#01Oct 30, 2026
cs.AI
CausalWAM: Learning the Causes of Actions in World Action Models
Juntao Cheng, Jinzhou Tang, Fan Feng and 2 more
World action models (WAMs) learn latent variables from observations and use these to both predict the evolution of the scene and to generate actions. The prediction has to be of the whole scene, whereas only a portion of the scene causes actions. WAMs fitted to demonstrations do not, in general, guarantee that they will generate actions solely from the latent causes of the demonstrated actions (the action-relevant latent variables), as the model could just as well learn to imitate in this way whilst entangling the action-relevant latent variables with the nuisance variables. We therefore separate out what causes action from what prediction depends on. We prove that under a sparsity constraint the latent variables used to generate actions are an invertible function of the action-relevant latent variables alone and the true structure is identified up to a permutation of the latent variables. This requires neither sufficient temporal dependence nor any assumptions on how the unobserved regimes evolve and holds even when the action-relevant latent variables are statistically dependent on the rest. We therefore propose CWAM (Causal WAM), which incorporates the constraint into a pretrained WAM by adding a sparse routing path to its action head, with the world modeling objective remaining unchanged. Experiments on both synthetic data and real-world robots validate the theory as well as showcase the improved efficiency in closed-loop success.
#02Oct 30, 2026
cs.LG
Differentially Private Synthetic Data from Sliced Chebyshev Moments
Lucas Rosenblatt, R. Teal Witter, Christopher Musco
Research on practical differentially private (DP) synthetic data has largely focused on methods that approximately preserve low-dimensional marginals of a target distribution, and can thus only hope to preserve higher-dimensional, global structure as a lucky by-product. At the same time, existing methods that target global accuracy guarantees pay a price exponential in the data dimension, $d$. In this work, we address this ``curse of dimensionality'' by presenting a new DP synthetic data algorithm, SPLICE, that comes with a compelling global distributional guarantee, even in high-dimensions, and moreover, is practically state-of-the-art. Our algorithm is based on measuring noisy sliced Chebyshev polynomial moments of the target distribution and fitting a distribution to match, a twist on recent polynomial methods for 1-D synthetic data. We prove that, given a dataset of $n$ examples, SPLICE returns a private distribution with Sliced Wasserstein-1 distance $\tilde{O}(1/\sqrt{n})$ from the target, for constant privacy parameters. Notably, this bound is independent of the data dimension, $d$. Along the way, we prove a moment matching result of independent interest: for a distribution on the unit ball, matching the first $O(1/α)$ Chebyshev moments along $\tilde{O}(d/α^2)$ random directions guarantees $α$ Sliced Wasserstein error. Finally, we provide a practical implementation of the algorithm that borrows tools from the tensor decomposition literature and achieves state-of-the-art performance compared to prior DP synthetic data methods on an extensive benchmark.
#03Oct 30, 2026
cs.LG
Counting on Dummies: Privacy Amplification with Observable Counts and Truncated Batches
Vitaly Feldman, Audra McMillan, Kunal Talwar
In many practical deployments of Differentially Private Stochastic Gradient Descent (DP-SGD), the server processes data in batches. Randomly sampling these batches allows for better privacy bounds via privacy amplification results. Most sampling schemes with provable privacy amplification, including Poisson sampling and random allocation, result in variable batch sizes. The privacy guarantee of these schemes requires that the batch sizes are not revealed. In distributed settings, the server performing the aggregation or any party observing the communication traffic may learn these batch sizes. Furthermore, in both centralized and distributed settings, memory and computation constraints may require each batch to be of some maximum size $s$, necessitating truncation of the batch when it exceeds this limit. It is known that this truncation can result in a significant increase in privacy loss. In this work, we address both of these challenges via a simple mechanism that uses a random number of \emph{dummy points} to privatize the batch size and maintain the privacy guarantee even under truncation. We demonstrate that our mechanism is easy to implement in a distributed setting, and provide a general analysis of this mechanism for both Poisson sampling and random allocation. Our analysis is designed to support efficient and relatively tight privacy accounting. It also effectively amplifies the privacy of the count releases by subsampling, making the expected number of dummy points asymptotically smaller than what is needed to directly privatize the (sensitivity-one) batch sizes with non-negative noise. For Poisson sampling with truncated batches, we demonstrate empirically that our mechanism achieves better privacy--efficiency tradeoffs than the direct accounting for truncation recently given by (Ganesh, 2025).
#04Oct 30, 2026
cs.LG
Hyperbolic Inverse Reinforcement Learning
Iulia Rusu, Anoop Praturu, Sergei Gepshtein and 1 more
Inverse reinforcement learning (IRL) seeks to infer the reward function underlying observed behavior, but its predictive accuracy and interpretability depend on how that reward is computed from the underlying features. While prior IRL reward functions have been implemented through a variety of techniques including linear weights, neural networks, or other function approximators, none make assumptions about the geometry of the underlying feature space. Inspired by geometric organization observed in neural circuits, we introduce Hyperbolic inverse reinforcement learning (Hyperbolic IRL), which parameterizes reward as a function of Hyperbolic distance between the feature vector and a learned parameter vector, as well as its Euclidean distance variant. We tested our methods against a range of linear and nonlinear IRL baselines under both deterministic and stochastic policies. Our Hyperbolic approach achieved comparable performance to state-of-the-art models on established benchmarks and excelled in the low data limit and across dense environments. Applied to human navigation among multiple exhibits in a museum room, Hyperbolic IRL reveals reward structure that depends not only on individual exhibit-distance features, but also on non-separable conjunctions between them. Together, these results demonstrate that a Hyperbolic reward parameterization can improve both the predictive accuracy and interpretability of IRL, providing a framework for studying how non-separable, conjunctive structure can begin to explain behavior.
#05Oct 30, 2026
math.OC
Near-Optimal Second-Order Convex Finite-Sum Optimization under Individual Smoothness
Xinliang Zhang, Lesi Chen, Zonghan Li and 1 more
We study the stochastic second-order oracle complexity of solving smooth convex finite-sum optimization with $n$ components. Very recently, Tsedenov \& Kovalev (2026) showed that the minimax optimal complexity under averaged smoothness and convexity is $\tildeΘ(n + n^{6/7} ε^{-2/7})$ by establishing nearly matching upper and lower bounds. In this paper, we show that individual smoothness and convexity provably enable further acceleration, where the lower complexity bound is $Ω(n+ n^{5/7} ε^{-2/7})$ under this stronger assumption. Then, by establishing a novel second-order self-bounding inequality, we design a new Taylor-corrected lazy Newton method, which can lead to a better complexity of $\tilde{\mathcal{O}}(n + n^{5/7} ε^{-2/7})$ by applying the optimal Monteiro-Svaiter acceleration, matching our lower bound up to only logarithmic factors.