#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.AI
Who Is Sycophantic to Whom? Confident LLMs, Human Deference, and the Collapse of Trust Calibration
Deepthika S, Pawni Yadav, B. Sankar
Research on sycophancy asks whether large language models (LLMs) bend towards what their users want to hear. We ask the reverse question: when an LLM is confident, consistent, and wrong, do users bend towards it? In a within-subjects experiment, 32 participants learned up to five science topics by chatting with five assistants built on the same model (GPT-5-mini). Unknown to participants, each assistant's briefing had 0, 25, 50, 75, or 100% of its facts replaced by plausible falsehoods, and every assistant spoke with full confidence. A surprise quiz after each topic offered the correct fact, the planted falsehood, and two distractors, with a confidence rating for every answer. Across 104 quizzes and 1,040 answers, scores fell from 7.4 to 2.9 out of 10, and the planted option was chosen on 60% of falsified items against 11% of correctly taught ones (odds ratio 12.5). Transcript coding showed that whenever the assistant stated a falsehood, it was adopted about 65% of the time at every falsification level. Absorbed falsehoods were held with high confidence (8.4/10), the modeled confidence advantage of right over wrong answers vanished, and the discrimination of confidence for correctness fell from an AUROC of 0.70 to chance, while post-task trust ratings barely moved. Participants tended to return to the chat more when the assistant was worse, but returning went with more absorption, not less, and 30% of all turns pasted quiz questions back to the source being checked. The assistant itself was almost never sycophantic and never conceded under pushback. We introduce a baseline-corrected Human Deference Index to quantify this human-side sycophancy and argue that trustworthiness is a property of the human-AI pair, that sycophancy evaluations should measure both directions, and that learning interfaces must make reliability legible claim by claim.
#03Oct 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.
#04Oct 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.
#05Oct 22, 2026
cs.LG
On the Token Collapse Phenomenon in Textual Graph Soft Prompting
Andrea Giuseppe Di Francesco, Rishabh Jain, Franco Maria Nardini and 3 more
Recent methods for injecting graph structure into LLM prompts include graph soft prompting, in which a graph neural network (GNN) learns graph-specific tokens that capture relational information among entities in textual prompts. G-Retriever combines graph soft prompts with a verbalized description of the same graph to strengthen the textual prompt signal. We conduct an in-depth analysis of G-Retriever and uncover a pathological behavior we term token collapse. Across three benchmarks, three graph encoders, two LLM families, and both frozen and LoRA-adapted models, G-Retriever's graph tokens become almost indistinguishable across inputs. We provide evidence that the same failure is inherited by subsequent methods, even with multi-token pooling. Under the standard setup, swapping a token with the dataset mean, a token from another example, or one derived from a corrupted graph produces no resolved answer-level effect in accuracy. Moreover, a learned constant prompt that never accesses the graph matches or surpasses G-Retriever on all three benchmarks. These findings indicate that, rather than conveying graph content as intended, the collapsed token functions primarily as a generic soft prompt. We also examine conditions linked to this collapse and propose a two-stage procedure that yields non-collapsed tokens while maintaining competitive performance in most cases. However, token variability alone does not prove that the model uses graph information: via interventions and decoding probes, we show that depending on the configuration, a token can reflect the question, an answer prior, or graph-derived content that the LLM may or may not use. Overall, our results offer a practical approach to evaluating graph-token alignment rather than inferring it from task accuracy alone. Code to reproduce our experiments is available at https://github.com/difra100/Token_Collapse_KGQA.