Transition Learning

World models learn environment dynamics from interaction experience. These dynamics depend on the current state and actions, as well as on properties that persist across interactions. Yet standard predictive training can reduce error using local evidence alone, without organizing persistent information into reusable context. We introduce SPRII, a training principle that uses relations between interactions as weak supervision for persistent context while retaining the learner's native objective. For example, different trajectories of the same system share persistent properties even when their states and actions differ. SPRII uses such relations to guide context learning without numerical property labels. Two composable components encourage contexts from related interactions to agree (Align) and use one interaction's context to predict another's future (Cross). Our analysis distinguishes three linked questions: what persistent information is accessible in the learned context (Formation), how that context influences a fixed predictor (Use), and whether it reduces task error (Value). Success at one stage does not guarantee success at the next. Controlled experiments show that more reliable relations improve representation organization, but adding a shared-property constraint can reduce access to a property that remains shared. Context substitutions change predictions at fixed model weights, while the benefit from history depends on prediction horizon and readout. Evaluations span thirteen settings, including controlled physical systems, public dynamics tasks, robotic and tactile data, and partner interaction, across multiple learner families. Relative to the corresponding baselines, SPRII yields average gains of over 10% in downstream task performance and over 15% in persistent-property readout. The project page is available at https://persistent-learning-review.netlify.app/interactive.html.

Vibrational spectral prediction can become inaccurate when localized stereoelectronic environments perturb intermediate response states and high-risk response units dominate characteristic spectral fingerprints, making prediction across external chemical space difficult. SO(3) Equivariant Neural Kalman Networks (SENK) form a response-state cascade that combines an equivariant transformer backbone for Hessian, dipole-derivative and polarizability-derivative learning, an Equivariant Neural Kalman bridge for state-dependent refinement and reliability sensing, and an NBO-informed electronic-prior pathway coupling consistency regularization with bounded, branch-specific guided spectral calibration. SENK outperforms DetaNet on QM9S and QMe14S while preserving full-spectrum IR and Raman fidelity from small molecules to drug-like systems. SENK remains stable and selectively improves spectrally sensitive features in biomolecular systems with complex stereoelectronic effects. It therefore integrates tensor prediction, reliability diagnosis and physics-informed calibration, supporting transferable vibrational spectroscopy from molecular systems to functional molecular materials.

Simulated students generated by computational models provide a practical way to evaluate tutoring strategies and pedagogical approaches used by human and AI tutors. However, such simulations should account for disengaged behaviors, including gaming the system, wheel-spinning, and off-task behavior, because tutors may need different responses for different learner states. We present Disengagement-Aware Student Simulators (DAS2), a reproducible pre-deployment protocol that models five learner-engagement states: engaged, gaming, wheel-spinning, off-task, and mixed, and evaluates AI tutor performance across these states. Using ASSISTments09, two coders independently labeled 100 sampled tutoring sessions based on anonymized interaction-log summaries. They achieved 84% agreement (Cohen's kappa = 0.78), and among agreed cases, human consensus labels matched DAS2 rule-based labels in 81% of cases (kappa = 0.75). Conditioning simulations on intended learner states reduced the correctness-rate gap between simulated and authentic sessions from 0.54 to 0.20 for gaming and from 0.51 to 0.18 for wheel-spinning. Fine-tuned Qwen2.5-7B better matched authentic response-time distributions, while prompt-only GPT-4o generated more distinguishable learner states. Evaluation of five AI tutors from the Claude, Llama, Gemini, Qwen, and GPT families showed that relative rankings remained stable across learner states and interaction lengths, while absolute performance varied, revealing state-specific differences in tutor support. Human validation further showed that automated tutor evaluation does not fully align with human judgment. DAS2 provides a pre-deployment framework for evaluating how AI tutors respond to diverse learner-engagement states before deployment.

Machine learning emulators have become essential for accelerating expensive Earth-system simulations, but most existing approaches remain passive forecasters: they reproduce simulator trajectories under prescribed forcings without an explicit interaction mechanism for user-specified interventions. This limits their use in interactive scientific workflows and Earth-system digital twins, where users often need to explore how a system would respond if selected state components were changed. We propose an action-conditioned world-modeling framework for Earth-system emulation that reformulates simulator trajectories as supervision for controllable state-transition learning. The key idea is transition-action pretraining: naturally observed state changes are treated as label-free action supervision, allowing the model to learn both prescribed dynamics and action-conditioned responses without manually annotated interventions. We further introduce masked response learning to infer unobserved variables under partial state edits and learn coupled system dependencies. We test this framework on ecosystem dynamics across six global regions and multiple stand ages. Experiments show that the model preserves competitive long-horizon emulation accuracy while enabling controllable structural interventions and coherent responses in coupled ecosystem-cycle variables. These results suggest a practical route from passive Earth-system emulators toward interactive, intervention-aware scientific surrogates.

