State Representation Learning

A fundamental challenge in embodied AI is verifying if agents build internal models of spatial structure or merely learn to mimic task-specific expert trajectories. This is critical as foundational approaches rooted in action-centric tasks (e.g., VLN) and reasoning-centric tasks (e.g., EQA) often share a common limitation: they lack a learning signal that forces them to encode fine-grained spatial relationships (like topology or distance) over long-range, fragmented experiences. To address this, we first propose LASAR, an architecture featuring a dual-memory system designed to maintain both episodic experiences and a semantic cognitive map. We then introduce Spatio-temporal Contextual Representation Learning (ST-CRL), a contrastive objective designed to train this architecture. ST-CRL leverages spatio-temporal cues from cognitive queries generated through annotated spatio-temporal context in simulation to build sample pairs, thereby forming the internal cognitive map from the agent's experiences. Experiments demonstrate that our method achieves 2%-3.5% gains in both zero-shot generalization on standard VLN-CE and VSI-Bench benchmarks. We also demonstrate that our proposed cognitive map has high self-consistency.

Identifying latent state representations and dynamics is essential when direct modeling in observation space is infeasible, particularly under partial and high-dimensional observations. In such settings, representation learning and physics-aware modeling are inherently coupled. We study this problem for latent port-Hamiltonian systems, a structured class encompassing both conservative and dissipative dynamics. We propose a two-stage identify-then-project framework. First, a contrastive teacher learns continuous-time latent dynamics from partial observations. Then, a student projects the identified teacher representation and dynamics onto a port-Hamiltonian submanifold via a learned affine chart, yielding a physically consistent realization. As a conceptual counterfactual, we also consider a single-stage variant that jointly learns latent identification and port-Hamiltonian structure, but find it to be less reliable, motivating the proposed two-stage teacher-student framework. We show theoretically that affine projection is the natural bridge between the affine gauge of contrastive latent identification and the port-Hamiltonian systems. Empirically, we demonstrate that the proposed two-stage approach preserves the teacher's dynamics while enforcing physical structure, and performs more reliably than the single-stage alternative, particularly in dissipative regimes and high-dimensional visual settings.

Learning latent representations from temporal, multimodal, and partially observed data requires specifying what information a latent state should retain, discard, and organize. Existing approaches encode these requirements through heterogeneous objectives, making methods difficult to compare and learned representations difficult to interpret. We propose Constrained Latent State Modeling (CLSM), a conceptual framework that characterizes latent states through six complementary properties: predictive sufficiency, minimality, temporal coherence, observation compatibility, invariance to nuisance factors, and structural constraints. CLSM separates these properties from the surrogate objectives used to induce them and from the diagnostics used to evaluate them, and clarifies how combinations of constraints can improve identifiability by restricting the space of admissible representations. We reinterpret major representation-learning families through this common design space and illustrate the framework with a controlled synthetic benchmark. The experiments show how objectives produce distinct latent organizations and empirical trade-offs depending on the prediction target, surrogate formulation, parameterization, and optimization. Companion repository containing the reference implementation, reproducible experiments, documentation, and model cards: https://github.com/gwenole-quellec/clsm

Latent action models (LAMs) aim to learn action-like representations from unlabeled videos by compressing frame-to-frame changes. The frames of in-the-wild videos, however, contain not only the agent's own state but exogenous state such as background clutter. Since the exogenous state introduces changes unrelated to actions, it hinders reliable latent action learning. This paper investigates this problem analytically by extending a linear LAM framework to explicitly model exogenous state. Our analysis reveals two insights: (1) minimizing the standard reconstruction objective produces latent actions that encode exogenous information from future observation; and (2) learning in a representation space that focuses on endogenous components is a key to mitigating the interference of noise. We further show that previously proposed auxiliary objectives, such as action-supervision, provably encourage latent actions to be consistent across exogenous states. These findings are validated through experiments on both linear and nonlinear LAMs, providing a unified theoretical analysis of how exogenous state hinders latent action learning and why common remedies work.

