State-Tracking

Neural algorithmic reasoning has emerged as a popular research direction. It aims to train neural networks to mimic the step-by-step behavior of classical rule-based algorithms. More specifically, the execution of such algorithms can be abstracted as a sequence of states, where each state represents the intermediate outcome after an execution step. The training objective is to generate state sequences that replicate the underlying algorithmic process. A common framework for this task adopts an encoder-processor-decoder architecture, where the encoder learns representations of states, the processor simulates algorithmic steps, and the decoder reconstructs output states. While prior work has focused on improving the processor, the role of the encoder in representation learning has received little attention. Most methods rely on simple MLP encoders, raising the question of whether such representations are sufficiently informative for supporting algorithmic reasoning. This paper investigates how to improve encoder representations for neural algorithmic reasoning. We propose a reconstruction module that aims to recover the input state from its encoded representation. This auxiliary reconstruction task encourages the encoder to retain critical information about the input. We demonstrate that incorporating this task during training improves the performance of existing neural architectures on standard benchmarks. Furthermore, we observe that current encoders often underutilize the correlations among features within a state. To address this, we draw inspiration from self-supervised learning and design an enhanced variant of the auxiliary task that encourages the encoder to capture intra-state feature dependencies. Experimental results show that our method enables the encoder to learn richer representations, thereby enhancing the performance of existing processors on algorithmic reasoning tasks.

Extended chain-of-thought reasoning can degrade performance on deterministic state-tracking tasks, not due to preference biases, but limits rooted in the information-theoretic capacity of decoder-only attention. We establish: (1) an Attention Bottleneck Theorem with a complementary achievability construction, bounding state-tracking capacity as $O(H \cdot \log(L/H) \cdot \sqrt{d_h})$; (2) a context-dependent error model yielding super-exponential accuracy decay; (3) the State-Space Jaccard metric distinguishing capability from preference failures; (4) a Deterministic Horizon $d^* \in [19, 31]$ beyond which tool delegation becomes necessary. Across 12 models and 8 task domains (including SWE-Bench, WebArena, and SQL-Multi), tool-integrated reasoning consistently outperforms neural chain-of-thought; on the primary model suite it reaches 86-94% accuracy versus 24-42% for neural chain-of-thought. Fine-tuning on optimal-length traces yields $<$5% improvement, confirming an architectural ceiling, and high cross-model correlation ($r = 0.81$-$0.91$) indicates these failures are architectural rather than training-specific. Our results provide principled guidance for when pure neural reasoning should yield to hybrid approaches in agentic systems.

Entity tracking (ET), the ability to keep track of states, is a fundamental skill that underlies complex reasoning. An increasing amount of work investigates how transformer language models (LMs) solve entity binding $\textit{without}$ state changes. However, there is limited understanding of how non-toy LMs address ET problems of realistic difficulties expressed in natural language. To this end, we investigate the mechanisms underlying ET in more complex scenarios featuring multiple state-changing operations. We find that LMs do not incrementally track world states across tokens or query-relevant states across layers, but simply aggregate relevant information in parallel at the last token when the query becomes evident. We further investigate mechanisms of individual operations ($\texttt{PUT}$, $\texttt{REMOVE}$, $\texttt{MOVE}$) to characterize this non-incremental ET mechanism. Surprisingly, LMs implement the $\texttt{REMOVE}$ operation with a fragile global suppression tag; this global removal mechanism predicts various failure modes that we confirm behaviorally. We provide a mechanistic solution of nullifying this tag to partially address this issue. Overall, our findings reveal that LMs solve a fundamentally sequential task using a non-sequential strategy. More broadly, our work illustrates how behavioral and mechanistic analyses can fruitfully interact. Behavioral results inform mechanistic hypotheses, and insights from mechanistic analyses help build stronger behavioral evaluations by predicting failure modes missing from existing evaluations.

