Initial Human Belief Distributions

Large language models (LLMs) provide a flexible interface for long-horizon robot planning, but generated plans often fail to respect embodiment constraints, recover from planning errors, or reason effectively under partial observability. We present GAVEL, a framework for verifying and repairing long-horizon LLM planning built around an explicit graph world model. The graph represents relevant object-relations, action pre-conditions and effects, and probabilistic beliefs over unobserved object locations. This model can predict the consequences of LLM-generated actions before execution, detect violations, and repair those whose corrections follow directly from the world model. This method also reserves LLM replanning solely for errors requiring semantic reasoning. For multi-task instructions, GAVEL reasons over distributions of possible object locations to reorder remaining subtasks and minimize expected search cost. We evaluate GAVEL on BEHAVIOR-1K across 100 single long-horizon tasks and 500 multi-task instructions. With Qwen3-8B, GAVEL improves single-task success from 41.2% to 91.8% and multi-task success from 19.9% to 92.6%. Distributional belief reasoning also reduces travel distance by approximately 5.4% compared with a static variant. These improvements show that an explicit graph world model harness can substantially improve the reliability and efficiency of long-horizon embodied planning across compact and frontier hosted LLM capabilities.

An agent chooses an action based on her private information and a recommendation from an informed but potentially misaligned adviser. With a known probability, the adviser truthfully reports his signal; with the remaining probability, he can send any message. We characterize optimal robust decision rules that maximize the agent's worst-case expected payoff. Every optimal rule is equivalent to a trust-region policy in belief space: the adviser's reported beliefs are taken at face value if they fall within the trust region but are otherwise clipped to the trust region's boundary. We derive alignment thresholds above which advice is strictly valuable and fully characterize the solution in both binary-state and binary-action environments.

Scientific agents must learn not only how to reason, but also what to believe. However, existing LLM agents typically express scientific hypotheses in free-form text, leaving their beliefs implicit and difficult to test or revise. We introduce EvoSCM, which equips scientific agents with explicit structural causal models that evolve as new experimental evidence is collected. EvoSCM maintains a population of competing SCM hypotheses, each encoding a candidate causal explanation of the environment, and evolves them through a closed discovery loop. In each round, the agent abduces latent mechanisms from accumulated evidence, designs discriminative interventions, and commits to falsifiable predictions that it tests through experimentation. Discrepancies between prediction and observation are inductively distilled into correction rules that revise the causal structures and mechanisms of each hypothesis, and the agent then deductively validates the revised population against accumulated evidence and structural consistency to guide the next round. We evaluate EvoSCM on DiscoverPhysics, a benchmark requiring agents to uncover the hidden dynamics of noncanonical physical worlds through experimentation. EvoSCM consistently improves scientific discovery over baselines, yielding more accurate explanations and predictions while making more effective use of experimental interactions.

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

In noisy social dilemmas, intended actions are stochastically corrupted before execution, so an observed defection may reflect hostile intent or action error. Standard Markov Decision Process (MDP) formulations treat executed actions as states, structurally precluding this distinction and causing systematic over-retaliation. We introduce a Partially Observable MDP (POMDP) formulation encoding opponent intentions as latent states and executed actions as noisy observations, solved within the active inference (AIF) framework with a cost function that decomposes into epistemic and pragmatic components that jointly address inferring current intent and learning how intent evolves. In the Iterated Prisoner's Dilemma with symmetric noise, we derive a critical noise threshold governing cooperation collapse, connecting it to a fixed-point condition on learned priors. Experiments reveal that the value of intention inference is context-dependent: the POMDP provides consistent advantages against conditionally cooperative opponents, but mutual intention inference under sufficient noise produces correlated belief-driven collapse. The advantage is specific to games where intent attribution is decision-relevant.

Belief update concerns changes in an agent's beliefs induced by changes in the underlying world. Standard Katsuno-Mendelzon update assumes that an epistemic input can be incorporated from every initially possible world, whereas credibility-limited belief update restricts, for each source world, the successor worlds regarded as credible or reachable. Nevertheless, existing credibility-limited approaches treat the epistemic input as an indivisible whole, and therefore cannot represent cases in which only part of a compound epistemic input can be realized. We introduce selective credibility-limited belief update, in which the epistemic input is transformed, relative to each source world, into a weaker proxy before the credibility-limited transition is performed. We provide semantic and axiomatic characterizations of the resulting class of update operators. We then identify two well-behaved sub-classes; namely, consistency-preserving update operators, which require every transformed epistemic input to be credible from its source world whenever the original epistemic input is consistent, and maximal consistency-preserving update operators, which additionally require the selected proxy to be maximally informative among the credible consequences of the original epistemic input. Finally, we establish the generality of the proposed framework by showing that credibility-limited belief update is recovered as a special case, while Katsuno--Mendelzon belief update emerges when credibility restrictions are removed and the transformation functions are taken to be identities. These results demonstrate that the framework provides a unified and strictly more expressive account of belief update, encompassing established approaches while supporting source-dependent selective acceptance.

