#01Oct 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.
#02Oct 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.
#03Oct 22, 2026
stat.ML
Reliable AI-Assisted Decisions via Selective Auditing
Isaac Gibbs, Elise L. Han, Ryan J. Tibshirani and 1 more
We consider online monitoring of an AI system that produces a sequence of decisions. At each round, the system outputs a proposed decision together with a confidence score estimating the trustworthiness of the decision. The decision and confidence score need not be produced by the same model: for example, one agent may propose a decision, while a separate verifier agent evaluates it and outputs a correctness or safety score. Based on this information, we must decide whether to accept the AI decision automatically or consult an expert, such as a human auditor, who reviews the proposal and either accepts or corrects it. We formulate this task as an online constrained optimization problem in which the goal is to minimize the frequency of expert auditing while guaranteeing that the fraction of AI errors that go unaudited stays below a user-defined threshold. We derive a family of algorithms with provable error-control guarantees with no assumptions, including a method that is optimally efficient: it asymptotically attains the best achievable auditing rate for both adversarial and i.i.d. data streams. Experiments on screening harmful requests to large language models, qualitative text annotation, and data labeling show that our methods achieve valid error control in practice while substantially reducing the need for human auditing compared to baselines.
#04Oct 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.
#05Oct 22, 2026
cs.LG
Rethinking Sequence Compression with Test-time Regression
Sihan Yang, Jie Huang, Hanxuan Li and 4 more
Sequence compression is a fundamental operation and a critical information bottleneck in efficient language and multimodal models, and yet prevailing approaches based on pooling or learned projections remain underperforming. We revisit sequence compression through the lens of test-time regression: input tokens define a regression problem whose fitted coefficients form the compressed representation. Importantly, the regression problem is learned end-to-end via backpropagation, while its coefficients are computed efficiently in closed form during the forward pass. This leads to TTR-Compressor, a general alternative to conventional pooling and projection-based compression. We evaluate TTR-Compressor as the compressor for block-wise sparse attention and the visual token merger for multimodal large language models. On block-wise sparse attention, TTR-Compressor improves RULER performance over attention-based compressors by a large margin. For visual token merging, it consistently outperforms the standard MLP merger and matches its performance with 55.6% fewer visual tokens. These results establish test-time regression as an effective primitive for sequence compression in efficient language and multimodal models.