LLM multi-agent systems often coordinate through natural-language dialogue or loosely structured shared memory, making intermediate state difficult to validate, attribute, and audit. We introduce PatchBoard, a schema-grounded collaboration architecture that replaces inter-agent dialogue with validated JSON Patch mutations over a shared structured state. An Architect agent constructs a task-specific schema and workflow rules, while a deterministic kernel validates each proposed state mutation against schema constraints, role-specific write contracts, and runtime invariants before committing it transactionally. On 630 matched ALFWorld episodes, PatchBoard achieves an 84.6% success rate, compared with 30.8% for LangGraph and 61.6% for Flock, while reducing tokens per successful task to 45.5k, compared with 368.3k and 64.2k, respectively.

Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a smooth map and an explicit source of randomness. Stochastic Lifting exploits this structure by attaching an independent, high-dimensional random label to each state transition in the training data and fitting a transition map from the current state and label to the next state using a standard regression loss. The labels act as auxiliary coordinates that let the model represent multiple plausible next states from similar current states, avoiding collapse to a mean prediction in the finite-sample size regime. At inference, fresh labels are sampled at each time step and the learned map is rolled forward autoregressively, generating diverse trajectories with a single network evaluation per time step.

Driving a system from one state to another through targeted interventions is a fundamental challenge in science, yet most predictive models offer limited mechanistic insight and no principled framework for decision-making. Here we present COAST (Causally Optimal Actions for State Transitions), a causal-intelligence approach for the in-silico design of constrained interventions that induce user-defined state transitions. Given data characterizing source and target states, COAST learns context-specific causal graphs and structural causal models, attributes observed distributional shifts to mechanism-level causal drivers, and introduces a novel constraint-aware multi-objective optimization formulation that balances transition efficacy, intervention complexity, and target-state stability. The approach is modular and domain-agnostic, integrating feature selection, causal discovery, causal modeling, and intervention identification and evaluation through interchangeable components. Across synthetic benchmarks and real biological datasets, COAST recovers key causal drivers and identifies robust single- and multi-target intervention strategies that achieve desired state transitions, accompanied by transparent mechanistic rationales to guide experimental validation.

A central puzzle for the behavioural sciences and for human-facing artificial intelligence is the persistence of within-person variability. The same individual, presented with the same observable input, produces different outcomes on different occasions, and different individuals produce divergent outcomes that no observable covariate fully predicts. We argue that this variability belongs in the dynamic latent state of the person, and that human outcomes are controllable in a precise and operational sense through interventions that target the state and its weighting at the moment a decision is being formed. We define a state as the time-indexed weighting vector over the dimensions that govern how an individual's biology, physiology, and neuropsychology process the next event into a decision and an outcome. The relationship between state, decision, and outcome is causal rather than correlational. The weighting vector is dynamic at sub-daily timescales. The conscious channel through which outcomes are reportable is a narrow attentional bottleneck whose contents are themselves state-dependent. Taken together, these claims imply that the outcome of a given event is controllable, conditionally, on the state-trajectory at the time of intervention. We motivate the framework with six strands of established evidence (causal inference, predictive processing, allostasis, attentional bottleneck, chronobiology, computational psychiatry) and a 24-month observational base from a deployed behavioural platform spanning more than 200,000 consented users across four occupational personas (research period 2023 to 2026). We derive seven testable predictions, list six operational requirements for state-aware systems, and discuss implications for digital health, education, AI personalisation, and personal agency.

Variational Quantum Algorithms (VQAs) potentially offer a pathway to practical quantum advantage, but their optimization is heavily hindered by barren plateaus and numerous local minima. While classically simulable Clifford circuits can warm-start VQAs to accelerate convergence, existing heuristic-based initialization methods struggle to scale within vast combinatorial search spaces. To overcome this bottleneck, we propose CRiSP (a Clifford Reinforcement Learning agent for State Preparation), a framework that formulates discrete prefix selection as a sequential decision-making problem. CRiSP utilizes Neural-Guided Monte Carlo Tree Search, driven by a Transformer-based policy trained via self-play, to insert learned Clifford gates before fixed parameterized rotations. This enables the construction of high-quality initial states entirely through polynomial-time classical stabilizer simulation without altering the underlying circuit architecture. By integrating a curriculum learning strategy that progressively expands the search horizon, the agent efficiently scales to deep circuits. Evaluated on QAOA benchmarks of up to $22$ qubits and $1{,}370$ parameters, CRiSP outperforms state-of-the-art Clifford initialization methods by a mean of $3.17\times$ (max $45.02\times$) in average energy accuracy and $2.44\times$ (max $16.01\times$) in best-achieved energy accuracy. Assessments on VQE tasks further demonstrate the framework's robustness and generalizability.