World models let agents plan against predicted physical state, but that state drifts; re-observation is costly and delayed, and repair can fail. We present TRACE-RealWorld (TRW), to our knowledge the first commitment-level consistency contract for world models. TRW treats predicted state as a materialized view and a physical commitment as a read whose authorization can expire. Typed, calibrated claims specify consequence-conditioned freshness and priced verification. Adaptive refresh generalizes dual-Kalman synchronization to consult the world when evidence could change a decision; dependency-scoped SagaLLM compensation repairs reversible commitments invalidated after authorization. Under an event-aligned risk oracle and recovery-liveness assumptions, we prove that synchronization and compensation are insufficient alone, whereas their composition gives a conditional consistency guarantee. Otherwise, the argument yields an auditable decomposition of violations into named debts. We implement TRW in Flood-SAR, a search-and-rescue simulator over real geography, and test six preregistered questions at frozen operating points on held-out seeds. Adaptive refresh reduces stale execution but does not dominate fixed refresh on cost, coverage, or rescue outcomes. Localized repair reduces repair work by 9.56 units per mission and restoration latency by 80.7 seconds relative to global recovery; the observed residual-violation difference is zero without establishing equivalence. Detection coverage is 0.83-0.89, and 10 of 97 invoked restorations are incomplete by mission end. The campaign treats empirical slack as sensitivity inputs rather than discharging the theorem's assumptions or providing a simultaneous population certificate. Exact replay reconstructs a disputed dispatch. TRW thus makes a world model an auditable predictive interface rather than a self-validating source of truth.

Building socially calibrated large language models, which can learn from others without simply yielding to them, requires more than reducing sycophancy as a one-dimensional failure mode. Models must distinguish when to incorporate others' perspectives from when to maintain a well-grounded moral judgment. We study the broader resistance-compliance process governing this distinction. Across three studies, we show that models' judgment revision is structured along three dimensions that parallel classic phenomena in human social psychology: the distance between an incoming view and the model's initial position, the source attribution of that view, and the coalition structure supporting it. Models are generally more receptive to nearby positions, more influenced by views presented as their own prior judgments, and differently responsive to group pressure. These findings recast sycophancy as one expression of a broader judgment-updating process shaped by social influence. Our framework provides a principled basis for distinguishing constructive belief revision from sycophantic compliance, thereby supporting better alignment in morally consequential interactions.

This paper defines TRACE (Typed Reasoning And Commitment Evidence): a typed, versioned schema for recording reasoning traces, a reference procedure for writing records against it, and one operating discipline, no durable state change without a record. The paper argues in three layers that reasoning is not in the language model: the autoregressive mechanism natively computes association; chain-of-thought and reinforcement learning inherit its limits; and the formal constructs of reasoning theory, from Socratic procedure to Pearl's ladder, are absent as machinery. The schema answers the absence with fields and tests: the TraceRecord and its causal specialization, an eight-stage reference writer, a gate-first measurement regime, the TRACE-Bench protocol, and the consumers, memory admission, plan gating, temporal regret, and verdict reuse, whose more auditable decisions are the measure of the record. A record-consumer contract states what a record guarantees and what a consumer must honor in return, making the schema an operational interface rather than a passive document. Two worked examples run in the main text: a music-lessons argument traced from sentence to typed verdict, separating association, intervention, and prescription; and a flood search-and-rescue vignette in which a predictive world model reports confident plan success that its own support and out-of-distribution scores contradict, so the record defers the commitment, requests a bounded observation, revises append-only, and clears a different branch. The vignette is illustrative, not empirical; closed-loop evaluation is left to future work, so the contribution is the schema and its contract, not a performance claim. Appendices carry the full schema, writer algorithms and cost model, clinical and policy illustrations, the benchmark protocol, convergence metrics, and usage scenarios.

