling the method to open\-ended scientific workflows will require better evidence verification, stronger uncertainty calibration, and mechanisms for long\-term memory beyond the current context window\.

## 7Conclusion

We show that surprisal in continual LLM\-driven discovery should be non\-stationary: hypotheses must be evaluated relative to beliefs updated by prior evidence\. Static surprisal, as used in AutoDiscovery, can reward hypotheses already implied by earlier discoveries, leading to redundant search\. We address this with evidence\-informed LLM beliefs, updating priors in context from previously tested hypotheses and using the resulting belief state to compute non\-stationary surprisal\. We find that embedding\-based retrieval over prior discoveries best approximates posterior beliefs, revealing that many static surprisals are spurious\. Finally, we incorporate non\-stationary beliefs into search through belief\-update filtering and diversity maximization, improving accumulated non\-stationary surprisal across five discovery domains\. These results suggest that long\-horizon LLM discovery systems must not only generate and verify hypotheses, but also continually revise what counts as surprising\.

## References

- Agarwal et al\. \[2025a\]D\. Agarwal, M\. G\. Arivazhagan, R\. Das, S\. Swamy, S\. Khosla, and R\. Gangadharaiah\.Searching for optimal solutions with LLMs via bayesian optimization\.In*The Thirteenth International Conference on Learning Representations*, 2025a\.URL[https://openreview\.net/forum?id=aVfDrl7xDV](https://openreview.net/forum?id=aVfDrl7xDV)\.
- Agarwal et al\. \[2025b\]D\. Agarwal, B\. P\. Majumder, R\. Adamson, M\. Chakravorty, S\. R\. Gavireddy, A\. Parashar, H\. Surana, B\. D\. Mishra, A\. McCallum, A\. Sabharwal, and P\. Clark\.Autodiscovery: Open\-ended scientific discovery via bayesian surprise\.In*The Thirty\-ninth Annual Conference on Neural Information Processing Systems*, 2025b\.URL[https://openreview\.net/forum?id=kJqTkj2HhF](https://openreview.net/forum?id=kJqTkj2HhF)\.
- Agrawal et al\. \[2025\]S\. Agrawal, K\. V\. Kher, S\. Mittal, S\. Maheshwari, and V\. N\. Balasubramanian\.Mira: Memory\-integrated reconfigurable adapters: A unified framework for settings with multiple tasks\.In*Advances in Neural Information Processing Systems*, 2025\.
- Alchourrón et al\. \[1985\]C\. E\. Alchourrón, P\. Gärdenfors, and D\. Makinson\.On the logic of theory change: Partial meet contraction and revision functions\.*The journal of symbolic logic*, 50\(2\):510–530, 1985\.
- Bran et al\. \[2023\]A\. M\. Bran, S\. Cox, O\. Schilter, C\. Baldassari, A\. D\. White, and P\. Schwaller\.Augmenting large language models with chemistry tools\.*Nature Machine Intelligence*, 6:525 – 535, 2023\.URL[https://api\.semanticscholar\.org/CorpusID:258059792](https://api.semanticscholar.org/CorpusID:258059792)\.
- Brown et al\. \[2020\]T\. Brown, B\. Mann, N\. Ryder, M\. Subbiah, J\. D\. Kaplan, P\. Dhariwal, A\. Neelakantan, P\. Shyam, G\. Sastry, A\. Askell, et al\.Language models are few\-shot learners\.*Advances in neural information processing systems*, 33:1877–1901, 2020\.