We study the control of Markov decision processes in which the quality of a policy is evaluated by a dynamic, time-consistent Markov risk measure rather than by an expected discounted cost. The main obstacle to combining such measures with reinforcement learning is that a transition risk mapping depends on the transition kernel in a nonlinear way, and therefore cannot be estimated from a single observed transition. We remove this obstacle by employing mini-batch transition risk mappings: the mapping is applied to the empirical measure of $N$ independent next-state samples, and the result is averaged. The resulting mapping is again coherent. However, as an expected value of a function of $N$ next-state values, it admits an unbiased one-sample estimator. We embed this mapping into a double deep Q-network, analyze the two sources of estimation bias that arise, and obtain a risk-averse Q-learning method applicable to state spaces far beyond the reach of tabular schemes. The method is applied to an underwater robot navigation problem, in which a vehicle must visit collection points, gather stochastic information payloads, and deliver them at transmission points, while exposed at each step to the risk of destruction. A hierarchical decomposition delegates path execution to an exact graph search and confines learning to the high-level ``collect or transmit'' decision. A low-dimensional feature map, invariant under the symmetries of the problem, replaces the raw state--configuration encoding. In experiments on $300$ held-out environments, the resulting policies transfer to instance sizes never seen in training, and already $N=2$ reduces the upper semideviation of the outcome distribution while simultaneously improving its mean whenever the simulator is misspecified---an empirical counterpart of the duality between coherent risk measures and distributional robustness.

We study what can be recovered about the transition probabilities of a Markov decision process from optimal actions alone. This is closely related to the inverse problem considered by Letcher et al., who ask when the dynamics can be recovered from numerical $Q$-values. Here the numerical values themselves are not observed; only the optimal actions are known, for every reward in a given class. For state-action rewards $r(s,a)$, knowing the optimal actions for every reward also tells us how much better one action is than another when each is followed by the same fixed policy. This is still not enough to determine the transition probabilities uniquely. We prove that two kernels give the same optimal actions for every reward exactly when $$Q_{s,a} = \Bigl(P_{s,a}+\tfrac1γe_s^{\mathsf T}(L-I)\Bigr)L^{-1}$$ for one invertible matrix $L$ satisfying $L\mathbf 1=\mathbf 1$. Near a kernel with strictly positive entries, there is an $n(n-1)$-dimensional family of different kernels with this property. The result is unchanged if we consider only rewards having a unique optimal action at every state. We then compare this with rewards of the forms $r(s)$ and $r(s,a,s')$. Rewards that depend on the next state can usually recover the transition kernel itself: every row at a state with at least two actions is determined, and we describe exactly when a row at a state with one action can remain hidden. State rewards reveal less: two kernels give the same optimal actions exactly when every deterministic policy is optimal for the same set of rewards. The results show how the form of the reward affects what can be learned about the dynamics from optimal actions alone.

We introduce the Unified Neural Variational Measurement of Proficiency (UNVaMP) architecture, a knowledge tracing method that integrates observed student-item interactions with internal memory to produce evolving latent representations of student knowledge. These representations support accurate predictions of future responses while enabling explicit control over the smoothness of estimated learning trajectories. UNVaMP can be configured as either a purely neural model or a hybrid model that predicts responses through an interpretable measurement function over the latent space. We show that a pure neural configuration (UNVaMP-MLP) achieves the strongest predictive performance among compared models on three out of four datasets. Meanwhile, a hybrid configuration (UNVaMP-MIRT, using a 1PL MIRT measurement function) lags only slightly behind UNVaMP-MLP, indicating that the predictive cost of interpretability is modest. Beyond predictive accuracy, UNVaMP provides the following: a principled mechanism for controlling volatility when estimating student latent variables, quantification of uncertainty over student knowledge state estimates, and flexible input specification that supports heterogeneous student-item interaction features. In addition, the hybrid UNVaMP-MIRT configuration generates interpretable moment-in-time student knowledge state estimates. Using an experimental dataset, we show that auxiliary inputs induce structured changes in the predictive behavior of UNVaMP-MIRT, consistent with sensitivity to underlying structure beyond response correctness. Furthermore, through a simulation study, we show that UNVaMP yields well-behaved knowledge state estimates under controlled measurement conditions. In total, these results indicate that UNVaMP is both useful for real-world education systems and capable of recovering underlying structure from student-item interactions.