Autonomous systems under partial observability act on beliefs, not raw sensor events. QANTIS treats the quantum processor as a calibrated belief-update service in that loop: it receives a prior and an observation model, estimates the rare-event evidence term, and returns an ordinary posterior to a classical planner. This paper asks whether that service can be reused across a sequential Tiger POMDP horizon on present IBM Heron hardware without corrupting the planner-facing posterior. We answer with a controlled hardware case study rather than an end-to-end autonomy or wall-clock speedup claim. The study compares no amplification, guarded Grover amplification, and all-step fixed-point amplification on the same trajectory, then checks whether the returned posterior would change the downstream action. All-step FPAA preserves the Tiger posterior across the reported 8-step and 12-step primary runs, and the 20-step and 32-step controls remain inside the same operating band. In every reported decision check, the hardware posterior and the exact Bayes posterior select the same immediate action. Boundary-aware BIQAE stabilizes amplitude estimation near zero and near one, while a rare-event sweep maps the logical sample-complexity envelope for one-in-a-million evidence. The result is an operating envelope for a hardware-calibrated belief-update primitive, not a standalone hardware-advantage claim.

We present NEST (Nested Episodic State Topology), a foundational graph-theoretic representational ontology for modeling cognition as structured state formation and transformation rather than as a finished empirical model. Concepts, episodes, percepts, and task contexts are represented as typed, weighted graphs whose nodes may carry internal subgraph payloads; edges are typed under six relation classes -- causal, containment, temporal, associative, evidential, and spatial. Durable belief graphs are separated from capacity-limited working-memory graphs that may host transient non-belief content. WM-belief grounding, conflict catalogs, and belief-update operators specify how transient structure is tested against stored knowledge and how belief is revised. A reusable operator toolkit -- activation, graph-property functionals, working-memory transitions, awareness and trajectory functionals, and belief update -- organizes the formal core. Derived diagnostics such as fragmentation, involvement, signed evaluation, coherence, and active conflict define familiar phenomena in the same ontology; self-related processing is modeled through designated self-image subgraphs within belief. Subsequent sections instantiate this core without new primitives: phenomena signatures, a task-instantiation schema for action selection and failure modes, and compatibility mappings that embed ACT-R, Soar, Sigma, the Common Model of Cognition, Global Workspace Theory, semantic networks, Theory-Theory, and chunking as constrained regions of one language. Mappings constitute the culminating technical section; discussion addresses scope, limitations, and open research directions. The contribution is intentionally foundational: a transparent representational substrate for later empirical, computational, and domain-specific work.

Physical sensing and actuation noise floors should inform how much belief resolution a decision-making system can reliably use. We introduce Finite Reliability Representations (FRR), a framework for covering belief spaces by reliability cells: regions within which the optimal action-value function Q*(b,u) varies by at most a tolerance epsilon, uniformly over actions. The framework is formulated on beliefs rather than states and uses a cover rather than an equivalence quotient, because approximate decision-closeness is not transitive in general. A central technical point is that noisy Bayesian updates should not be treated as globally contractive on arbitrary beliefs. We therefore separate three objects: the fixed-observation filter map, the predictive observation law, and the controlled belief-transition kernel. For nonlinear continuous-state systems, FRR is obtained under a reachable-set Lipschitz modulus for the belief-transition kernel. For finite-state POMDPs, the same construction becomes exact on the belief simplex: prediction is linear, Bayesian correction is a normalized positive linear map, sensor noise enters through observation-distribution distinguishability, and actuation uncertainty enters through an action-execution channel. Under the corresponding action-value Lipschitz condition, an FRR cover supports a cell-constant policy whose suboptimality is bounded by 2 epsilon/(1 - gamma). We also introduce reliability entropy, the logarithm of the minimal number of reliability cells, as a measure of certified decision-relevant belief complexity. The framework distinguishes representation sufficiency from fundamental performance floors imposed by sensing, process, and actuation noise. It applies to finite POMDPs, linear-Gaussian filters, locally linearized nonlinear filters, and particle-filter implementations through analytic or empirical certification of reliability cells.

In distributed systems, the classical State Machine Replication (SMR) model assumes that correct replicas execute deterministic transitions to yield identical bitwise states. However, the rise of agentic distributed systems -- where autonomous, stochastic, and model-driven agents orchestrate infrastructure -- presents scenarios where deterministic, bitwise replication is insufficient. Replicas operating with generative models may exhibit divergent reasoning paths, summaries, and token boundaries, yet reach semantically equivalent and correct operational decisions. Forcing bitwise agreement across these stochastic participants degrades execution flexibility, induces context amnesia, and limits performance. We argue that in such settings replicas should agree on belief, not bits. We propose Epistemic State Replication (ESR), a belief-replication layer for agentic distributed systems that shifts the replication boundary from data visibility to knowledge visibility. We formalize the epistemic node state as a pair K = (L, B) separating the deterministic, immutable evidence log (L) from the stochastic, evolving belief lineage (B). To govern execution safety, we define Semantic Linearizability, which requires operations to reflect the latest committed operational meaning within a verifier-bounded semantic compatibility metric, and Bounded Eventual Coherence, which bounds expected semantic divergence under fair delivery, monotonic evidence, bounded verifier disturbance, and a contractive graft operator. We outline protocols for propagating derived insights using structured epistemic deltas, and formalize Verifiable Semantic Rollbacks to prune faulty premises from belief lineages without inducing context amnesia. We prototype ESR and report preliminary simulation results that show feasibility under the stated assumptions and illustrate reductions in secondary cognitive faults.