As end-to-end robotic policies are progressively deployed in the real world to solve real tasks, they face a gap between the training and inference conditions. Scaling the amount and diversity of the training data has shown some success in improving zero-shot generalization, yet robots still fail when faced with new, unseen test conditions. For instance, while robots with fixed frames of reference are common, those with moving frames pose a greater challenge for deployment. To address this specific instance of the issue, we present a study of strategies for encoding the robot's proprioceptive state to improve both in- and out-of-distribution performance at test time. Through a systematic study of joint representations, we find that a simple episode-wise relative frame provides the best trade-off between task performance and robustness, outperforming the baselines in extensive real-robot experiments conducted in a realistic test environment. The results suggest a practical path to leveraging data collected by robots with varying frames of reference and deployment to unseen test configurations.

We introduce WriteSAE, a sparse autoencoder for the matrix updates written into recurrent language-model state. In Gated DeltaNet, Mamba-2, and RWKV-7, each token writes a matrix-shaped update to a recurrent cache; a residual-stream SAE has vector-shaped atoms and cannot replace that update directly. WriteSAE learns rank-1 matrix atoms with the same shape as the model's own write. This lets us test a direct replacement: at positions where the SAE activates an atom, we remove the model's write, insert the atom scaled by its SAE activation, and continue the forward pass. The atom gives a closer final token distribution than deleting the write on 92.4% of evaluated positions; averaged per atom, the rate is 89.8%. For Gated DeltaNet, a formula using the forget gate, read query, and output embedding predicts the resulting logit change with $R^2 = 0.98$. The same replacement test transfers to Mamba-2-370M at 88.1%. In generation, the formula chooses a write direction; writing it into three consecutive cache positions at $3\times$ the norm of the model's write makes tokens initially ranked 100--1000 by the unmodified model appear in 100% of continuations, up from 33.3%. To our knowledge this is the first cache-level steering intervention reported in a state-space or hybrid recurrent layer.

We study policy gradient methods for reinforcement learning in non-Markovian decision processes (NMDPs), where observations and rewards depend on the entire interaction history. To handle this dependence, the agent maintains an internal state that is recursively updated to provide a compact summary of past observations and actions. In contrast to approaches that treat the agent state dynamics as fixed or learn it via predictive objectives, we propose a reward-centric formulation that jointly optimizes the agent state dynamics and the control policy to maximize the expected cumulative reward. To this end, we consider a class of Agent State-Markov (ASM) policies, comprising an agent state dynamics and a control policy that maps the agent state to actions. We establish a novel policy gradient theorem for ASM policies, extending the classical policy gradient results from the Markovian setting to episodic and infinite-horizon discounted NMDPs. Building on this gradient expression, we propose the Agent State-Markov Policy Gradient (ASMPG) algorithm, which leverages the recursive structure of the agent state dynamics for efficient optimization. We establish finite-time and almost sure convergence guarantees, and empirically demonstrate that, on a range of non-Markovian tasks, ASMPG outperforms baselines that learn state representations via predictive objectives.

This paper investigates robust representation learning in offline goal-conditioned reinforcement learning (GCRL). Particularly in sparse reward scenarios, learning representations that align state and goal latents is a challenge, as the encoder can learn goal-agnostic features that destabilize policy learning. We address this issue by learning the encoder's representation with alignment objectives that capture the environment across multiple scales, from local physical dynamics to long-horizon goal-directed structure. Concretely, we propose MSPR, a framework that leverages multi-scale predictive supervision to enforce goal-directed alignment within the latent space. We demonstrate that MSPR leads to strong performance on both vision and state-based tasks. Furthermore, we show that our approach is resilient under realistic, challenging data regimes, maintaining state-of-the-art performance across a wide variety of tasks.

Online reinforcement learning (RL) relies on the Markov property for guaranteed performance, but real-world applications often lack well-defined states given raw observed variables. While causal RL has attracted growing interest, existing work typically assumes Markovian states are provided and focuses on using causality to accelerate learning, leaving a fundamental gap: \emph{given a longitudinal causal graph over observed variables, how does one construct MDP states that provably satisfy the Markov property?} We address this by providing a procedure that constructs a provably minimal state representation. In deep RL, we observe that the minimal representation alone empirically fails to improve performance, indicating that neural networks cannot directly exploit Markovian minimality. To address this, we propose \textbf{MOSE} (Multi-Order State Exposure), which feeds multi-order historical state constructions into the same $Q$-function. MOSE consistently outperforms both the minimal state construction and single-window policies on common benchmarks and synthetic datasets. Including the minimal representation alongside MOSE can further improve performance. Our results establish a core principle for causal deep RL: minimal sufficiency is not enough, and \emph{controlled redundancy} is necessary to unlock the benefit of causal state information.