Large language model post-training methods such as supervised fine-tuning (SFT), reinforcement learning (RL), and distillation are often analyzed through their loss functions: maximum likelihood, policy gradients, forward KL, reverse KL, or related objective-level variants. We study a complementary factor: the state distribution on which supervision is applied. For an autoregressive policy, a state is a prompt plus generated prefix. SFT trains on fixed dataset states, while RL and on-policy distillation (OPD) train on states induced by the current learner. We formalize post-training as state-distribution shaping and run a controlled smallscale study using Qwen3-0.6B-Base on GSM8K, with TruthfulQA and MMLU as retention evaluations. Our results show three phenomena. First, a mild SFT run improves GSM8K with little forgetting, while a stress SFT run causes substantial retention loss. Second, OPD from a degraded SFT teacher surpasses that teacher on GSM8K, TruthfulQA, and MMLU, despite using the teacher as its only supervision source. Third, a lightweight on-policy RL run improves GSM8K while preserving retention. These results support a state-centric view of post-training: the source and locality of training states can be as important as the form of the supervision signal.

It has been recently shown that lifted STRIPS models can be learned correctly and efficiently from action traces alone; i.e., applicable action sequences from a hidden STRIPS model. The result is remarkable because the states are not assumed to be observable at all, and yet it is not practical enough as STRIPS actions include arguments that are not needed for selecting the actions. This shortcoming has been addressed by assuming that the action traces come instead from a hidden STRIPS+ model where some action arguments are implicit in the hidden action preconditions. A limitation of this approach, however, is that it assumes that the states are fully observable. In this work, we relax these restrictions and consider the problem of learning STRIPS+ action domains from traces in a more general context where the traces carry partial information about both actions and states. In particular, we formulate algorithms and completeness results for three general cases, all of which assume full observability of selected action arguments. In the first case, no observability of the state is assumed; in the second case, full observability of some state predicates is assumed, and in the third case, local observability of some state predicates is assumed instead. Given a STRIPS+ domain, these results characterize the conditions under which an equivalent domain can be learned from traces. Experimental results are reported.

Clarification-seeking behavior is widely regarded as a desirable property of LLM agents, enabling them to resolve ambiguity before acting on underspecified tasks. However, the security implications of this interaction pattern remain unexplored. We investigate whether the transition from standard execution to a clarification-seeking state increases an agent's susceptibility to prompt injection attacks. We introduce ASPI (Ambiguous-State Prompt Injection), a benchmark of 728 task-attack scenarios that isolates clarification as a distinct agent state and measures how this state transition affects vulnerability under controlled conditions. Each benchmark instance is evaluated under matched execution and clarification settings: in the execution setting, the agent acts on a fully specified instruction and encounters adversarial content only through tool-returned data; in the clarification setting, the agent must first request and incorporate additional user input before acting. We evaluate ten frontier LLMs and find that clarification-seeking consistently and substantially amplifies vulnerability. For instance, attack success rises from 1.8% to 34.0% for o3 and from 2.2% to 35.7% for Gemini-3-Flash. A decomposition analysis reveals that this gap reflects both a state-dependent shift in how models process incoming content and a channel-specific effect arising from the agent-solicited clarification interface. These findings demonstrate that standard execution-time security evaluation systematically underestimates the attack surface of interactive agents, and that robustness under fully specified tasks does not translate to robustness under ambiguity. For reproducibility, our data and source code are available at https://github.com/scaleapi/aspi.