- Chhikara et al\. \[2025\]P\. Chhikara, D\. Khant, S\. Aryan, T\. Singh, and D\. Yadav\.Mem0: Building production\-ready ai agents with scalable long\-term memory\.*arXiv preprint arXiv:2504\.19413*, 2025\.
- Couëtoux et al\. \[2011\]A\. Couëtoux, J\.\-B\. Hoock, N\. Sokolovska, O\. Teytaud, and N\. Bonnard\.Continuous upper confidence trees\.In*Learning and Intelligent Optimization: 5th International Conference, LION 5, Rome, Italy, January 17\-21, 2011\. Selected Papers 5*, pages 433–445\. Springer, 2011\.
- Coulom \[2006\]R\. Coulom\.Efficient selectivity and backup operators in monte\-carlo tree search\.In*International conference on computers and games*, pages 72–83\. Springer, 2006\.
- Earman \[1992\]J\. Earman\.*Bayes or bust?: A critical examination of Bayesian confirmation theory*, volume 92\.MIT Press Cambridge, MA, 1992\.
- Gärdenfors \[1988\]P\. Gärdenfors\.*Knowledge in flux: Modeling the dynamics of epistemic states\.*The MIT Press, 1988\.
- Geng et al\. \[2025\]J\. Geng, H\. Chen, R\. Liu, M\. H\. Ribeiro, R\. Willer, G\. Neubig, and T\. L\. Griffiths\.Accumulating context changes the beliefs of language models\.*arXiv preprint arXiv:2511\.01805*, 2025\.
- Gottweis et al\. \[2025\]J\. Gottweis, W\.\-H\. Weng, A\. Daryin, T\. Tu, A\. Palepu, P\. Sirkovic, A\. Myaskovsky, F\. Weissenberger, K\. Rong, R\. Tanno, K\. Saab, D\. Popovici, J\. Blum, F\. Zhang, K\. Chou, A\. Hassidim, B\. Gokturk, A\. Vahdat, P\. Kohli, Y\. Matias, A\. Carroll, K\. Kulkarni, N\. Tomasev, Y\. Guan, V\. Dhillon, E\. D\. Vaishnav, B\. Lee, T\. R\. D\. Costa, J\. R\. Penadés, G\. Peltz, Y\. Xu, A\. Pawlosky, A\. Karthikesalingam, and V\. Natarajan\.Towards an ai co\-scientist, 2025\.URL[https://arxiv\.org/abs/2502\.18864](https://arxiv.org/abs/2502.18864)\.
- Gu et al\. \[2024\]K\. Gu, R\. Shang, R\. Jiang, K\. Kuang, R\.\-J\. Lin, D\. Lyu, Y\. Mao, Y\. Pan, T\. Wu, J\. Yu, Y\. Zhang, T\. M\. Zhang, L\. Zhu, M\. A\. Merrill, J\. Heer, and T\. Althoff\.Blade: Benchmarking language model agents for data\-driven science\.*arXiv*, 2024\.URL[https://arxiv\.org/abs/2408\.09667](https://arxiv.org/abs/2408.09667)\.
- Howson and Urbach \[2006\]C\. Howson and P\. Urbach\.*Scientific reasoning: the Bayesian approach*\.Open Court Publishing, 2006\.
- Hu et al\. \[2025\]J\. Hu, Z\. Zhang, G\. Chen, X\. Wen, C\. Shuai, W\. Luo, B\. Xiao, Y\. Li, and M\. Tan\.Test\-time learning for large language models\.*arXiv preprint arXiv:2505\.20633*, 2025\.
- Itti and Baldi \[2005\]L\. Itti and P\. Baldi\.Bayesian surprise attracts human attention\.*Advances in neural information processing systems*, 18, 2005\.
- Jansen et al\. \[2026\]P\. Jansen, P\. Clark, D\. Downey, and D\. S\. Weld\.Generating literature\-driven scientific theories at scale, 2026\.URL[https://arxiv\.org/abs/2601\.16282](https://arxiv.org/abs/2601.16282)\.