In his 1996 doctoral thesis, Maurice Pagnucco created the first AGM-like abductive expansion operation. Taking his operation as a basis, as well as a taxonomy -- inspired by Atocha Aliseda -- responsible for highlighting and formalizing the main components of abductive reasoning, the main aim of this paper is to present a new paraconsistent AGM-like abductive expansion operation -- capable of assimilating contradictory explanatory hypotheses without trivialization and the consequent absurd epistemic state -- with its postulates and its transitively relational partial meet construction. To a large extent, the formal development presented in this paper was only made possible by the recent creation of the paraconsistent logic RCbr, an LFI (Logics of Formal Inconsistencies) that establishes properties especially relevant to belief revision contexts, in particular, the ability to be self-extensional -- i.e., to satisfy the replacement property. This is the first of two papers: the paraconsistent abductive expansion operation announced here -- which is part of a new system called AGMpabd -- despite bringing many interesting features, does not assign any relevant epistemic role to the paraconsistent operators of negation and consistency. Only in a second paper will an analogous paraconsistent abductive expansion operation -- which is part of another new system, AGMcircabd -- be enhanced in this direction. Nevertheless, to the best of my knowledge, the operation developed in this paper is the first of its kind in the AGM literature.

Large language models (LLMs) are typically deployed in multi-turn conversations, where each turn provides new evidence that should reduce epistemic uncertainty about their environment. Acting rationally then requires inferring the unobserved quantities that govern it and updating beliefs about them as evidence accumulates. Yet most evaluations only score the model's final-turn answer in a single-turn format, leaving this process unexamined. We ask how closely LLMs' belief updates match those of a rational Bayesian reasoner in multi-turn settings, and introduce BayesBench, a suite of simulation environments that probe this across three progressively complex tasks: (i) Bayesian estimation, where the model infers an unknown parameter from sequential evidence; (ii) Bayesian prediction, where the model turns inferred beliefs about a latent variable into outcome forecasts; and (iii) latent-framed Bayesian prediction, where observations are filtered through a user-persona framing, requiring joint inference over the latent state and the persona. Across seven LLMs (3B--70B), scaling improves latent inference and evidence accumulation, with updates occasionally matching the Bayesian posterior. However, these gains do not reliably carry over to downstream prediction, exposing a gap between inferring latent structure and using it to rationally update beliefs about the target outcome.

Autonomous scientific discovery systems increasingly use large language models (LLMs) to propose new hypotheses, but many such systems condition primarily on experimental memory: archives of high-scoring candidates or heuristic summaries of recent trials. We argue that discovery agents should instead maintain explicit, uncertainty-aware beliefs about hypothesis quality. We introduce BayesEvolve, a belief-guided discovery framework that converts experimental evidence into a predictive belief state and uses this belief to guide future experimentation. As a controlled testbed for belief-guided discovery, we evaluate BayesEvolve on shifted BBOB-style black-box optimization tasks, leaving program and laboratory discovery domains to future work. BayesEvolve improves sample efficiency over memory- and archive-guided LLM baselines under a fixed evaluation budget. We further show that the belief state is predictive on held-out candidate pools, that controlled decision-rule ablations favor belief-guided selection with an annealed uncertainty bonus, and that BayesEvolve exhibits productive late-stage concentration rather than unfocused exploration.

Belief revision is a process in which an agent begins to believe in something she previously did not. I begin the paper by presenting, based on (Gärdenfors, 1998; Hansson, 1999), postulates for belief revision that constitute the basis of the AGM theory. I will then briefly show the semantics of a modal logic introduced in (van Ditmarsch, 2005), which I call $P$'. This logic formalizes static epistemic states and has greater expressive power than AGM in doing so because it captures the quantitative notion of "degrees of conviction". The third step is to introduce revision operators on $P$ and, mostly following (van Ditmarsch, 2005), obtain the Dynamic Epistemic Logic (DEL) I call $P*$'. It models processes of belief revision in several ways. Original results are presented in the following two sections. The first one of these sections revolves around a formalization of AGM postulates within $P*$ by proving some theorems related to the satisfaction of those postulates by revisions defined in $P*$. The last section features an analysis of $P*$'s revisions that go beyond the mere satisfaction of postulates. I compare their formal behavior with respect to some philosophical criteria. At last, I conclude that the functions presented in (van Ditmarsch, 2005) are not good formalizations of the philosophical intuition behind AGM. Instead, it is captured by the function $*^0$ originally defined in this paper (but highly inspired by (van Benthem, 2007)). An implementation of this function is also provided.