We present a general neurosymbolic reasoning and learning methodology based on a modular integration of answer set programming with an energy based model substrate. Key contributions are: (1) supporting joint optimisation in the continuous latent space through explicit ASP-based declarative semantics fully incorporating background knowledge, constraints, non-monotonic inference; and (2) advancing recent works at the interface of answer sets, probabilistic logic, and answer set modulo theories by providing a generalised model and practical platform for ASP-centric robust, end-to-end training for applications in dynamic domains (e.g., involving perception and interaction). We provide a practical implementation, and demonstrate basic use and application (with MNIST), and evaluate with the visual question-answering benchmark Clevr and the multi-object tracking benchmark MOT.

We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model. The resulting Gibbs distribution describes a family of equilibrium learning states generated by the data. We formulate the consistency conditions of the associated finite-volume distributions and derive nonlinear integral fixed-point equations whose solutions characterize the admissible learning states. These equations provide a rigorous connection between empirical loss landscapes and probabilistic inference on trees. For translation-invariant solutions, the problem reduces to the analysis of positive compact operators induced by data-dependent kernels, allowing us to establish existence and uniqueness conditions in the one-dimensional setting. Furthermore, we show that hierarchical learning systems may exhibit phase-transition phenomena: for certain empirical kernels on Cayley trees, multiple Gibbs measures emerge beyond a critical inverse temperature, corresponding to distinct equilibrium prediction regimes. Numerical experiments with non-separable kernels illustrate the appearance of multiple solution branches and demonstrate the coexistence of several data-induced learning states. Our results provide a new perspective on energy-based learning, where data do not merely determine an optimal model through minimization but define an entire probabilistic landscape of possible inference states.

Many multivariate dynamical systems are observed only through trajectories, leaving the mechanisms governing their joint dynamics hidden. Existing approaches can impose interpretable dynamics or learn flexible state transitions, yet the resulting interaction structure is typically either specified in advance or left implicit within the learned dynamics. We introduce MF-Net, a recurrent dynamical model that represents all variables in a shared field state and updates this state through a learned relation law. Each variable carries a field component, and these components evolve jointly through a learnable mechanical transition. Here, mechanical refers to the relation-to-motion organization of the transition, where learned relations shape state-dependent flows, field responses, and motion tendencies that move the field state forward. The resulting structure is part of the rollout itself: learned relations influence how the field moves, and the same internal quantities support both forecasting and structural readout. Across known-law interaction systems, chaotic benchmarks, real neural recordings, and ecological time series, MF-Net achieves competitive short- and medium-horizon forecasting while retaining inspectable structural readout. On the 40-dimensional Lorenz--96 testbed, MF-Net achieves an eight-step $R^2$ of $0.798\pm0.018$; across five seeds, its learned relation matrix recovers the local coupling support with a local/nonlocal strength ratio of $19.80\pm1.00$ and Precision@$K$ of $1.000\pm0.000$. MF-Net provides a structure-readable dynamical modeling framework in which learned relations are trained through forward evolution and, on real data, interpreted as functional predictive couplings under appropriate observational limits.

Inference and control in engineered physical systems pay a heavy physics cost at deployment: state estimators, inverse-problem solvers, model-predictive controllers, schedulers, and observers are often not closed-form and must re-solve a numerical optimization per instance, with the operator re-supplied each time. Physics-informed learning moves this cost to training, but uses a single encoder pathway whose latent geometry de-learns under fine-tuning and admits no quantitative transfer guarantee. We propose an asymmetric two-pathway architecture that resolves both issues. A teacher encoder consumes privileged dense states from a high-fidelity simulator and represents the system through operator-polynomial features stable under spectral perturbation; a student encoder learns the same latent geometry from sparse field data and operator descriptors. At deployment the teacher is discarded, and the frozen student runs in a single forward pass with a transfer certificate. The design connects to privileged-information learning, knowledge distillation, and cross-modal distillation, but targets cross-instance transfer rather than fixed-instance prediction: topology and operator may change, while the latent task does not. We establish sufficient and near-necessary transfer conditions via Wasserstein proximity between latent laws, yielding a zero-shot error bound, and develop a finite-sample certification protocol with active expansion when coverage is incomplete. The framework applies wherever a system admits an operator with reportable spectrum. On power-system estimation, it achieves zero-shot transfer to 100 unseen topologies, a 95% certificate pass rate, accuracy competitive with topology-aware Newton--Raphson, and sub-millisecond inference. These results suggest asymmetric pathways plus operator-anchored latent geometry provide a foundation for certified zero-shot inference and control.