- Kang et al\. \[2025\]J\. Kang, M\. Ji, Z\. Zhao, and T\. Bai\.Memory OS of AI agent\.In C\. Christodoulopoulos, T\. Chakraborty, C\. Rose, and V\. Peng, editors,*Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing*, pages 25961–25970, Suzhou, China, Nov\. 2025\. Association for Computational Linguistics\.ISBN 979\-8\-89176\-332\-6\.doi:10\.18653/v1/2025\.emnlp\-main\.1318\.URL[https://aclanthology\.org/2025\.emnlp\-main\.1318/](https://aclanthology.org/2025.emnlp-main.1318/)\.
- Kassner et al\. \[2021\]N\. Kassner, O\. Tafjord, H\. Schütze, and P\. Clark\.BeliefBank: Adding memory to a pre\-trained language model for a systematic notion of belief\.In M\.\-F\. Moens, X\. Huang, L\. Specia, and S\. W\.\-t\. Yih, editors,*Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing*, pages 8849–8861, Online and Punta Cana, Dominican Republic, Nov\. 2021\. Association for Computational Linguistics\.doi:10\.18653/v1/2021\.emnlp\-main\.697\.URL[https://aclanthology\.org/2021\.emnlp\-main\.697/](https://aclanthology.org/2021.emnlp-main.697/)\.
- Kuratov et al\. \[2026\]Y\. Kuratov, M\. Kairov, A\. Bulatov, I\. Rodkin, and M\. Burtsev\.Gradmem: Learning to write context into memory with test\-time gradient descent\.In*Third Workshop on Test\-Time Updates \(Main Track\)*, 2026\.URL[https://openreview\.net/forum?id=GidQ1tmQ2G](https://openreview.net/forum?id=GidQ1tmQ2G)\.
- L Griffiths et al\. \[2008\]T\. L Griffiths, C\. Kemp, and J\. B Tenenbaum\.*Bayesian models of cognition*\.Carnegie Mellon University, 2008\.
- Liu et al\. \[2024\]T\. Liu, N\. Astorga, N\. Seedat, and M\. van der Schaar\.Large language models to enhance bayesian optimization\.In*International Conference on Learning Representations*, 2024\.
- Lu et al\. \[2024\]C\. Lu, C\. Lu, R\. T\. Lange, J\. Foerster, J\. Clune, and D\. Ha\.The ai scientist: Towards fully automated open\-ended scientific discovery, 2024\.URL[https://arxiv\.org/abs/2408\.06292](https://arxiv.org/abs/2408.06292)\.
- Madaan et al\. \[2023\]A\. Madaan, N\. Tandon, P\. Gupta, S\. Hallinan, L\. Gao, S\. Wiegreffe, U\. Alon, N\. Dziri, S\. Prabhumoye, Y\. Yang, S\. Gupta, B\. P\. Majumder, K\. Hermann, S\. Welleck, A\. Yazdanbakhsh, and P\. Clark\.Self\-refine: Iterative refinement with self\-feedback\.In*Thirty\-seventh Conference on Neural Information Processing Systems*, 2023\.URL[https://openreview\.net/forum?id=S37hOerQLB](https://openreview.net/forum?id=S37hOerQLB)\.
- Majumder et al\. \[2024\]B\. P\. Majumder, H\. Surana, D\. Agarwal, S\. Hazra, A\. Sabharwal, and P\. Clark\.Position: data\-driven discovery with large generative models\.In*Forty\-first International Conference on Machine Learning*, 2024\.
- Majumder et al\. \[2025\]B\. P\. Majumder, H\. Surana, D\. Agarwal, B\. D\. Mishra, A\. Meena, A\. Prakhar, T\. Vora, T\. Khot, A\. Sabharwal, and P\. Clark\.Discoverybench: Towards data\-driven discovery with large language models\.In*The Thirteenth International Conference on Learning Representations*, 2025\.URL[https://openreview\.net/forum?id=vyflgpwfJW](https://openreview.net/forum?id=vyflgpwfJW)\.