Streaming 3D reconstruction under a strict constant-memory budget hinges on how the recurrent state is updated as the stream evolves. We profile TTT3R-style per-token gates across five benchmarks and discover a structural bottleneck: the gate is intrinsically bounded in magnitude (median $0.31$; never exceeding $0.6$) and nearly frame-invariant, yielding an effective memory horizon of only $\sim$3 frames per state token, which serves as the structural origin of long-sequence drift. We trace this to a missing axis: existing inference-time methods modulate updates only at the per-token, intra-frame level, while the orthogonal frame-level question of \emph{how strongly each frame should contribute to the state} has been treated as content-independent. We close this gap with a scalar frame-level gate $α_t \in (0, 1]$ derived in closed form from frame-to-frame changes of internal features---a graded write weight, inspired by classical Simultaneous Localization and Mapping (SLAM) keyframe selection, that never discards a frame and requires no parameters, no training, and no extra forward pass. Across six benchmarks spanning camera pose, video depth, and 3D reconstruction at sequence lengths up to $4,661$ frames, our gate cuts ATE by $51\%$ on long TUM-RGBD pose sequences, reduces AbsRel by $13.0\%$ on Bonn video depth, and on KITTI long-sequence pose estimation surpasses both LongStream and Keyframe-VO in average ATE, while retaining strictly constant memory at zero training cost.

We study event-graph substrates: a class of world models that represent agent state as an append-only log of typed RDF triples and answer counterfactual queries by forking the log under a structured intervention vocabulary. Substrates are inspectable at the triple level, support exact counterfactuals, and transfer across domains without learned components. We formalize the class, prove a duality between explanatory and counterfactual queries that reduces both to the same causal-ancestor traversal, and evaluate a 1,400-line CLEVRER-DSL interpreter atop a domain-agnostic substrate runtime at full CLEVRER validation scale (n=75,618). The substrate exceeds the NS-DR symbolic oracle on all four per-question categories (by 9.89, 20.26, 17.65, and 0.80 percentage points), and exceeds the parametric ALOE baseline on descriptive and explanatory while lagging on predictive and counterfactual. We also introduce twin-EventLog, a 500-specification Park-canonical Smallville counterfactual benchmark on which the substrate exceeds Llama-3.1-8B with full context by 18.80 points joint accuracy.

Large language model (LLM) agents have increasingly advanced service applications, such as booking flight tickets. However, these service agents suffer from unreliability in long-horizon tasks, as they often produce policy violations, tool hallucinations, and misaligned actions, which greatly impedes their real-world deployment. To address these challenges, we propose NOD (Navigator-Operator-Director), a heterogeneous multi-agent architecture for service agents. Instead of maintaining task state implicitly in dialogue context as in prior work, we externalize a structured Global State to enable explicit task state tracking and consistent decision-making by the Navigator. Besides, we introduce selective external oversight before critical actions, allowing an independent Director agent to verify execution and intervene when necessary. As such, NOD effectively mitigates error propagation and unsafe behavior in long-horizon tasks. Experiments on $τ^2$-Bench demonstrate that NOD achieves higher task success rates and critical action precision over baselines. More importantly, NOD improves the reliability of service agents by reducing policy violations, tool hallucinations, and user-intent misalignment.

Commercial video generation systems such as Seedance2.0 and Veo3.1 have rapidly improved, strengthening the view that video generators may be evolving into "world simulators." Yet the community still lacks a benchmark that directly tests whether a model can reason about how an observed world should evolve over time. We introduce WorldReasonBench, which reframes video generation evaluation as world-state prediction: given an initial state and an action, can a model generate a future video whose state evolution remains physically, socially, logically, and informationally consistent? WorldReasonBench contains 436 curated test cases with structured ground-truth QA annotations spanning four reasoning dimensions and 22 subcategories. We evaluate generated videos with a human-aligned two-part methodology: Process-aware Reasoning Verification uses structured QA and reasoning-phase diagnostics to detect temporal and causal failures, while Multi-dimensional Quality Assessment scores reasoning quality, temporal consistency, and visual aesthetics for ranking and reward modeling. We further introduce WorldRewardBench, a preference benchmark with approximately 6K expert-annotated pairs over 1.4K videos, supporting pair-wise and point-wise reward-model evaluation. Across modern video generators, our results expose a persistent gap between visual plausibility and world reasoning: videos can look convincing while failing dynamics, causality, or information preservation. We will release our benchmarks and evaluation toolkit to support community research on genuinely world-aware video generation at https://github.com/UniX-AI-Lab/WorldReasonBench/.

