Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.38903

Structural-Test Geometry as an Inductive Bias for Partially Observable World Models

Todd Y. Zhou
View original source ↗Read source document ↗Export metadata ↓

Abstract

Predictive world-model objectives need not organize latent histories according to distinctions required for later control. With privileged simulator access during training, should response-derived structural information be predicted, decoded, or imposed directly on latent geometry--and how do these choices compare with structured belief distillation? We define posterior-marginalized structural tests whose response distributions induce a pseudometric over histories, then train quotient-preserving (QP) world models by aligning shared latent Euclidean distances to that metric. Across a fixed six-task diagnostic suite, the largest differences appear under held-out structural variation: QP improves planning success by 26.1 points $[21.5,30.7]$ over metric decoding and 6.4 points $[3.8,9.0]$ over structured belief distillation. On GridWorld, metric decoding accurately recovers held-out structural distances ($ρ=.91$) while its native latent geometry remains more distorted than QP's (paired IQD difference $.22$ $[.20,.24]$), showing that relational recoverability and direct geometric alignment can diverge.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Todd Y. Zhou. 2026-10-28. Structural-Test Geometry as an Inductive Bias for Partially Observable World Models. https://arxiv.org/abs/2610.38903

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dynamic Strategy Selection

We consider the problem of dynamically selecting among competing strategies using observable predictors. To mitigate estimation noise and excessive switching, we regularise the estimated policy with a switching cost, which may exceed actual transaction costs when these are too small to provide sufficient regularisation. Since switching costs make current choices affect future decisions, we formulate the problem using dynamic programming. The optimal policy is estimated using a reinforcement learning algorithm based on iterated regressions, making the procedure simple to implement. We apply the method to monthly rotation among momentum, value, profitability, and defensive U.S. equity factors over a sample of about 60 years. Using a parsimonious set of state variables, the estimated policy outperforms both the myopic dynamic policy and the best fixed factor in hindsight in out-of-sample evaluation. Under weak conditions, we show theoretically that the decision rule estimated from empirical data is asymptotically consistent for the unknown optimal decision rule. Simulation results illustrate the finite-sample relevance of these asymptotic results.

cs.LG↗
arXiv2026

Mamba Hawkes Process for Event Sequence Modeling

Modeling asynchronous event sequences is crucial in numerous real-world applications such as healthcare monitoring, financial transaction analysis, and so on. Traditional temporal point processes, including Hawkes Processes, often fail to capture complex dependencies due to their parametric limitations. While neural approaches like RNNs and Transformers have improved flexibility, they struggle with computational inefficiency, and attention saturation. In this paper, we introduce the Mamba Hawkes Process (MHP), the first framework to integrate selective state space model (Mamba) with temporal point processes. MHP leverages time-varying state transitions and input-dependent gating to efficiently encode event history and capture long-term dependencies with linear complexity. Importantly, we provide theoretical guarantees showing that MHP generalizes both classical multi-exponential Hawkes processes and exponential-decay gated RNNs, underscoring its expressive power and theoretical soundness. To address the inherent constraints of pure state space models in handling heterogeneous event interactions, we further develop Adaptive Mamba Hawkes Process (A-MHP) that incorporates two novel mechanisms: a Time-Scaling Mechanism that adaptively weights time intervals based on event type and history, and a Dual-Channel State Transition that adaptively processes event content and temporal dynamics for more refined state updates. Extensive experiments on synthetic and realworld datasets demonstrate that MHP and A-MHP consistently outperform state-of-the-art baselines in event prediction tasks, particularly in long-sequence scenarios. Our work establishes a scalable and theoretically grounded paradigm for event sequence modeling, with practical implications for predictive maintenance, anomaly detection, and dynamic system analysis.

cs.LG↗
arXiv2026

The Price of Failure Risk: Clipped Barrier Policy Gradients with Convex Regularization

In many control problems, actions consume a resource budget, such as a wear allowance, and the probability of exhausting it within a given horizon must stay below a tolerance. A simple, widely used approach is to augment the state with the remaining budget, subtract an interior barrier from the utility and penalize exhaustion, so that policy-gradient methods can be applied unchanged. We clip the combined one-step reward from below at a level m to keep the returns of exploratory policies finite. The clip level is a price of failure risk, since the clipped value decomposes exactly into the utility before failure, the cost of the interior margin and m times a geometric failure risk. Consequently, an approximately optimal policy maximizes utility net of margin cost among policies with no greater risk. Its risk exceeds that of any comparison policy by at most order 1/m and can be certified from its value or from validation data. Our main result proves exponential convergence of the population policy-gradient flow for every parameter regularizer that is convex along generalized geodesics and sufficiently strong relative to the price. This extends the mean-field analysis from relative entropy to weight decay and to finite networks. Relative entropy adds parameter noise and a pull toward a prior, whereas weight decay provides only the pull. Action regularization bounds changes in failure risk by the relative entropy to a reference policy. The bounds are evaluated on an exact maintenance benchmark, a fuel-tank controller, a solvable flow and a benchmark-suite task.

cs.LG↗