- Martin and Osherson \[1997\]E\. Martin and D\. Osherson\.Scientific discovery based on belief revision\.*The Journal of Symbolic Logic*, 62\(4\):1352–1370, 1997\.
- Mitchener et al\. \[2025\]L\. Mitchener, A\. Yiu, B\. Chang, M\. Bourdenx, T\. Nadolski, A\. Sulovari, E\. C\. Landsness, D\. L\. Barabasi, S\. Narayanan, N\. Evans, et al\.Kosmos: An ai scientist for autonomous discovery\.*arXiv preprint arXiv:2511\.02824*, 2025\.
- Phan et al\. \[2025\]P\. Phan, D\. Agarwal, K\. Srinivas, H\. Samulowitz, P\. Kapanipathi, and A\. McCallum\.Migrate: Mixed\-policy grpo for adaptation at test\-time\.*arXiv preprint arXiv:2508\.08641*, 2025\.
- Rezazadeh et al\. \[2025\]A\. Rezazadeh, Z\. Li, W\. Wei, and Y\. Bao\.From isolated conversations to hierarchical schemas: Dynamic tree memory representation for LLMs\.In*The Thirteenth International Conference on Learning Representations*, 2025\.URL[https://openreview\.net/forum?id=moXtEmCleY](https://openreview.net/forum?id=moXtEmCleY)\.
- Sun et al\. \[2020\]Y\. Sun, X\. Wang, Z\. Liu, J\. Miller, A\. A\. Efros, and M\. Hardt\.Test\-time training with self\-supervision for generalization under distribution shifts\.In*Proceedings of the 37th International Conference on Machine Learning*, pages 9229–9248\. PMLR, 2020\.
- Tenenbaum et al\. \[2006\]J\. B\. Tenenbaum, T\. L\. Griffiths, and C\. Kemp\.Theory\-based bayesian models of inductive learning and reasoning\.*Trends in cognitive sciences*, 10\(7\):309–318, 2006\.
- Tenenbaum et al\. \[2011\]J\. B\. Tenenbaum, C\. Kemp, T\. L\. Griffiths, and N\. D\. Goodman\.How to grow a mind: Statistics, structure, and abstraction\.*science*, 331\(6022\):1279–1285, 2011\.
- Thagard \[1989\]P\. Thagard\.Explanatory coherence\.*Behavioral and brain sciences*, 12\(3\):435–467, 1989\.
- Thagard \[1992\]P\. Thagard\.*Conceptual Revolutions*\.Princeton University Press, 1992\.URL[http://www\.jstor\.org/stable/j\.ctv36zq4g](http://www.jstor.org/stable/j.ctv36zq4g)\.
- Xiao et al\. \[2024\]C\. Xiao, P\. Zhang, X\. Han, G\. Xiao, Y\. Lin, Z\. Zhang, Z\. Liu, and M\. Sun\.InfLLM: Training\-free long\-context extrapolation for LLMs with an efficient context memory\.In*The Thirty\-eighth Annual Conference on Neural Information Processing Systems*, 2024\.URL[https://openreview\.net/forum?id=bTHFrqhASY](https://openreview.net/forum?id=bTHFrqhASY)\.
- Yamada et al\. \[2025\]Y\. Yamada, R\. T\. Lange, C\. Lu, S\. Hu, C\. Lu, J\. Foerster, J\. Clune, and D\. Ha\.The ai scientist\-v2: Workshop\-level automated scientific discovery via agentic tree search, 2025\.URL[https://arxiv\.org/abs/2504\.08066](https://arxiv.org/abs/2504.08066)\.
- Yang et al\. \[2024\]C\. Yang, X\. Wang, Y\. Lu, H\. Liu, Q\. V\. Le, D\. Zhou, and X\. Chen\.Large language models as optimizers\.In*International Conference on Learning Representations*, 2024\.
- Zhang et al\. \[2023\]Y\. Zhang, Z\. Wang, and J\. Shang\.Clusterllm: Large language models as a guide for text clustering, 2023\.URL[https://arxiv\.org/abs/2305\.14871](https://arxiv.org/abs/2305.14871)\.