The theory of state tracking in recurrent architectures has predominantly focused on expressive capacity: whether a fixed architecture can theoretically realize a set of symbolic transition rules. We argue that equally important is error control, the dynamics governing hidden-state drift along the directions that distinguish symbolic states. We prove that affine recurrent networks, a class of models encompassing State-Space Models and Linear Attention, cannot correct errors along state-separating subspaces once they preserve state representations. Consequently, practical affine trackers do not learn robust state tracking; rather, they learn finite horizon solutions governed by accumulated state-relevant error. We characterize the mechanics of this failure, showing that tracking remains readable only while the accumulating within-class spread remains small relative to the initial between-class separation. We demonstrate empirically on group state-tracking tasks that this breakdown is predictable: tracking collapses when the distinguishability ratio crosses the readability threshold of the trained decoder. Across trained models, the point of this crossing predicts the horizon at which downstream accuracy fails. These results establish that robust state tracking is determined not only by an architecture's theoretical expressivity but crucially by its error control.

Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations. Gradient-based parameter learning for such systems is challenging because algebraic variables are implicitly defined, event times depend on the parameters, and reset maps introduce discontinuities. This paper studies differentiable parameter optimization for semi-explicit DAEs with events. We formulate the learning problem as a constrained least-squares problem with DAE dynamics, algebraic constraints, guard equations, and reset maps. We then develop two complementary gradient-computation strategies. The first is an automatic-differentiation-through-simulation method that solves algebraic variables inside the vector field, differentiates the algebraic solve using the implicit function theorem, and handles events through segmented differentiable integration. The second is an explicit discrete-adjoint method that represents the forward simulation as an event-split residual system and computes gradients by solving for the Lagrange multipliers of smooth-segment and event residuals. The formulation clarifies that residual terms in the adjoint method are equality constraints, not heuristic penalties. We compare the two approaches in terms of gradient interpretation, event-time handling, implementation complexity, and local validity. Both methods provide gradients for the event path selected by the forward simulation and are valid under fixed event ordering and transversal guard crossings.

Building and maintaining state to learn policies and value functions is critical for deploying reinforcement learning (RL) agents in the real world. Recurrent neural networks (RNNs) have become a key point of interest for the state-building problem, and several large-scale reinforcement learning agents incorporate recurrent networks. While RNNs have become a mainstay in many RL applications, many key design choices and implementation details responsible for performance improvements are often not reported. In this work, we discuss one axis on which RNN architectures can be (and have been) modified for use in RL. Specifically, we look at how action information can be incorporated into the state update function of a recurrent cell. We discuss several choices in using action information and empirically evaluate the resulting architectures on a set of illustrative domains. Finally, we discuss future work in developing recurrent cells and discuss challenges specific to the RL setting.

Humans typically use natural language to update teammates on task states. Since not all updates are communicated, discrepancies arise between the team members' mental models that negatively affect overall team performance. How can we categorize such discrepancies? Do misalignments detected in team dialogue predict future mental model misalignments? Traditional shared mental model (SMM) assessment methods rely on retrospective expert coding that cannot capture real-time coordination dynamics. We propose a framework to identify and categorize four types of mental model discrepancies: unsupported beliefs, false beliefs, belief contradictions, and omissions, all of which can naturally emerge in team dialogues. Using dialogues from twenty dyad teams performing collaborative object identification tasks across four sequential levels, we demonstrate that these discrepancy patterns contain predictive signals. Averaging historical discrepancy counts achieves meaningful prediction accuracy using uniform weighting as an exploratory baseline, with differential predictability across discrepancy types.