We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results). (I) Trace types. FinTrace(s0,sn) is an inductive family of typed execution traces. FinTrace and Star(Step) are isomorphic as path types but not judgementally equal; TraceElim exposes the event label e:Event explicitly, giving a more ergonomic interface for event-driven induction. We prove the Trace-Reachability Correspondence, Deterministic Replay, and a canonicity framework via reducibility candidates with a Transport Lemma (RC-elim deferred; all other Core results are Coq-verified). (II) Sheaf semantics. Trace-indexed propositions are contravariant sheaves over the free trace partial-order category Tf. A Separation Theorem (explicit countermodel) distinguishes proof-theoretic monotonicity from semantic non-monotonicity. The term model is an initial CwF (syntactic universal property, not classical completeness). (III) AGM belief revision. We give an explicit constructive partial meet contraction algorithm verified against (C1)-(C4). All eight AGM postulates (R1)-(R8) are theorems. Proofs of R7 and R8 use the Disjunctive Entrenchment Lemma, given a self-contained constructive derivation. (IV) Integration. B^AGM fails the sheaf composition law BP-comp for sequential revision (explicit countermodel, Coq-verified). We introduce Single-Step Revision Systems (SSRS), prove B^AGM is a valid SSRS (Coq-verified), and show this suffices for trace morphisms, retraction characterisation, and revision witnesses. The BP-comp failure reveals a fundamental tension between path-dependent belief revision and functor consistency, not previously identified.

This article proposes a set-theoretic framework for belief change, called Abstract Worlds Semantics, in which no logical syntax is assumed. Inspired by Grove's (1988) results, our approach treats worlds as primitive elements, over which world contraction and world revision operators are defined. This semantic framework enables a unified analysis of belief change models. Within this framework, we unify classical and non-prioritized belief change constructions by defining versatile operators. When classical propositional logic is considered, our framework provides a homogeneous account of AGM, KM, and Multiple Change models. In summary, AWS systematizes belief change frameworks and operators, simplifying and generalizing belief change theory over belief sets.

Long-horizon interactions require language models to manage accumulating information: when to update their state, when to preserve their state, and what to ignore. We study this challenge as Contextual Belief Management (CBM): maintaining a predicted belief state aligned with formal evidence while isolating task-irrelevant noise. To make CBM measurable, we introduce BeliefTrack, a closed-world benchmark spanning Rule Discovery and Circuit Diagnosis, where a finite belief space and symbolic verifiers enable exact turn-level evaluation. BeliefTrack diagnoses three failures: Failed Stay, Failed Update, and Failed Isolation. Across multiple LLMs, vanilla models exhibit severe CBM failures, while explicit belief-tracking prompts provide limited gains. In contrast, reinforcement learning with belief-state rewards reduces failure rates by 70.9% on average. Further probing reveals latent belief-state dynamics behind these failures, and representation-level steering reduces failure rates by 46.1% across two tasks (Code is available at https://github.com/zjunlp/CBM).

Uncrewed aerial vehicles (UAVs) are increasingly used for exploration-driven monitoring in hazardous environments such as disaster zones, contaminated sites, wildfire areas, and damaged infrastructure, where limited flight endurance must be allocated between visiting reported locations and gathering new information. In these settings, prior information regarding hazards is often incomplete, spatially imprecise, and subject to change during execution. For example, initial reports may identify a region where a hazard is likely to exist, but the actual hazard may be displaced, partially observed, or entirely unreported. We present an integrated exploration-aware UAV route optimization and path planning framework for hazard monitoring under uncertain and evolving prior information. The environment is represented as a spatial risk map, where each location has an associated belief of hazardous conditions. Reported hazards are modeled as uncertain regions of interest (ROIs) rather than confirmed target locations, requiring the UAV to inspect reported areas while also using its limited flight endurance to explore informative regions. The proposed method solves a vehicle routing problem over reported ROIs, augments the route with auxiliary pseudo-nodes to improve spatial coverage, allocates the remaining flight distance budget across route segments, and optimizes dynamically feasible B-spline trajectories for local exploration. During execution, UAV measurements update a grid-based belief map, and the remaining trajectory is replanned when new information and the remaining budget justify adaptation. Across 48 scenario configurations, online replanning improves average KL reduction by 15.9% over the offline optimized planner and 48.6% over straight-line traversal.