Mechanistic interpretability seeks to explain a model's behaviour by finding its circuit: the sparse subgraph of the model's computation that is causally responsible for it. Automated methods have made this search systematic, but each one starts afresh for every behaviour, and the effort spent finding one circuit does nothing for the next. Circuit discovery has thus been automated, but not amortised. We ask whether circuit discovery can itself be learned. We frame it as a sequential decision problem over the computation graph of GPT-2 small, in which a policy removes edges until it reaches a compact subgraph that preserves the behaviour, guided by a faithfulness reward defined through causal intervention. A single policy trained across twelve behaviours recovers a faithful circuit for each, and once frozen it transfers to behaviours it never saw during training, recovering their known circuits without further search. A short warm-start improves these transferred circuits, returning far smaller ones than training from scratch. While the learned policy does not match a per-behaviour search on circuit size or cost, it shows that circuit discovery is a learnable, transferable procedure rather than a search repeated for every behaviour.

Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.

Recent research in educational data mining, especially knowledge tracing, has focused on predicting learners' future knowledge states to support adaptive instruction. However, in many real-world educational settings, learning data are often available only as single-time-point assessments without temporal information, making existing time-series-based approaches difficult to apply. In this paper, we propose a novel framework for predicting future skill acquisition using only snapshot data. Specifically, we address the problem of predicting the next skill to be acquired from skill mastery patterns estimated by cognitive diagnostic models (CDMs). In the absence of temporal information, we exploit inclusion relations among learners' skill sets to induce a pseudo-temporal ordering, interpreting expanding skill sets as a proxy for learning progression. To efficiently approximate unobserved acquisition paths, we introduce a neural model that captures latent skill acquisition dynamics through expected skill increments. Experiments on both synthetic and real-world datasets demonstrate that the proposed method consistently outperforms baseline approaches, with particularly strong advantages as the skill space becomes larger. These results indicate that meaningful skill acquisition patterns can be inferred from snapshot data alone, providing a practical framework for adaptive learning support in data-constrained educational environments.

Model-based reinforcement learning improves sample efficiency by learning a world model. However, existing latent world models such as DreamerV3 do not explicitly enforce local smoothness in their learned transition dynamics, leaving a useful inductive bias for transition dynamics learning unexploited. We propose GPLD, a gradient-penalized latent dynamics regularizer for DreamerV3 that applies a row-wise Jacobian penalty to the posterior latent distribution to encourage locally smooth transition learning. We show that this penalty can be interpreted as the continuous-latent analog of finite-difference smoothing of transition laws in discrete embedded-state MDPs, and estimate it efficiently using Hutchinson-style stochastic probes. Empirically, across DeepMind Control proprioceptive tasks, GPLD improves aggregate sample efficiency, with particularly strong gains on higher-complexity locomotion environments. On more challenging quadruped tasks, GPLD reaches high-return behavior earlier and exhibits more consistent late-stage learning over longer horizons. Explicit local smoothness regularization is a simple and effective way to improve latent world models for smooth continuous control environments. Code for GPLD is available at github.com/romils9/gpld-mbrl .

Knowledge Tracing (KT) models students' knowledge states based on learning interactions to predict performance. While deep learning-based KT models have boosted predictive accuracy, most models rely on deterministic vector embeddings and opaque latent state transitions, limiting interpretability regarding how specific past behaviors influence predictions. To address this limitation, we propose Probabilistic Logical Knowledge Tracing (PLKT), an interpretable KT framework that formulates prediction as a goal-conditioned evidence reasoning process over historical learning behaviors. Instead of representing knowledge states as deterministic vector embeddings, PLKT employs robust Beta-distributed probabilistic embeddings to represent student knowledge states. This probabilistic foundation allows us to model the uncertainty of historical behaviors and perform explicit logical operations (e.g., conjunction), constructing transparent reasoning paths that reveal how specific past interactions contribute to the prediction. Extensive experiments show that PLKT outperforms state-of-the-art KT methods while achieving superior interpretability. Our code is available at https://anonymous.4open.science/r/PLKT-D3CE/.

