#01Oct 22, 2026
cs.CV
Beyond Best-of-$k$: Prior-Consistent DAPS for Ambiguous Nonlinear Inverse Problems
Merve Kocabas, Benjamin A. Burns, Andreas Geiger and 2 more
Diffusion models have become strong priors for solving inverse problems. However, nonlinear inverse problems such as phase retrieval remain challenging when multiple measurement-consistent solutions are distinguishable only by the prior; we call such measurements ambiguous. Existing diffusion-based samplers rely on local approximations during reconstruction. For an ambiguous measurement, these approximations can allow measurement guidance to favor a measurement-consistent mode that is close to a prior-supported mode but is itself not supported by the prior. Evaluation often masks this type of failure by reporting the best-of-$k$ runs, where the best is selected by comparison to the ground truth. We introduce Prior-Consistent DAPS (PC-DAPS), a variant of Decoupled Annealing Posterior Sampling (DAPS) designed to address this failure case by maintaining multiple candidate solutions within a single sampling run. As annealing noise decreases, PC-DAPS prunes and replaces weaker candidates according to their prior consistency, without any ground-truth access. PC-DAPS reduces the incidence of prior-inconsistent samples and improves sample quality on nonlinear inverse problems while preserving sample quality and diversity on linear inverse problems.
#02Oct 22, 2026
math.NA
Phase Transition from Random Features to Fully Trainable Networks
Xin He, Huan Lao, Xiliang Lu and 1 more
Constructing accurate and computationally tractable approximation spaces is a fundamental task in scientific computing. Partially trainable neural networks bridge fixed random features and fully adaptive representations. This paper quantifies a phase transition pattern in approximation bounds and observes analogous behavior in training errors: a rapid but smooth initial improvement followed by diminishing returns, with a sharper transition under greater initialization mismatch. Under polynomial spectral decay with exponent $α>1$ and leverage compatibility, we establish a squared $L_2$ approximation rate $\mathcal{O}((κ_P\log(m/δ)/m)^α)$ for two-layer networks of width $m$ and trainable proportion $P$, where $κ_P=(P/κ_1^*+(1-P)/κ_0^*)^{-1}$. The bound holds uniformly over the unit ball of a reproducing kernel Hilbert space (RKHS) with probability at least $1-δ$. The constants $κ_0^*$ and $κ_1^*$ quantify the fixed and trainable groups' sampling mismatches relative to the target RKHS. For spherical biased-ReLU features in dimension $d$, we verify these assumptions with $α=(d+2)/(d-1)$ and $κ_0^*=4\sqrt{2}τ(d+1)/d$ for initialization scale $τ\ge1$, and $κ_1^*=1$ under ridge leverage sampling. For $d=5$ and $τ=10$, a trainable proportion of approximately $4.1\%$ captures $90\%$ of the reduction in the approximation bound from $P=0$ to $P=1$. A structured three-layer example illustrates how a few trainable first-layer neurons exploit fixed downstream blocks through nonlinear composition. Numerical experiments across diverse settings, including networks with up to 15 layers, exhibit similar phase transitions in training errors.
#03Oct 22, 2026
cs.CV
Sensorimotor Alignment: A Platonic Proxy for Embodied Policy Success
Yunfei Xie, Howard H. Qian, Shiyi Lan and 2 more
Robotic foundation models are typically evaluated through costly closed-loop rollouts, which motivates cheap offline proxies for model capability. The Platonic Representation Hypothesis (PRH) suggests that as representations improve, different modalities such as vision and language converge toward a shared statistical model of reality. We ask whether motion trajectories form another such modality: as embodied models become more capable, should their sensory representations converge toward the structure of physical motion? To examine this, we propose Sensorimotor Alignment ($S^2$), a training-free offline metric that measures how well a model's sensory representation aligns with the geometry of physical motion. We find that $S^2$ correlates positively with downstream robot task success across embodied model families, making it a low-cost offline proxy for prioritizing models before closed-loop evaluation. $S^2$ can also identify promising vision-language model (VLM) backbones even before costly fine-tuning into vision-language-action models (VLAs). Beyond this correlation, $S^2$ offers representation-level explanations for phenomena observed in VLAs and world action models (WAMs). With $S^2$, we extend PRH to embodied models and make sensorimotor alignment empirically measurable, offering insight into why an embodied model succeeds beyond its closed-loop success rate.
#04Oct 22, 2026
cs.LG
Causal Chain of Thought: Mitigating Attention Leakage via Context Isolation
Gabriele Dominici, Teague McMillan, Fazl Barez and 2 more
Chain-of-thought (CoT) prompting elicits step-by-step rationales that appear to explain model predictions, but there is no guarantee these steps causally drive the final answer. In standard autoregressive generation, dense attention allows each reasoning step to attend to the full context, enabling the model to derive answers through direct lookup while generating plausible-sounding but post-hoc justifications. We introduce CausalCoT, an inference framework that enforces causal transparency by decomposing problems into a directed acyclic graph of atomic sub-questions, evaluating each node in an isolated context containing only its direct causal parents. This Markovian structure removes attention pathways to non-parent content, making downstream predictions sensitive to local reasoning rather than global context leakage. Across a diverse suite of reasoning benchmarks, CausalCoT preserves competitive predictive performance while improving explanation faithfulness, increasing causal sensitivity of intermediate reasoning steps by an average of 12 and up to 21 percentage points over the strongest baseline. The structured dependency graph additionally enables test-time interventions in which local corrections propagate predictably through downstream reasoning.
#05Oct 22, 2026
cs.LG
METTA: Memory-Enhanced Test-Time Adaptation for Meta-Reinforcement Learning
Ali Najar, Hosein Hasani, Amir Kooshan Fattah and 2 more
Meta-reinforcement learning aims to train agents that adapt quickly to unseen tasks from limited interaction, but this requires representing task evidence over long interaction histories. Classical recurrent agents compress experience into hidden states, while transformer-based agents retrieve from past trajectories at quadratic memory and computation cost. In this work, we propose Memory-Enhanced Test-Time Adaptation (METTA) for meta-reinforcement learning. It decomposes the fast adaptation phase into two temporal scales: a causal neural memory performs fine-grained within-episode adaptation with linear sequence complexity, while compact episode-level summaries support long-range cross-episode task inference without attending over the full interaction history. Moreover, equipping agents with neural memory provides sufficient expressive capacity and test-time training capability, enabling effective adaptation to unseen held-out tasks and task families at meta-test time. On unseen held-out Meta-World ML10/45 test environments, METTA achieves a success rate over $50\%$ while maintaining a low training budget and short wall-clock time. On long-context sparse-reward PointMaze tasks, it outperforms transformer-based baselines by exhibiting more structured exploration behavior. These results show that METTA provides an efficient path toward more adaptive and scalable long-context meta-RL.