Theory of Mind (ToM), the ability to infer others' knowledge, intentions, and emotions, is commonly evaluated in large language models (LLMs) using end-point question answering, where performance is judged solely by the final answer to a social reasoning query. This paradigm obscures whether the model actually constructs the underlying mental-state representations required for robust reasoning, particularly in scenarios involving divergent, evolving, or mistaken beliefs. In order to address this research gap, we introduce OmniToM, a benchmark that directly evaluates these representations by requiring explicit modeling of belief structures for all relevant actors within a narrative. These structures are composed of belief propositions: minimal statements of what an actor takes to be true about the world or another actor's mental state, allowing knowledge, intentions, emotions, and false beliefs to be analyzed in a common format. Models are evaluated in two stages: Stage 1: Belief Extraction, which extracts from the story the beliefs relevant to its social dynamics, and Stage 2: Belief Labeling, which assigns each belief a seven-dimensional schema label covering recursive order, truth status, knowledge access, explicitness, content type, mental source, and context. Built from 895 stories from the existing ToMBench story corpus and augmented with 22,343 labeled belief propositions, OmniToM uses a human-calibrated LLM-assisted annotation pipeline. Across diverse models in zero-shot evaluation, OmniToM reveals an actor-specific belief-tracking bottleneck: current LLMs struggle with the knowledge-access and representational decisions required to transform narrative facts into actors' beliefs and shared mental states.

Human decision-making is sequential and uncertainty-aware, yet standard neural networks often rely on static, dense forward computation with limited visibility into evidence acquisition, uncertainty evolution, or when computation should stop. We introduce \textbf{Neural Bayesian Sequential Routing (NBSR)}, a framework that models neural inference as active evidence accumulation over a hierarchical Directed Acyclic Graph (DAG). Within a Dirichlet--Categorical conjugate framework, neural experts query a persistent global knowledge oracle to extract positive evidence vectors, which act as pseudo-counts and update a Dirichlet belief state by exact conjugate addition. Coupled with a Gumbel-Softmax Straight-Through estimator, this update enables hard, path-dependent routing while preserving surrogate gradients for end-to-end training. The resulting Dirichlet precision and entropy provide mechanisms for uncertainty quantification, entropy-based early exiting, OOD abstention, and cost-aware evidence acquisition. We prove that, under strictly positive evidence extraction, total Dirichlet precision increases monotonically along any valid trajectory and marginal predictive variance is bounded, formalizing sequential ``hypothesis sharpening''; under idealized capacity and optimization assumptions, the terminal Dirichlet expectation recovers the Bayes-optimal conditional distribution. Empirical evaluations across visual categorization, structured medical diagnosis, language modeling, partially observable control, and cost-aware Bayesian experimental design show that NBSR achieves competitive predictive performance while providing transparent routing traces, path-dependent evidence attribution, uncertainty-aware decision control, and resource-rational inference. Overall, NBSR offers a mathematically grounded framework for interpretable, modular, and resource-rational agentic AI.

Large language models (LLMs) are increasingly deployed on long-horizon tasks in partially observable environments, where they must act while inferring and tracking a complex environment state over many steps. This leads to two challenges: partial observability requires maintaining uncertainty over unobserved world attributes, and long interaction history causes context to grow without bound, diluting task-relevant information. A principled solution to both challenges is a belief state: a posterior distribution over environment states given past observations and actions, which compactly encodes history for decision making regardless of episode length. In LLM agents, however, the open-ended nature of text makes it unclear how to represent such a distribution. Therefore, we introduce Agent-BRACE: Agent Belief state Representation via Abstraction and Confidence Estimation, a method that decouples an LLM agent into a belief state model and a policy model, jointly optimized via reinforcement learning. The belief state model produces a structured approximation of the belief distribution: a set of atomic natural language claims about the environment, each annotated with an ordinal verbalized certainty label ranging from certain to unknown. The policy model conditions on this compact, structured approximate belief rather than the full history, learning to select actions under explicit uncertainty. Across long-horizon, partially observable embodied language environments, Agent-BRACE achieves an average absolute improvement of +14.5% (Qwen2.5-3B-Instruct) and +5.3% (Qwen3-4B-Instruct), outperforming strong RL baselines while maintaining a near-constant context window independent of episode length. Further analysis shows that the learned belief becomes increasingly calibrated over the course of an episode as evidence accumulates.