## Appendix AAdditional Analyses

### A\.1Context Representations: Top\-kkComparisons

![Refer to caption](https://arxiv.org/html/2606.29182v1/x8.png)Figure 6:Effect ofkkin𝒞top\-​k\\mathcal\{C\}\_\{\\text\{top\-\}k\}\.We vary the number of retrieved prior discoveries used to construct the evidence\-informed context and report both the total number of surprisals in the run and the average number of input\+output tokens used\. We find that increasingkkdoes not monotonically improve performance, instead showing best performance atk=5k=5andk=25k=25, while saving14\.34×14\.34\\timesand8\.45×8\.45\\timesfewer tokens, respectively, than using the full search trajectory\.
### A\.2Context Representations: Reasoning Effort

![Refer to caption](https://arxiv.org/html/2606.29182v1/x9.png)Figure 7:Performance\-cost tradeoff at different levels of LLM reasoning\.We vary the GPT\-5\-mini reasoning effort setting fromminimaltohighand plot the reduction in total surprisals as compared to a static beliefs run against the average number of input\+output tokens used\. Higher reasoning effort can improve surprisal reduction but increases inference cost, allowing us to select thelowsetting, which is at the “elbow” \(point of diminishing returns\)\. Surprisingly, we also find that surprisal reduction diminishes slightly at the highest reasoning setting\.
### A\.3Improving Search: Belief\-Update Filtering

![Refer to caption](https://arxiv.org/html/2606.29182v1/x10.png)Figure 8:Proportion of non\-stationary surprisals as a function of prior belief shift\.Across hypotheses generated from 5 datasets and 3 repeat runs using static search, we find that there is a decreasing trend, which emerges at a shift threshold of 0\.2, where as belief shift increases, the proportion of non\-stationary surprisals goes down\. This indicates that when beliefs significantly update with evidence from past discoveries, the present hypotheses may often be derivable\.
### A\.4Improving Search: All Results

![Refer to caption](https://arxiv.org/html/2606.29182v1/x11.png)Figure 9:Search improvements under non\-stationary surprisal evaluation\.Search variants by accumulated non\-stationary surprisal count across 5 discovery domains and 3 repeats runs\. Our proposed method combining belief\-update filtering with diversity maximization \(with online\-deduplication\) shows the best performance across all methods, yielding a 30\.63% gain \(≈41\\approx 41surprisals\) over the original static\-reward search and a 13\.37% gain \(≈21\\approx 21surprisals\) over original search \+ online\-deduplication, showing a 17\.26 percentage point contribution from our hypothesis selection modifications\. Online de\-duplication, additionally, consistently improves performance across all methods, while simply replacing static surprisal rewards with non\-stationary surprisal has no consistent effect\.
### A\.5Improving Search: Hypothesis Diversity

![Refer to caption](https://arxiv.org/html/2606.29182v1/x12.png)Figure 10:Evidence\-informed search improves semantic diversity\.We compare the diversity of hypotheses produced by standard search and Evidence\-Informed Search across static and non\-stationary belief variants, with and without online de\-duplication\. As expected, adding online de\-duplication increases the number of unique hypotheses across variants\. Uniqueness alone does not capture semantic diversity: hypotheses discovered by Evidence\-Informed Search exhibit lower average pairwise cosine similarity than those found by standard search, indicating broader semantic coverage\. In contrast, replacing static beliefs with non\-stationary beliefs by itself does not induce a meaningful diversity difference, suggesting that the diversity gains arise primarily from the experiment selection mechanisms we introduce in evidence\-informed search rather than the belief representations\. Lastly, we find that the PCA\-reduced 3\-dimensional convex hull volume is unable to provide meaningful discrimination between the different methods\.

## Appendix BHuman Expert Study

TBA\.

## Appendix CLLM Prompts

### C\.1Non\-Stationary Belief Elicitation

System PromptYou are a research scientist skilled at analyzing scientific hypotheses\. Your task is to provide your belief about the given hypothesis\. Use your prior knowledge and any previously tested hypotheses as potential evidence to support or refute the hypothesis\. Trust the evidence when it is relevant; trust your prior knowledge when it is more convincing\.