Zero-shot composed image retrieval (ZS-CIR) retrieves a target image from a reference image and a text modification without human-annotated CIR triplets. Projection-based ZS-CIR methods are attractive because they do not rely on LLMs at inference and remain lightweight, but they often underperform LLM-based approaches on complex semantic modifications. This gap reflects a semantic transition bottleneck in projection-based ZS-CIR: endpoint-level matching can let the edit text act as a target-side attribute cue rather than grounding it as a source-conditioned semantic transition. We further show that adding semantic transition supervision to the same text adapter creates an endpoint--transition conflict between endpoint alignment and semantic transition alignment. To address this conflict, DeCIR decouples endpoint and transition learning. It constructs paired forward/reverse edit tuples from image-caption pairs, trains separate low-rank text adapter branches for endpoint alignment and semantic transition alignment, and merges them with Low-Rank Directional Merge (LRDM) into one deployable adapter. Extensive experiments on CIRR, CIRCO, FashionIQ, and GeneCIS demonstrate that DeCIR consistently improves projection-based ZS-CIR without increasing inference complexity.

Learning predictive world models from visual observations is a core problem in embodied AI, with applications to model-based reinforcement learning and robotic planning. Existing latent world models typically generate future states with unconstrained neural transition functions, while modern video generation systems often prioritize perceptual plausibility or introduce physical structure through auxiliary losses, external guidance, or separate dynamics modules. As a result, long-horizon rollouts can remain weakly grounded in the physical principles that govern real dynamics, leading to compounding error, energy drift, and physically inconsistent futures. We propose Least Action World Models (LaWM), a latent world-modeling framework that operationalizes the Principle of Least Action in learned visual latent space: future rollouts are governed by a learned Lagrangian action functional rather than produced only by an unconstrained transition predictor. Our main technical realization is a latent variational integrator: LaWM encodes observations into learned generalized coordinates, learns a latent discrete Lagrangian over consecutive latent states, constructs a discrete action functional, and advances prediction by solving the corresponding discrete integration condition. Thus, physical structure is not merely used to score, regularize, or constrain a completed trajectory; it defines the latent transition rule itself. Because the transition is induced by a discrete variational principle, LaWM provides a structure-preserving bias for long-horizon visual prediction. Across physics-clean synthetic dynamics and embodied robot interaction benchmarks, LaWM improves physical invariance, background consistency, motion smoothness, and appearance and geometric prediction metrics over video-generation and world-model baselines.

A new interpretable experiential learning model based on state history and global feedback is presented. It is capable of learning a behavioral model represented by a transition graph between sets of states, with transitions attributed with utility and evidence count. This model is expected to be suitable for solving reinforcement learning problem in resource-constrained environments. The model was thoroughly evaluated on the OpenAI Gym Atari Breakout benchmark, demonstrating performance comparable to some known neural network-based solutions.

Vision-and-Language Navigation (VLN) aims to enable an embodied agent to follow natural-language instructions and navigate to a target location in unseen 3D environments. We argue that adapting VLMs to VLN requires endowing them with two complementary capabilities for acquiring such awareness, namely backward action reasoning (why) and forward transition prediction~(how). Based on this insight, we propose SpaAct, a simple yet effective training framework that activates the dynamic spatial awareness in VLMs. Specifically, SpaAct introduces two spatial activation tasks: Action Retrospection, which asks the model to infer the executed action sequence from visual transitions, and Future Frame Selection, which forces the model to predict the visual transitions conditioned on history and action. These two objectives provide lightweight supervision on both backward action reasoning and forward transition prediction, encouraging the model to build dynamic spatial awareness in a VLM-friendly way. To further stabilize adaptation, we design TriPA, a Tri-factor Progressive Adaptive curriculum learning method that organizes training samples from easy to hard, allowing the model to gradually acquire navigation skills from basic locomotion to long-horizon reasoning. Experiments on standard VLN-CE benchmarks show that SpaAct consistently improves VLM-based navigation and achieves state-of-the-art performance. We will release the code and models to support future research.