LLM agents that operate over long context depend on external memory to accumulate knowledge over time. However, existing methods typically store each observation as a single deterministic conclusion (e.g., inferring "API~X failed" from temporary errors), even though such observations are inherently partial and potentially ambiguous. By committing to one conclusion and discarding uncertainty, these methods introduce self-reinforcing error: the agent acts on the stored conclusion, never revisits alternatives, and reinforces the conclusion over time. To address this issue, we propose BeliefMem, which shifts the memory paradigm from committing to a single conclusion per observation to retaining multiple candidate conclusions with their probabilities. Concretely, BeliefMem stores the candidate conclusions as separate memory entries, each carrying a probability that is updated via Noisy-OR rules as new observations arrive. At retrieval, all candidates surface together with their probabilities, keeping alternatives visible to the agent. Since each conclusion in memory retains its probability, BeliefMem preserves the uncertainty that the deterministic paradigm discards, enabling the agent to act with high confidence on well-evidenced knowledge while retaining the capacity to update its confidence when new evidence arrives. Empirical evaluations on LoCoMo and ALFWorld benchmarks show that, even with limited data, BeliefMem achieves the best average performance, remarkably outperforming well-known baselines. More broadly, such probabilistic memory produces substantial gains and explores a new direction for agent memory in partially observable environments.

Negotiation agents must infer what their counterpart values, update those beliefs over dialogue turns, and choose actions under uncertainty. End-to-end large language models (LLMs) can imitate negotiation dialogue, but their opponent beliefs are usually implicit and difficult to inspect. We propose BOND (Bayesian Opponent-belief Negotiation Distillation), a framework for auditable negotiation. BOND consists of an LLM-based Bayesian teacher that scores dialogue contexts against the six possible opponent priority orderings, updates a posterior over those orderings, and uses the posterior for menu-based decision making, as well as a smaller 8B student language model that emits both negotiation actions and normalized posterior beliefs as tagged text. In the CaSiNo negotiation dataset, BOND outperforms the state-of-the-art and achieves mean Brier score 0.085 over opponent-priority posteriors. The distilled student preserves much of this belief signal, achieving Brier 0.114, below the uniform six-ordering reference of 5/36, approximately 0.139. Compared with a 70B structured-CoT baseline, the significantly smaller 8B student model yields substantially better elicited posterior calibration. We further showcase auditability through posterior trajectories, belief-versus-policy error decomposition, and posterior-prefix interventions. These diagnostics reveal that distillation preserves a scoreable belief report more strongly than causal belief-conditioned control, making weak belief-action coupling visible, not hidden.

Can LLMs simulate how humans form and change beliefs in social networks? We put this to the test by replicating an established study on belief dynamics, evaluating 12 LLMs across multiple model families and parameter sizes. The answer is a clear no, and in systematic ways. LLMs fail to capture initial human belief distributions and tend to be overall more conformist than humans, shifting their responses to align with those around them. They also take a nuanced approach to emulating human homophilic tendencies within networks. Our findings carry a double payoff: they highlight fundamental properties of LLM behavior, and they raise a sharp warning against deploying LLMs as human proxies in social simulations.

We investigate the belief revision problem in epistemic planning, i.e., what will be the beliefs of all agents in a multi-agent system after an agent gains the belief in some state property. Based on the standard representation in epistemic planning of agents' beliefs via a single multi-agent Kripke model, we generalize the classical AGM belief revision postulates to the multi-agent setting, with the aim to provide a formal framework for evaluating dynamic epistemic reasoning frameworks in which the beliefs of all agents as the result of actions are computed. As an example of a simple operator that satisfies all of the generalized AGM postulates, we present generalized full-meet multi-agent belief revision. We moreover define a generalization of the standard postulates for iterated revision, present a more sophisticated, event model based revision operator, and discuss the potential issues in defining an epistemic operator on Kripke models that can satisfy all of the generalized postulates for iterated multi-agent belief revision.

Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This paper addresses both. We represent the reasoning state as an epistemic state graph encoding extracted claims, evidential relations, open questions, and confidence weights. We define the order-gap as the distance between the states reached by expand-then-consolidate versus consolidate-then-expand; a small order-gap suggests that the two orderings agree and further iteration is unlikely to help. Our main result gives a necessary and sufficient condition for the linearised order-gap to be non-degenerate near the fixed point, showing when the criterion is informative rather than algebraically vacuous. This is a local condition, not a global convergence guarantee. We apply the framework to recursive reasoning systems and sketch its application to agent loops, tree-of-thought reasoning, theorem proving, and continual learning.