We present a new operator-theoretic representation learning framework for offline reinforcement learning that recovers the directed temporal geometry of a controlled Markov process from hitting time observations. While prior art often produces symmetric distances or fails to satisfy the triangle inequality, our framework learns a Hilbert-space displacement geometry where expected hitting times are realized as linear functionals of latent displacements. We prove that this representation exists under latent linear closure and is uniquely identifiable up to a bounded linear isomorphism. For finite-dimensional implementations, we show that global hitting-time error is bounded by one-step transition error amplified by the environment's transient spectral radius. Furthermore, we provide finite-sample guarantees accounting for approximation, statistical complexity, and trajectory-label mismatch. Derived from this theory, we curate Isomorphic Embedding Learning (IEL) as a new goal-agnostic foundation policy learning algorithm that anchors a HILP-style consistency objective with explicit hitting-time regression to ensure that the learned geometry reflects actual decision-time progress. This asymmetric and compositional structure enables robust graph-based multi-stage planning for long-horizon navigation. Our experiments demonstrate that IEL improves the state of the art of learning foundation policy policies from offline maze locomotion data. Our code can be found on https://github.com/MagnusBoock/IEL

We introduce Semantic State Abstraction Interfaces (SSAI): a methodological template for mapping sparse unstructured text into $K$ auditable, named coordinates with neutral defaults on no-news days, designed to separate representation hypotheses from optimisation variance in sequential decision systems. Our contribution is the framework and its evaluation protocol, not a claim that SSAI outperforms denser alternatives. We instantiate SSAI with $K=4$ axes (sentiment, risk, confidence, volatility forecast) on a US-equity panel (30 NASDAQ-100 names, FNSPID news, 2019--2023 test), and evaluate it across direct factor portfolios, supervised ridge forecasters, and RL agents (DP-PPO, SAC) that share the same fixed $φ$. The four-factor factor portfolio reaches 307.2% cumulative return and Sharpe 1.067, but apparent gains versus buy-and-hold (243.6%) fail coverage-stratified controls, reverse at $\geq 0.2$% costs, and are statistically fragile versus a sentiment-only baseline; a PC1 composite and a FinBERT portfolio baseline are stronger ranking signals in this setting. Ridge and RL blocks diagnose representation versus optimiser effects. We position SSAI as an interpretability-performance diagnostic and reusable protocol for sparse-text decision systems.

A cooperative robot swarm is a collective of computationally-limited robots that share a common goal. Each robot can only interact with a small subset of its peers, without knowing how this affects the collective utility. Recent advances in distributed multi-agent reinforcement learning have demonstrated that it is possible for robots to learn how to interact effectively with others, in a manner that is aligned with the common goal, despite each robot learning independently of others. However, this requires each robot to represent a potentially combinatorial number of interaction states, challenging the memory capabilities of the robots. This paper proposes an alternative approach for representing spatial interaction states for multi-robot reinforcement learning in swarms. A modular (decomposed) representation is used, where each feature of the state is handled by a separate learning procedure, and the results aggregated. We demonstrate the efficacy of the approach in numerous experiments with simulated robot swarms carrying out foraging.

A world model matters to an agent only through the state it constructs. That state must preserve some information, discard other information, and support some future function: prediction, control, planning, memory, grounding, or counterfactual reasoning. This paper treats world-model research as latent state design under sufficiency constraints. We propose a functional taxonomy that groups methods by what their latent state is for, rather than by architecture or application domain: predictive embedding, recurrent belief state, object/causal structure, latent action interface, grounded planning interface, and memory substrate. These roles expose distinctions that architecture-based groupings hide, including the gap between predictive sufficiency and control sufficiency, and the gap between passive video prediction and counterfactual action modeling. The taxonomy supports an evaluation framework that judges a model by the sufficiency constraint its latent state was built to satisfy. We compare methods along seven axes: representation, prediction, planning, controllability, causal/counterfactual support, memory, and uncertainty. We use the resulting matrix as a diagnostic for what a latent state preserves, discards, and enables. The conclusion that follows is that an actionable world model is the one whose state construction matches the task, not the one that preserves the most information.