User PromptHypothesis: \{hypothesis\}=== Previous Hypotheses ===1\. \{previous hypothesis 1\} \(belief based on experimental evidence: p1\)2\. \{previous hypothesis 2\} \(belief based on experimental evidence: p2\)3\. \{previous hypothesis 3\} \(belief based on experimental evidence: p3\)⋯\\cdotsHere’s the hypothesis again: \{hypothesis\}Reason carefully before making your assessment\.

## NeurIPS Paper Checklist

1. 1\.Claims
2. Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope?
3. Answer:\[Yes\]
4. Justification: We have reviewed the literature sufficiently and run sufficient experiments to be confident in our claims\.
5. Guidelines: - •The answer\[N/A\]means that the abstract and introduction do not include the claims made in the paper\. - •The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations\. A\[No\]or\[N/A\]answer to this question will not be perceived well by the reviewers\. - •The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings\. - •It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper\.
6. 2\.Limitations
7. Question: Does the paper discuss the limitations of the work performed by the authors?
8. Answer:\[Yes\]
9. Justification: Please see Section 6 Limitations\.
10. Guidelines: - •The answer\[N/A\]means that the paper has no limitation while the answer\[No\]means that the paper has limitations, but those are not discussed in the paper\. - •The authors are encouraged to create a separate “Limitations” section in their paper\. - •The paper should point out any strong assumptions and how robust the results are to violations of these assumptions \(e\.g\., independence assumptions, noiseless settings, model well\-specification, asymptotic approximations only holding locally\)\. The authors should reflect on how these assumptions might be violated in practice and what the implications would be\. - •The authors should reflect on the scope of the claims made, e\.g\., if the approach was only tested on a few datasets or with a few runs\. In general, empirical results often depend on implicit assumptions, which should be articulated\. - •The authors should reflect on the factors that influence the performance of the approach\. For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting\. Or a speech\-to\-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon\. - •The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size\. - •If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness\. - •While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren’t acknowledged in the paper\. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community\. Reviewers will be specifically instructed to not penalize honesty concerning limitations\.
11. 3\.Theory assumptions and proofs
12. Question: For each theoretical result, does the paper provide the full set of assumptions and a complete \(and correct\) proof?
13. Answer:\[N/A\]
14. Justification: The paper does not include theoretical results\.
15. Guidelines: - •The answer\[N/A\]means that the paper does not include theoretical results\. - •All the theorems, formulas, and proofs in the paper should be numbered and cross\-referenced\. - •All assumptions should be clearly stated or referenced in the statement of any theorems\. - •The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch to provide intuition\. - •Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material\. - •Theorems and Lemmas that the proof relies upon should be properly referenced\.
16. 4\.Experimental result reproducibility
17. Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper \(regardless of whether the code and data are provided or not\)?
18. Answer:\[Yes\]
19. Justification: The paper includes details where necessary\. We will additionally be open\-sourcing all our code\.
20. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •If the paper includes experiments, a\[No\]answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not\. - •If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable\. - •Depending on the contribution, reproducibility can be accomplished in various ways\. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model\. In general\. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model \(e\.g\., in the case of a large language model\), releasing of a model checkpoint, or other means that are appropriate to the research performed\. - •While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution\. For example 1. \(a\)If the contribution is primarily a new algorithm, the paper should make it clear how to reproduce that algorithm\. 2. \(b\)If the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully\. 3. \(c\)If the contribution is a new model \(e\.g\., a large language model\), then there should either be a way to access this model for reproducing the results or a way to reproduce the model \(e\.g\., with an open\-source dataset or instructions for how to construct the dataset\)\. 4. \(d\)We recognize that reproducibility may be tricky in some cases, in which case authors are welcome to describe the particular way they provide for reproducibility\. In the case of closed\-source models, it may be that access to the model is limited in some way \(e\.g\., to registered users\), but it should be possible for other researchers to have some path to reproducing or verifying the results\.
21. 5\.Open access to data and code
22. Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material?
23. Answer:\[No\]
24. Justification: We do not yet include access to the code in the paper, but commit to releasing it\.
25. Guidelines: - •The answer\[N/A\]means that paper does not include experiments requiring code\. - • - •While we encourage the release of code and data, we understand that this might not be possible, so\[No\]is an acceptable answer\. Papers cannot be rejected simply for not including code, unless this is central to the contribution \(e\.g\., for a new open\-source benchmark\)\. - •The instructions should contain the exact command and environment needed to run to reproduce the results\. See the NeurIPS code and data submission guidelines \([https://neurips\.cc/public/guides/CodeSubmissionPolicy](https://neurips.cc/public/guides/CodeSubmissionPolicy)\) for more details\. - •The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc\. - •The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines\. If only a subset of experiments are reproducible, they should state which ones are omitted from the script and why\. - •At submission time, to preserve anonymity, the authors should release anonymized versions \(if applicable\)\. - •Providing as much information as possible in supplemental material \(appended to the paper\) is recommended, but including URLs to data and code is permitted\.
26. 6\.Experimental setting/details
27. Question: Does the paper specify all the training and test details \(e\.g\., data splits, hyperparameters, how they were chosen, type of optimizer\) necessary to understand the results?
28. Answer:\[Yes\]
29. Justification: We include all details whenever experiments setup was required\.
30. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them\. - •The full details can be provided either with the code, in appendix, or as supplemental material\.
31. 7\.Experiment statistical significance
32. Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
33. Answer:\[Yes\]
34. Justification: Yes, we report std\. and error bars in all our results\.
35. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The authors should answer\[Yes\]if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper\. - •The factors of variability that the error bars are capturing should be clearly stated \(for example, train/test split, initialization, random drawing of some parameter, or overall run with given experimental conditions\)\. - •The method for calculating the error bars should be explained \(closed form formula, call to a library function, bootstrap, etc\.\) - •The assumptions made should be given \(e\.g\., Normally distributed errors\)\. - •It should be clear whether the error bar is the standard deviation or the standard error of the mean\. - •It is OK to report 1\-sigma error bars, but one should state it\. The authors should preferably report a 2\-sigma error bar than state that they have a 96% CI, if the hypothesis of Normality of errors is not verified\. - •For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range \(e\.g\., negative error rates\)\. - •If error bars are reported in tables or plots, the authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text\.
36. 8\.Experiments compute resources
37. Question: For each experiment, does the paper provide sufficient information on the computer resources \(type of compute workers, memory, time of execution\) needed to reproduce the experiments?
38. Answer:\[Yes\]
39. Justification: All our experiments were run on CPU with LLM API keys, so we do not need heavy computing machinery\. Our runs do take long, which we will further clarify in rebuttal and later\.
40. Guidelines: - •The answer\[N/A\]means that the paper does not include experiments\. - •The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage\. - •The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute\. - •The paper should disclose whether the full research project required more compute than the experiments reported in the paper \(e\.g\., preliminary or failed experiments that didn’t make it into the paper\)\.
41. 9\.Code of ethics
43. Answer:\[Yes\]
44. Justification: Yes, it does\.
45. Guidelines: - •The answer\[N/A\]means that the authors have not reviewed the NeurIPS Code of Ethics\. - •If the authors answer\[No\], they should explain the special circumstances that require a deviation from the Code of Ethics\. - •The authors should make sure to preserve anonymity \(e\.g\., if there is a special consideration due to laws or regulations in their jurisdiction\)\.
46. 10\.Broader impacts
47. Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
48. Answer:\[Yes\]
49. Justification: We discuss the positive impact our work could have on long\-horizon discovery as well as on other discovery systems\. We have also talked about limitations\.