Rational belief revision is commonly viewed as being based on a preference order between possible worlds, with the resulting new belief set being those sentences true in all the most preferred models of the incoming new information. Usually, such a preference order is taken to be a total preorder. Nevertheless, there are other, more general classes of ordering that can also be employed. In this paper, we explore two such classes that have been studied within the theory of rational choice but have seen limited or no application in belief revision. We begin with interval orders, introduced by Fishburn in the '80s, which associate with each possible world a nonnegative interval' of plausibility. We then move on to biorders, studied by Aleskerov, Bouyssou, and Monjardet, which generalise interval orders by allowing the intervals to have negative lengths, a feature that can be used to capture a notion of dissonance or instability. We provide axiomatic characterisations of these two resulting families of belief revision operators, as well as of two further families of interest that lie between interval orders and biorders. We show that while biorder-based revisions satisfy the Success postulate, they do not always yield consistent outputs. By modifying their definition to discard inputs that lead to inconsistency as incredible', we derive new families of so-called non-prioritised revision that satisfy the Consistency postulate, but not the Success one. These families are linked to credibility-limited revision operators of Hansson et al., but for which the set of credible sentences does not satisfy the single-sentence closure condition. We argue that the biorder-based approach is well-suited for scenarios where an agent might initially reject new information, but may accept it when presented with additional explanation.

Deliberative multi-agent systems allow agents to exchange messages and revise beliefs over time. While this interaction is meant to improve performance, it can also create dangerous conformity effects: agreement, confidence, prestige, or majority size may be treated as if they were evidence, producing high-confidence convergence to false conclusions. To address this, we introduce PBRC (Preregistered Belief Revision Contracts), a protocol-level mechanism that strictly separates open communication from admissible epistemic change. A PBRC contract publicly fixes first-order evidence triggers, admissible revision operators, a priority rule, and a fallback policy. A non-fallback step is accepted only when it cites a preregistered trigger and provides a nonempty witness set of externally validated evidence tokens. This ensures that every substantive belief change is both enforceable by a router and auditable after the fact. In this paper, (a) we prove that under evidential contracts with conservative fallback, social-only rounds cannot increase confidence and cannot generate purely conformity-driven wrong-but-sure cascades. (b) We show that auditable trigger protocols admit evidential PBRC normal forms that preserve belief trajectories and canonicalized audit traces. (c) We demonstrate that sound enforcement yields epistemic accountability: any change of top hypothesis is attributable to a concrete validated witness set. For token-invariant contracts, (d) we prove that enforced trajectories depend only on token-exposure traces; under flooding dissemination, these traces are characterized exactly by truncated reachability, giving tight diameter bounds for universal evidence closure. Finally, we introduce a companion contractual dynamic doxastic logic to specify trace invariants, and provide simulations illustrating cascade suppression, auditability, and robustness-liveness trade-offs.

Penetration testing, the simulation of cyberattacks to identify security vulnerabilities, presents a sequential decision-making problem well-suited for reinforcement learning (RL) automation. Like many applications of RL to real-world problems, partial observability presents a major challenge, as it invalidates the Markov property present in Markov Decision Processes (MDPs). Partially Observable MDPs require history aggregation or belief state estimation to learn successful policies. We investigate stochastic, partially observable penetration testing scenarios over host networks of varying size, aiming to better reflect real-world complexity through more challenging and representative benchmarks. This approach leads to the development of more robust and transferable policies, which are crucial for ensuring reliable performance across diverse and unpredictable real-world environments. Using vanilla Proximal Policy Optimization (PPO) as a baseline, we compare a selection of PPO-based variants designed to mitigate partial observability, including frame-stacking, augmenting observations with historical information, and employing LSTM or TrXL architectures. We conduct a systematic empirical analysis of these algorithms across different host network sizes. We find that this task greatly benefits from history aggregation. Converging up to four times faster than other approaches. Manual inspection of the learned policies by the algorithms reveals clear distinctions and provides insights that go beyond quantitative results.

Tool use is often assumed to monotonically improve reasoning, where external evidence is expected to help when relevant and be ignored when irrelevant. We show that this assumption fails in a state-dependent way. Across benchmarks with Python and Wikipedia tools, external evidence reliably helps when initial beliefs are weak, but can flip already-correct answers when those beliefs are strong. We frame this as a misallocation of revision authority, arguing that deferring to external evidence is suboptimal when internal support for the correct answer surpasses the tool's expected output quality. This predicts that harm should concentrate on high-confidence no-tool cases. We test this prediction with threshold localization, wrong-trace audits, and a same-clue intervention showing that revision framing changes the damage caused by misleading evidence. These findings suggest that mixed no-tool/tool-assisted inference should arbitrate authority rather than privilege tool evidence by default. As a minimal demonstration, we introduce CASE, a label-free controller that selects between no-tool and tool-assisted trajectories using answer-state certainty and improves over existing confidence-based arbitration baselines.The code for our experiments is available at https://github.com/epsilondylan/State-Dependent-Belief-Revision.