Mamba's recurrent state h_t is, by construction, a compressed summary of every token seen so far. This raises a tempting hypothesis: if we extract token-level outputs y_t at fixed patch boundaries, we obtain semantic sentence summaries for free, with no pooling head, no fine-tuning, and no [CLS] token. We test this hypothesis carefully. Across five benchmarks (SST-2, CoLA, MRPC, STS-B, IMDb), we compare four strategies for extracting frozen sentence representations from a pretrained Mamba-130M backbone under a strict frozen-feature probing protocol, using three random seeds where computationally feasible. The results do not support the hypothesis: patch boundary readouts do not consistently outperform simple mean pooling. We identify and quantify two structural pathologies: severe anisotropy (mean pairwise cosine similarity 0.9999, std 0.000044) and representational collapse in the raw final SSM state (MCC = 0.000 on CoLA across all three seeds, confirmed via confusion matrix). We further propose orthogonal injection, a modified recurrence that constrains new information per

With the increasing availability of online information, recommender systems have become an important tool for many web-based systems. Due to the continuous aspect of recommendation environments, these systems increasingly rely on contextual multi-armed bandits (CMAB) to deliver personalized and real-time suggestions. A critical yet underexplored component in these systems is the representation of user state, which typically encapsulates the user's interaction history and is deeply correlated with the model's decisions and learning. In this paper, we investigate the impact of different embedding-based state representations derived from matrix factorization models on the performance of traditional CMAB algorithms. Our large-scale experiments reveal that variations in state representation can lead to improvements greater than those achieved by changing the bandit algorithm itself. Furthermore, no single embedding or aggregation strategy consistently dominates across datasets, underscoring the need for domain-specific evaluation. These results expose a substantial gap in the literature and emphasize that advancing bandit-based recommender systems requires a holistic approach that prioritizes embedding quality and state construction alongside algorithmic innovation. The source code for our experiments is publicly available on https://github.com/UFSCar-LaSID/bandits_blind_spot.

Multimodal large language models (MLLMs) have achieved impressive progress on general multimodal tasks, yet they remain brittle on dial-based measurement reading. In this paper, we study this problem through controlled benchmarks and feature-space probing, and show that current MLLMs not only achieve unsatisfactory accuracy on dial-based readout, but also suffer sharp performance drops under viewpoint and illumination changes even when the underlying dial state remains fixed. Our probing analysis further reveals that same-state samples under appearance variation are not consistently clustered, while neighboring states fail to preserve the local structure implied by continuous dial values. These findings suggest that existing MLLMs largely ignore the intrinsic state geometry of dial measurement tasks and instead rely on superficial appearance cues. Motivated by this diagnosis, we propose TriSCA, a tri-level state-consistent alignment framework for dial-based measurement reading. Specifically, TriSCA consists of state-distance-aware representation alignment, metadata-grounded observation-to-state supervision, and state-aware objective alignment. Extensive ablation studies and evaluation experiments on controlled clock and gauge benchmarks, together with evaluation on an external real-world benchmark, demonstrate the effectiveness of our method.

Identifying the dynamical state variables of a system from high-dimensional observations is a central problem across physical sciences. The challenge is that the state variables are not directly observable and must be inferred from raw high-dimensional data without supervision. Here we introduce DySIB (Dynamical Symmetric Information Bottleneck) as a method to learn low-dimensional representations of time-series data by maximizing predictive mutual information between past and future observation windows while penalizing representation complexity. This objective operates entirely in latent space and avoids reconstruction of the observations. We apply DySIB to an experimental video dataset of a physical pendulum, where the underlying state space is known. The method, with hyperparameters of the learning architecture set self-consistently by the data, recovers a two-dimensional representation that matches the dimensionality, topology, and geometry of the pendulum phase space, with the learned coordinates aligning smoothly with the canonical angle and angular velocity. These results demonstrate, on a well-characterized experimental system, that predictive information in latent space can be used to recover interpretable dynamical coordinates directly from high-dimensional data.

