Predictive State Representations

We encounter a system through its responses, yet its state concerns how the system is. Predicting further responses promises knowledge beyond what is immediately observed. What that knowledge tells us about the system's state depends on what we mean by a state in the first place. We give this notion a model-relative meaning: a state is the complete response profile over a specified query universe, and configurations agreeing on every query are regarded as the same state. From this perspective, a learned state is understood through the distinctions between these profiles that it retains. Prediction concerns selected observations; recovery concerns the profile as a whole. We examine their relationship through query ambiguity, state-space geometry, and the choice of prediction targets. Synthetic systems with known response laws and neural recordings provide complementary settings for this investigation. The aim is to clarify how prediction can become a way of knowing a system, and what it would mean for a learned state to preserve the state being studied.

We consider estimating the one-step-ahead conditional distribution of a multivariate stochastic process. Many existing approaches rely on assumptions such as finite-range memory, sparsity, or additivity, which can be poorly suited to processes with long-range nonlinear interactions. However, without such structural assumptions, nonparametric estimation is challenging due to the curse of dimensionality. To address this challenge, we introduce a new estimation approach based on the predictive states of a process, possibly with infinite-range memory. We show that our estimator achieves fast convergence rates when the past history can be compressed into a low-dimensional statistic that is sufficient for predicting the future. Specifically, we show that the statistical complexity of the estimation problem is determined by the intrinsic dimension of the predictive state space. We establish guarantees for an instantiation of our method based on deep neural network estimators, and we support these theoretical results with experiments.

GUI World Models (GUI-WMs) are increasingly used to predict future states for agent planning and simulation, yet most existing formulations condition only on the current GUI observation and action. We identify state aliasing, where the vis- ible interface omits transition-relevant environment state, so identical observable conditions can correspond to different valid futures. To diagnose this failure mode, we introduce StateAliasBench, a diagnostic benchmark that explicitly isolates such ambiguities via strict pairing. We further propose lightweight predictive- state recovery that infers structured state from history and augments otherwise frozen GUI-WMs through a deterministic state interface. Family-specific special- ists provide state recovery across heterogeneous state types, and multi-teacher dis- tillation consolidates them into a single unified estimator. Experiments show that existing GUI-WMs exhibit systematic failures under observation-only condition- ing, while predictive-state augmentation substantially restores state-sensitive pre- diction across evaluated WMs, preserves generative fidelity, and improves down- stream performance of GUI agents on AndroidWorld. These results suggest that reliable GUI world modeling should account not only for what is visible, but also for the hidden transition state that determines what happens next.

Humanoid locomotion requires control policies that remain stable under imperfect sensing while exploiting temporal context for consistent motion. We present RoboDreamer, a two-stage teacher--student framework that combines next-observation consistency with randomized continuous temporal masking. A teacher is first trained on clean observations, and a student is then distilled under masked recent observations, encouraging the policy to infer missing current information from history. At inference, the same masking interface is reused for implicit closed-loop action refinement and optional multi-step action chunking. Mamba is used as the temporal backbone, while matched ablations show that masking/distillation provides a substantial part of the gain and Mamba contributes additional tracking improvements with real-time latency. Experiments in IsaacLab, MuJoCo, and on a Unitree G1 demonstrate robust motion tracking under observation masking and successful real-world deployment.

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Training recurrent neural networks (RNNs) requires assigning credit across long sequences of computations. Standard backpropagation through time (BPTT) addresses this problem poorly: it is sequential in time, limiting parallelism, and suffers from vanishing or exploding gradients, making long-range associations difficult to learn. We propose Supervised Memory Training (SMT), a method for training nonlinear RNNs that sidesteps recurrent credit propagation entirely by reducing RNN training to supervised learning on one-step memory transition labels $(m_t, x_{t+1}) \rightarrow m_{t+1}$. SMT acquires these memory labels by training a Transformer-based encoder on a predictive state objective--retaining only information from the past necessary to predict the future. By decoupling what to remember from how to update memory, SMT enables time-parallel RNN training with a stable $O(1)$ length gradient path between any two tokens--without ever unrolling the RNN. We find that SMT outperforms BPTT when pretraining various RNN architectures on tasks like language modeling and pixel sequence modeling. SMT enables nonlinear RNNs to better capture long-range dependencies and train in parallel, potentially unlocking the scaling of models that build temporal abstractions of past experience.

A key challenge in scaling up Reinforcement Learning is generalizing learned behaviour. Without the ability to carry forward acquired knowledge an agent is doomed to learn each task from scratch. In this paper we develop a new formalism for transfer by virtue of state abstraction. Based on task-independent, compact observations (outcomes) of the environment, we introduce Outcome-Predictive State Representations (OPSRs), agent-centered and task-independent abstractions that are made up of predictions of outcomes. We show formally and empirically that they have the potential for optimal but limited transfer, then overcome this trade-off by introducing OPSR-based skills, i.e. abstract actions (based on options) that can be reused between tasks as a result of state abstraction. In a series of empirical studies, we learn OPSR-based skills from demonstrations and show how they speed up learning considerably in entirely new and unseen tasks without any pre-processing. We believe that the framework introduced in this work is a promising step towards transfer in RL in general, and towards transfer through combining state and action abstraction specifically.

As artificial agents become increasingly capable, what internal structure is necessary for an agent to act competently under uncertainty? Classical results show that optimal control can be implemented using belief states or world models, but not that such representations are required. We prove quantitative "selection theorems" showing that strong task performance (low average-case regret) forces world models, belief-like memory and -- under task mixtures -- persistent regime-tracking variables resembling functional primitives of emotion, along with informational modularity under block-structured tasks. Our results cover stochastic policies, partial observability, and evaluation under task distributions, without assuming optimality, determinism, or access to an explicit model. Technically, we reduce predictive modeling to binary "betting" decisions and show that regret bounds limit probability mass on suboptimal bets, enforcing the predictive distinctions needed to separate high-margin outcomes. In fully observed settings, this yields approximate recovery of the interventional transition kernel; under partial observability, it implies necessity of predictive state and belief-like memory, addressing an open question in prior world-model recovery work.

We are interested in enabling autonomous agents to learn and reason about systems with hidden states, such as locking mechanisms. We cast this problem as learning the parameters of a discrete Partially Observable Markov Decision Process (POMDP). The agent begins with knowledge of the POMDP's actions and observation spaces, but not its state space, transitions, or observation models. These properties must be constructed from a sequence of actions and observations. Spectral approaches to learning models of partially observable domains, such as Predictive State Representations (PSRs), learn representations of state that are sufficient to predict future outcomes. PSR models, however, do not have explicit transition and observation system models that can be used with different reward functions to solve different planning problems. Under a mild set of rankness assumptions on the products of transition and observation matrices, we show how PSRs learn POMDP matrices up to a similarity transform, and this transform may be estimated via tensor decomposition methods. Our method learns observation matrices and transition matrices up to a partition of states, where the states in a single partition have the same observation distributions corresponding to actions whose transition matrices are full-rank. Our numerical experiments suggest that explicit observation and transition likelihoods can be leveraged to generate new plans for different goals and reward functions after the model has been learned. We also show that learning a POMDP beyond a partition of states is impossible from sequential data by constructing two POMDPs that agree on all observation distributions but differ in their transition dynamics.