Understanding learners' cognitive and affective states underpins adaptive educational systems and effective teaching. Although research links nonverbal cues to internal states, no framework calibrates them to evidence. We present the Nonverbal Syntax Framework, drawn from a systematic review of 908 studies and 17,043 cue-state mappings (Turaev et al., 2026). The framework addresses three challenges: terminological fragmentation (behaviors described inconsistently), evidence heterogeneity (single observations to replicated findings), and state ambiguity (similar patterns indicating multiple states). Normalization consolidated 5,537 state labels into 2,010 canonical states (63.7%) and 11,521 cues into 6,434 normalized cues (44.2%) across nine behavioral channels. Dual-evidence assessment separately evaluates Component Evidence (coverage of cues and states) and Relationship Evidence (independent studies per cue-state link). 52% of "Very High" relationships rest on one paper, so separation enables calibrated rather than overconfident inference from preliminary findings. The framework's four levels comprise a Cue Vocabulary of 6,434 indicators classified as observable/instrumental; State Clusters linking 2,010 states to indicative cues; State Profiles with multimodal behavioral signatures and actionable specifications; and Discriminative Analysis distinguishing 1,215 confusable state pairs. We identify 480 actionable R1-R4 relationships (three or more independent papers), the replicated core of six decades of research, covering 35.5% of mappings across 47 key learning states and 111 distinct indicators. The remaining 91.5% (9,653 single-paper findings) form exploratory hypotheses for replication. The framework gives researchers an empirical foundation for identifying gaps, practitioners evidence-based tools for state inference, and technologists validated features for multimodal detection.

Understanding and representing complex climate variability is essential for both scientific analysis and predictive modeling. However, identifying meaningful climate regimes from raw variables is challenging, as they exhibit high noise and nonlinear dependencies. In this work, we explore the use of Masked Siamese Networks to discretize climate time series into semantically rich clusters. Focusing on daily minimum and maximum temperature, we show that the resulting representations: (i) yield clusters that reflect meaningful climate states under our modeling assumptions, offering a simplified representation for downstream use; (ii) enable sampling and analysis of specific climate scenarios; and (iii) exhibit statistical associations with El Niño events, underscoring their scientific relevance. Our findings highlight the potential of self-supervised discretization as a tool for climate data analysis and open avenues for incorporating richer climate indicators in future work.

Local prediction-error-based curiosity rewards focus on the current transition without considering the world model's cumulative prediction error across all visited transitions. We introduce Curiosity-Critic, which grounds its intrinsic reward in the improvement of this cumulative objective, and show that it admits a tractable per-step surrogate: the difference between the current prediction error and the asymptotic error baseline of the current state transition. We estimate this error baseline online with a learned critic co-trained alongside the world model; since the critic only has to learn how hard a transition is to predict, its estimate of the irreducible noise floor converges well before the world model saturates, redirecting exploration toward learnable transitions. The reward is higher for learnable transitions and collapses toward zero for stochastic ones, thereby separating epistemic (reducible) from aleatoric (irreducible) prediction error online. Prior prediction-error curiosity formulations, from Schmidhuber (1991) to learned-feature-space variants, emerge as special cases corresponding to specific approximations of this error baseline. Experiments on a stochastic grid world show that Curiosity-Critic outperforms prediction-error, visitation-count, and Random Network Distillation methods in training speed and final world model accuracy.

Surgical future prediction, driven by real-time AI analysis of surgical video, is critical for operating room safety and efficiency. It provides actionable insights into upcoming events, their timing, and risks-enabling better resource allocation, timely instrument readiness, and early warnings for complications (e.g., bleeding, bile duct injury). Despite this need, current surgical AI research focuses on understanding what is happening rather than predicting future events. Existing methods target specific tasks in isolation, lacking unified approaches that span both short-term (action triplets, events) and long-term horizons (remaining surgery duration, phase transitions). These methods rely on coarse-grained supervision while fine-grained surgical action triplets and steps remain underexplored. Furthermore, methods based only on future feature prediction struggle to generalize across different surgical contexts and procedures. We address these limits by reframing surgical future prediction as state-change learning. Rather than forecasting raw observations, our approach classifies state transitions between current and future timesteps. We introduce SurgFUTR, implementing this through a teacher-student architecture. Video clips are compressed into state representations via Sinkhorn-Knopp clustering; the teacher network learns from both current and future clips, while the student network predicts future states from current videos alone, guided by our Action Dynamics (ActDyn) module. We establish SFPBench with five prediction tasks spanning short-term (triplets, events) and long-term (remaining surgery duration, phase and step transitions) horizons. Experiments across four datasets and three procedures show consistent improvements. Cross-procedure transfer validates generalizability.