Multimodal clinical records contain structured measurements and clinical notes recorded over time, offering rich temporal information about the evolution of patient health. Yet these observations are sparse, and whether they are recorded depends on the patient's latent condition. Observation patterns also differ across modalities, as structured measurements and clinical notes arise under distinct recording processes. While prior work has developed methods that accommodate missingness in clinical time series, how to extract and use the information carried by the observation process itself remains underexplored. We therefore propose a patient representation learning framework for multimodal clinical time series that explicitly leverages informative missingness. The framework combines (1) a multimodal encoder that captures signals from structured and textual data together with their observation patterns, (2) a Bayesian filtering module that updates a latent patient state over time from observed multimodal signals, and (3) downstream modules for offline treatment policy learning and patient outcome prediction based on the learned patient state. We evaluate the framework on ICU sepsis cohorts from MIMIC-III, MIMIC-IV, and eICU. It improves both offline treatment policy learning and adverse outcome prediction, achieving FQE 0.679 versus 0.528 for clinician behavior and AUROC 0.886 for post-72-hour mortality prediction on MIMIC-III.

Autonomous Unmanned Aerial Vehicles (UAVs) have revolutionized industries through their versatility with applications including aerial surveillance, search and rescue, agriculture, and delivery. Their autonomous capabilities offer unique advantages, such as operating in large open space environments. Reinforcement Learning (RL) empowers UAVs to learn intricate navigation policies, enabling them to optimize flight behavior autonomously. However, one of its main challenge is the inefficiency in using data sample to achieve a good policy. In object-goal navigation (OGN) settings, target recognition arises as an extra challenge. Most UAV-related approaches use relative or absolute coordinates to move from an initial position to a predefined location, rather than to find the target directly. This study addresses the data sample efficiency issue in solving a 3D OGN problem, in addition to, the formalization of the unknown target location setting as a Markov decision process. Experiments are conducted to analyze the interplay of different state representation learning (SRL) methods for perception with a model-free RL algorithm for planning in an autonomous navigation system. The main contribution of this study is the development of the perception module, featuring a novel self-predictive model named AmelPred. Empirical results demonstrate that its stochastic version, AmelPredSto, is the best-performing SRL model when combined with actor-critic RL algorithms. The obtained results show substantial improvement in RL algorithms' efficiency by using AmelPredSto in solving the OGN problem.

Active inference, a neurally-inspired model for inferring actions based on the free energy principle (FEP), has been proposed as a unifying framework for understanding perception, action, and learning in the brain. Active inference has previously been used to model ecologically important tasks such as navigation and planning, but scaling it to solve complex large-scale problems in real-world environments has remained a challenge. Inspired by the existence of multi-scale hierarchical representations in the brain, we propose a model for planning of actions based on hierarchical active inference. Our approach combines a hierarchical model of the environment with successor representations for efficient planning. We present results demonstrating (1) how lower-level successor representations can be used to learn higher-level abstract states, (2) how planning based on active inference at the lower-level can be used to bootstrap and learn higher-level abstract actions, and (3) how these learned higher-level abstract states and actions can facilitate efficient planning. We illustrate the performance of the approach on several planning and reinforcement learning (RL) problems including a variant of the well-known four rooms task, a key-based navigation task, a partially observable planning problem, the Mountain Car problem, and PointMaze, a family of navigation tasks with continuous state and action spaces. Our results represent, to our knowledge, the first application of learned hierarchical state and action abstractions to active inference in FEP-based theories of brain function.

World models learned from high-dimensional visual observations allow agents to make decisions and plan directly in latent space, avoiding pixel-level reconstruction. However, recent latent predictive architectures (JEPAs), including the DINO world model (DINO-WM), display a degradation in test time robustness due to their sensitivity to ``slow features". These include visual variations such as background changes and distractors that are irrelevant to the task being solved. We address this limitation by augmenting the predictive objective with a bisimulation encoder that enforces control-relevant state equivalence, mapping states with similar transition dynamics to nearby latent states while limiting contributions from slow features. We evaluate our model on a navigation task (PointMaze) and on a manipulation task (PushT) under different test-time background changes and visual distractors. Across all benchmarks, our model consistently improves robustness to slow features while operating in a reduced latent space, up to $10\times$ smaller than that of DINO-WM. Moreover, our model is agnostic to the choice of pre-trained visual encoder and maintains robustness when paired with DINOv2, SimDINOv2, and iBOT features.