Barrier certificates are scalar functions over the state space of dynamical systems that separate all unsafe states from all reachable states. The existence of a barrier certificate formally verifies the safety of the dynamical system. Recent approaches synthesize barrier certificates by iteratively training a neural network. In each iteration, the candidate is formally verified - if successful, the barrier certificate is found. Instead, we propose a set-based training approach that tightly integrates verification into training via a set-based loss function that soundly encodes all barrier certificate properties. A loss of zero formally proves the validity of the barrier certificate, collapsing the iterative training and verification into a single training procedure. Our experiments demonstrate that our set-based training approach scales well with the system dimension and naturally handles complex nonlinear dynamics.

Physics-informed neural networks (PINNs) have recently emerged as a promising framework for integrating data-driven learning with physical knowledge. In this work, we propose a coupled PINN approach for the joint reconstruction of indoor temperature and humidity dynamics in greenhouse environments, together with simultaneous identification of key model parameters. The method incorporates a reduced-order physically motivated model into the learning process, enabling consistent estimation under sparse and noisy observations. The artificial intelligence contribution lies in the development of a coupled physics-informed neural learning framework that integrates governing dynamical constraints into neural network training, while the engineering application focuses on greenhouse climate state reconstruction and parameter identification. The proposed framework is evaluated on a controlled synthetic benchmark that mimics diurnal forcing conditions. Compared with a purely data-driven neural network baseline, the coupled PINN achieves improved reconstruction accuracy, reducing temperature and humidity errors while maintaining high coefficients of determination. The improvement is particularly pronounced in the humidity channel, where latent moisture dynamics are more difficult to infer from limited measurements. In addition to accurate state reconstruction, the method successfully recovers the dominant physical parameters governing the system dynamics, demonstrating its ability to learn interpretable representations beyond data interpolation. These results highlight the potential of physics-informed learning for greenhouse climate modeling and, more broadly, for data-scarce environmental systems.

The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem. Although Bayesian methods are well-suited to tackle such problems, computing the posterior probability density function (PDF) presents challenges. The likelihood function cannot be analytically formulated due to the unclear relationship between discrete states and structural responses, and the high-dimensional state parameters resulting from numerous components severely complicates the computation of the marginal likelihood function. To address these challenges, this study proposes a novel Bayesian inversion paradigm for discrete variables based on Probabilistic Graphical Models (PGMs). The Markov networks are employed as modeling tools, with model parameters learned from data and structural topology prior. It has been proved that inferring this PGM produces the same probabilistic estimation as the posterior PDF derived from Bayesian inference, which effectively solves the above challenges. The inference is accomplished by Graph Neural Networks (GNNs), and a graph property-based GNN training strategy is developed to enable accurate inference across varying graph scales, thereby significantly reducing the computational overhead in high-dimensional problems. Both synthetic and experimental data are used to validate the proposed framework

Reasoning in large language models is often discussed as a single capability, but some of its gains may stem from simpler underlying operations. We examine two such primitives, recall and state-tracking, through five controlled task families centered on state-based recall, and compare matched transformer and hybrid architectures with and without reasoning augmentation. Across the suite, reasoning-augmented variants substantially outperform instruction-only variants, often by large margins. This pattern is consistent with the State over Tokens view: externalized reasoning traces help because they carry the intermediate state forward in token space. By contrast, hybrid inductive bias does not yield a uniform advantage in accuracy once reasoning tokens are available. When architectural differences do appear, they follow task structure: the hybrid Think model is more robust on strictly sequential chained updates, whereas the transformer Think model is more robust on flat multi-hop retrieval. We therefore cast the main contribution of this study as a descriptive account of what drives performance on state-based recall tasks: reasoning-token augmentation appears to be the dominant factor, while hybrid advantages are narrower, task-dependent, and potentially more about inference efficiency than overall capability. We also release the codebase and data required to reproduce these results.