50. Guidelines: - •The answer\[N/A\]means that there is no societal impact of the work performed\. - •If the authors answer\[N/A\]or\[No\], they should explain why their work has no societal impact or why the paper does not address societal impact\. - •Examples of negative societal impacts include potential malicious or unintended uses \(e\.g\., disinformation, generating fake profiles, surveillance\), fairness considerations \(e\.g\., deployment of technologies that could make decisions that unfairly impact specific groups\), privacy considerations, and security considerations\. - •The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments\. However, if there is a direct path to any negative applications, the authors should point it out\. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate Deepfakes for disinformation\. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster\. - •The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from \(intentional or unintentional\) misuse of the technology\. - •If there are negative societal impacts, the authors could also discuss possible mitigation strategies \(e\.g\., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML\)\.
51. 11\.Safeguards
52. Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse \(e\.g\., pre\-trained language models, image generators, or scraped datasets\)?
53. Answer:\[N/A\]
54. Justification: Our paper poses no such risk\.
55. Guidelines: - •The answer\[N/A\]means that the paper poses no such risks\. - •Released models that have a high risk for misuse or dual\-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters\. - •Datasets that have been scraped from the Internet could pose safety risks\. The authors should describe how they avoided releasing unsafe images\. - •We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort\.
56. 12\.Licenses for existing assets
57. Question: Are the creators or original owners of assets \(e\.g\., code, data, models\), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
58. Answer:\[Yes\]
59. Justification: Yes, we have credited authors appropriately\.
60. Guidelines: - •The answer\[N/A\]means that the paper does not use existing assets\. - •The authors should cite the original paper that produced the code package or dataset\. - •The authors should state which version of the asset is used and, if possible, include a URL\. - •The name of the license \(e\.g\., CC\-BY 4\.0\) should be included for each asset\. - •For scraped data from a particular source \(e\.g\., website\), the copyright and terms of service of that source should be provided\. - •If assets are released, the license, copyright information, and terms of use in the package should be provided\. For popular datasets,[paperswithcode\.com/datasets](https://arxiv.org/html/2606.29182v1/paperswithcode.com/datasets)has curated licenses for some datasets\. Their licensing guide can help determine the license of a dataset\. - •For existing datasets that are re\-packaged, both the original license and the license of the derived asset \(if it has changed\) should be provided\. - •If this information is not available online, the authors are encouraged to reach out to the asset’s creators\.
61. 13\.New assets
62. Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
63. Answer:\[N/A\]
64. Justification: No new assets have been released\.
65. Guidelines: - •The answer\[N/A\]means that the paper does not release new assets\. - •Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates\. This includes details about training, license, limitations, etc\. - •The paper should discuss whether and how consent was obtained from people whose asset is used\. - •At submission time, remember to anonymize your assets \(if applicable\)\. You can either create an anonymized URL or include an anonymized zip file\.
66. 14\.Crowdsourcing and research with human subjects
67. Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation \(if any\)?
68. Answer:\[Yes\]
69. Justification: This information will be provided in the supplemental\.
70. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should be included in the main paper\. - •According to the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector\.
71. 15\.Institutional review board \(IRB\) approvals or equivalent for research with human subjects
72. Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board \(IRB\) approvals \(or an equivalent approval/review based on the requirements of your country or institution\) were obtained?
73. Answer:\[N/A\]
74. Justification: Our paper does not require IRB approval\.
75. Guidelines: - •The answer\[N/A\]means that the paper does not involve crowdsourcing nor research with human subjects\. - •Depending on the country in which research is conducted, IRB approval \(or equivalent\) may be required for any human subjects research\. If you obtained IRB approval, you should clearly state this in the paper\. - •We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurIPS Code of Ethics and the guidelines for their institution\. - •For initial submissions, do not include any information that would break anonymity \(if applicable\), such as the institution conducting the review\.
76. 16\.Declaration of LLM usage
77. Question: Does the paper describe the usage of LLMs if it is an important, original, or non\-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, or formatting purposes and does*not*impact the core methodology, scientific rigor, or originality of the research, declaration is not required\.
78. Answer:\[N/A\]
79. Justification: The method development in this paper was not done by LLMs\.
80. Guidelines: - •The answer\[N/A\]means that the core method development in this research does not involve LLMs as any important, original, or non\-standard components\. - •Please refer to our LLM policy in the NeurIPS handbook for what should or should not be described\.