Memory consolidation determines both what a learner can do now and which changes remain implementable later. We develop a finite-model synthesis of operational state abstraction and optimal control under the stability-evidence-revision (SER) framework. ``Poincaré meets Bellman'' names two complementary roles: qualitative dynamics identifies reusable action-response structure, and dynamic programming prices acquisition, retention, reuse, merging, and forgetting. Recurrence enters separately through the timing and value of future demands. We distinguish active quotient merging from historical information erasure, characterize exact repair by zero-error functional coding and causal migration, and derive a Bellman recursion over the joint law of hidden state and complete deployed memory. A first-return model yields an explicit retention rule. Conditional results show how factor sharing avoids enumerating combinations and how independent informative observations improve identification, while leaving some zero-error evidence budgets unchanged. Finite enumerations verify the coding and retention calculations. The synthesis gives an exact benchmark for specified finite models, without claiming universal recurrence, bounded-memory open-ended learning, or tractable global planning.

This paper presents a state representation framework for Markov decision processes (MDPs) that can be learned solely from state trajectories, requiring neither reward signals nor the actions executed by the agent. We propose learning the minimum action distance (MAD), defined as the minimum number of actions required to transition between states, as a fundamental metric that captures the underlying structure of an environment. MAD naturally enables critical downstream tasks such as goal-conditioned reinforcement learning and reward shaping by providing a dense, geometrically meaningful measure of progress. Our self-supervised learning approach constructs an embedding space where the distances between embedded state pairs correspond to their MAD, accommodating both symmetric and asymmetric approximations. We evaluate the framework on a comprehensive suite of environments with known MAD values, encompassing both deterministic and stochastic dynamics, as well as discrete and continuous state spaces, and environments with noisy observations. Empirical results demonstrate that the proposed approach not only efficiently learns accurate MAD representations across these diverse settings but also significantly outperforms existing state representation methods in terms of representation quality.

Offline reinforcement learning enables evaluation and optimization of sequential decisions from historical data, when it is not possible to deploy new policies online due to safety, cost, and other concerns. Big data advances enable rich state information, but may naively include reward- and action- irrelevant dynamics that are ultimately unnecessary for learning optimal actions. We introduce state abstractions that target preservation of the difference-of-Q functions, and we propose to learn these abstractions via causal machine learning of the difference-of-Q function and standard statistical sparse learning. Under a nonparametric additive-rewards model, we characterize when decision-centered abstractions are simpler than the full state space, motivating our estimation procedure. We develop a dynamic generalization of the R learner (Nie et al. 2021, Lewis and Syrgkanis 2021) for estimating difference of Q-functions, for discrete-valued actions a, a0. We leverage orthogonal estimation to improve convergence rates, even if the required estimates of Q and behavior policy converge at slower rates and prove consistency of policy optimization under a margin condition. The method can leverage black-box estimators of the Q-function and behavior policy to target estimation of a more structured Q-function contrast, and uses simple squared-loss minimization. We demonstrate variance improvements from our estimator and how our approach enables us to isolate the information needed for sequential decision-making, which can be less than that for state prediction, in simulated data and simulator-augmented real data.

Identifying the most suitable variables to represent the state is a fundamental challenge in Reinforcement Learning (RL). These variables must efficiently capture the information necessary for making optimal decisions. In order to address this problem, in this paper, we introduce the Transfer Entropy Redundancy Criterion (TERC), an information-theoretic criterion, which determines if there is entropy transferred from observable state variables to actions during training. We define an algorithm based on TERC that provably excludes variables from the observable state that do not affect the agent's policy during learning. This yields compact state representations that reduce inference time by up to 2.6 times. Our approach is policy-dependent, making it agnostic to the underlying learning algorithm. The efficiency gains we demonstrate arise at retraining and inference time on the reduced state. Our method improves both retraining and inference efficiency. We demonstrate its effectiveness across three distinct algorithm classes, namely tabular Q-learning, Actor-Critic, and Proximal Policy Optimization (PPO), evaluated in a range of environments. Furthermore, to highlight the differences between the proposed methodology and the current state-of-the-art feature selection approaches, we present a series of controlled experiments on synthetic data, before generalizing to real-world decision-making tasks. We also introduce a representation of the problem that compactly captures the transfer of information from observable state variables to actions as Bayesian networks.