Prompt-based interventions can change model behavior, but trained success alone does not identify where the behaviorally relevant state is represented. We study this question in controlled routing tasks using interfaces chosen on support data, held-out query evaluation, and matched necessity, sufficiency, and wrong-interface controls. On GPT-2 triop, an early interface supports exact transfer under these tests. On GPT-2 add/sub, zero-retrain compiled transfer at the fixed interface recovers most of donor routing accuracy, while trainable prompt slots can relearn the same behavior at several other positions only after additional support examples and optimization. These results distinguish fixed-interface reuse from prompt relocation in a setting where the two can be tested directly. Qwen routing provides a cross-architecture consistency check for the same matched-interface pattern at the operator token, although donor-specific identity on the local V-path remains unresolved. Generation and reasoning branches are used to map scope: they show broader transport or weaker controller identifiability once control depends on longer trajectories or harder selection. In controlled routing, fixed-interface transfer is therefore stronger evidence of reuse than trained prompt success alone.

Understanding physical transformation processes is crucial for both human cognition and artificial intelligence systems, particularly from an egocentric perspective, which serves as a key bridge between humans and machines in action modeling. We define this modeling process as Egocentric Instructed Visual State Transition (EIVST), which involves generating intermediate frames that depict object transformations between initial and target states under a brief action instruction. EIVST poses two challenges for current generative models: (1) understanding the visual scenes of the initial and target states and reasoning about transformation steps from an egocentric view, and (2) generating a consistent intermediate transition that follows the given instruction while preserving object appearance across the two visual states. To address these challenges, we propose the EgoIn framework. It first infers the multi-step transition process between two given states using TransitionVLM, fine-tuned on our curated dataset to better adapt to this task and reduce hallucinated information. It then generates a sequence of frames based on transition conditions produced by the proposed Transition Conditioning module. Additionally, we introduce Object-aware Auxiliary Supervision to preserve consistent object appearance throughout the transition. Extensive experiments on human-object and robot-object interaction datasets demonstrate EgoIn's superior performance in generating semantically meaningful and visually coherent transformation sequences.

Autonomous systems increasingly execute actions that directly modify shared state, creating an urgent need for precise control over which transitions are permitted to occur. Existing governance mechanisms evaluate policies prior to execution or reconstruct behavior post hoc, but do not enforce admissibility at the exact moment a state transition is committed. We introduce the atomic decision boundary, a structural property of admission control systems in which the decision and the resulting state transition are jointly determined as a single indivisible step in the labeled transition system (LTS) model of execution. We distinguish two classes: atomic systems, where evaluation and transition are coupled within a single LTS step, and split evaluation systems, where they are separate transitions interleaved by environmental actions. The separation introduces an architectural gap -- the decision is evaluated in one system state; the transition fires in a potentially different one -- that no policy, regardless of sophistication, can close from within a split architecture. Under realistic concurrent environments, we prove via a constructive counterexample trace that no construction can make a split system equivalent to an atomic system with respect to admissibility. Three corollaries follow: impossibility of execution-time guarantees in split systems, insufficiency of external state enrichment, and admissibility as an execution-time rather than evaluation-time property. We further formalize the Escalate outcome -- absent from classical TOCTOU analyses -- proving that it transfers rather than eliminates the atomicity requirement: resolution is safe if and only if it is itself atomic. We classify RBAC, ABAC, OPA, Cedar, and AWS IAM as split systems and ACP as atomic, providing a structural taxonomy of existing governance mechanisms. Admissibility is a property of execution, not evaluation.

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the Phasor Transformer block, a phase-native alternative representing sequence states on the unit-circle manifold $S^1$. Each block combines lightweight trainable phase-shifts with parameter-free Discrete Fourier Transform (DFT) token coupling, achieving global $\mathcal{O}(N\log N)$ mixing without explicit attention maps. Stacking these blocks defines the Large Phasor Model (LPM). We validate LPM on autoregressive time-series prediction over synthetic multi-frequency benchmarks against honest baselines: it beats a zero-parameter persistence baseline and, with the corrected gradient path, improves monotonically with depth before saturating, while remaining competitive-but-not-superior to self-attention at a fraction of the parameter count. Our results establish an explicit efficiency--accuracy frontier, showing that scalable temporal modeling in oscillatory domains can emerge from geometry-constrained phase computation with deterministic global coupling.

Over the last years, state-tracking tasks, particularly permutation composition, have become a testbed to understand the limits of sequence models architectures like Transformers and RNNs (linear and non-linear). However, these are often sequence-to-sequence tasks: learning to map actions (permutations) to states, which is incompatible with the next-token prediction setting commonly used to train language models. We address this gap by converting permutation composition into code via REPL traces that interleave state-reveals through prints and variable transformations. We show that linear RNNs capable of state-tracking excel also in this setting, while Transformers still fail. Motivated by this representation, we investigate why tracking states in code is generally difficult: actions are not always fully observable. We frame this as tracking the state of a probabilistic finite-state automaton with deterministic state reveals and show that linear RNNs can be worse than non-linear RNNs at tracking states in this setup.

Ambiguity-bearing inputs reach downstream systems through interfaces that favor a single resolved response before later context arrives. Even when alternatives are externalized, their representation and relative activation depend on the update rule. We address this state-maintenance problem within Non-Resolution Reasoning (NRR) by specifying a typed external text-to-state interface and explicit state-update contract. A mapping (phi: T -> S) constructs typed (v,c,w,m) records; declared operators make record carry-forward inspectable, while a record-weight entropy criterion separately tests normalized-weight concentration. The contract covers dampening, calibration, deferred resolution, contradiction-preserving integration, and temporal persistence. Across 580 constructed states/pairs, an executable suite performs 2,740 operator-state measurements. Tested non-violating transitions and calibration/identity checks show 0% record-weight entropy violations; a uniform-subtraction comparison violates the criterion at 1.7%, 6.1%, and 17.8% as subtraction increases. A separate 68-input construction audit finds multiple positive-weight typed records (mean record-weight entropy H = 1.087 bits) under the reported rule-based and archived LLM-assisted procedures, including a Japanese marker-set instantiation. The entropy criterion does not by itself certify record identity or cardinality, semantic adequacy, or end-to-end behavioral improvement. The repository provides deterministic reruns, archived prompt/output artifacts, transcript audit, and a fixed 18-set LLM-case sanity rerun. Phi therefore turns retained-state maintenance into a typed, executable, and falsifiable interface: record carry-forward is inspectable in declared operators, and normalized-weight concentration is separately testable before downstream commitment.

Despite rapid advances in large language models (LLMs), statistical reasoning remains underrepresented in existing LLM benchmarks, which often do not reflect the layered, proof-driven nature of real statistical practice. To address this gap, we introduce \textbf{StatEval}, the first large-scale benchmark for statistical reasoning across curricular and research-level settings. StatEval includes over 100,000 curated problems, with 20,000+ foundational questions spanning undergraduate and graduate curricula and 80,000+ research-level proof tasks extracted from leading statistical journals. To construct StatEval, we develop \textbf{TRACE} (Topology and Reasoning-Aware Context Extractor), a multi-agent pipeline with human-in-the-loop validation that converts unstructured academic texts into self-contained theorem-level reasoning tasks. We also propose an Adaptive Process-Based Scoring Pipeline for complex statistical proofs, enabling fine-grained evaluation beyond final-answer matching. Experiments show that while LLMs perform reasonably on foundational tasks, they struggle with rigorous research-level reasoning. Beyond evaluation, StatEval serves as a resource for improving reasoning, as retrieval-augmented generation and domain-specific alignment consistently enhance performance. Together, these results establish StatEval as both a benchmark and an infrastructure for advancing statistical reasoning in LLMs.

Fundamental tasks in computational chemistry, from transition state search to vibrational analysis, rely on molecular Hessians, which are the second derivatives of the potential energy. Yet, Hessians are computationally expensive to calculate and scale poorly with system size, with both quantum mechanical methods and neural networks. In this work, we demonstrate that Hessians can be predicted directly from a deep learning model, without relying on automatic differentiation or finite differences. We observe that one can construct SE(3)-equivariant, symmetric Hessians from irreducible representations (irrep) features up to degree $l$=2 computed during message passing in graph neural networks. This makes HIP Hessians one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and enables more favorable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance for transition state search, accelerated geometry optimization, zero-point energy corrections, and vibrational analysis benchmarks. We open-source the HIP codebase and model weights to enable further development of the direct prediction of Hessians at https://github.com/BurgerAndreas/hip