#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
When to Follow the Teacher: Advantage-Based On-Policy Distillation
Mahdi Sabbaghi, George Pappas, Hamed Hassani and 1 more
Online Policy Distillation (OPD) often outperforms offline methods such as Supervised Fine-Tuning (SFT) by training on trajectories sampled directly from the student. However, standard OPD trains the student to follow the teacher at every state of the trajectory, assuming that teacher guidance is always beneficial. We instead distinguish between what the teacher prefers and what actually helps the current student succeed. We introduce Advantage-Based On-Policy Distillation (AOPD), which weights teacher actions by their counterfactual advantage under the student. Teacher actions that improve the student's expected outcome are reinforced, while those that do not are downweighted. Directly computing these advantages requires trying alternative teacher actions at each step and running new rollouts from each. Instead, we show that the AOPD objective can be estimated using only standard student rollouts and their terminal rewards. Our estimator uses teacher importance weights on the student-sampled actions to provide unbiased advantage-weighted supervision, without any additional rollouts or reward evaluations. This allows AOPD to focus teacher supervision on actions that help the current student while preserving the rollout efficiency of standard OPD. Experiments on math, coding, and Medqa show gains over distillation and RL baselines in both external-teacher and self-distillation settings.
#03Oct 22, 2026
cs.LG
BeNice! Closing Looping's Inference-Memory Gap via KV-Sharing
Hayden Prairie, Jacob M. Ryan, Taylor Berg-Kirkpatrick and 1 more
Looped architectures scale quality while keeping parameter count fixed by repeatedly passing activations through the same block of layers. During inference, each recurrence generates independent KV-caches, causing memory to grow linearly. To address this challenge, prior work has proposed KV-sharing (i.e., sharing KV-caches across depth), finding that, in some cases, the KV-cache of the final recurrence can be shared with the earlier recurrences without quality loss, a property we denote as KV-shareability. However, the mechanisms underlying KV-shareability remain poorly understood, with even identically trained looped architectures not consistently exhibiting it. In this paper, we study how KV-shareability can be enabled in looped models. We propose a two-stage method: in the first stage, we use stochastic depth during pretraining, which induces contractive residual dynamics that drive representations toward a common limit across recurrences. In the second stage, we propose BeNice!, a post-training method that broadcasts the final recurrence's KV-cache into the first recurrence, training it to produce compatible residuals while preserving the original model's quality. As a result, BeNice! enables KV-shareability while matching standard finetuning's unshared validation perplexity. Using BeNice!, we show that KV-sharing is complementary to alternative KV-compression methods, composing with memory-efficient sequence mixers (e.g., multi-latent attention, Kimi delta attention) and low-precision KV-cache quantization (e.g., fp8, mxfp8, nvfp4). Finally, in simulated low-memory, long-context inference, KV-sharing improves cache hit rates by up to 31.4%, increases throughput by up to 23.6%, and reduces p90 time-to-first-token by up to 83.6%.
#04Oct 22, 2026
cs.LG
Diffusion Language Models for Perplexity-Aware Black-Box Attacks
Ali Al-Lawati, Elsayed Eshra, Dongwon Lee and 1 more
\emph{Continuous-space} attacks find prompts that trigger malicious behaviors, such as overthinking, in black-box LLMs by sampling or optimizing over a low-dimensional Gaussian latent space and decoding it to text through a \emph{random mapping} and nearest-token lookup. Because the random mapping is not learned from language, its prompts can be highly unnatural, and as such easily detectable through input guardrails, and the risk estimates they yield are not grounded in natural prompts. In this paper, we demonstrate that the same continuous latent-space framework can be coupled directly to a learned generative distribution over language, a continuous diffusion language model (dLLM), which removes the artificial random mapping while preserving the standard-Gaussian latent formulation and the downstream sampling or optimization procedure. We evaluate this approach under two settings: sampling-based estimation using \emph{RareTrap} and optimization-based search using \emph{ThinkTrap}. We find that character-level perplexity drops from $10^3$--$10^7$ to 3--5 in RareTrap and from 20--28 to 4.3--5.4 in ThinkTrap. We also find that model risk estimates can differ by an order of magnitude across the two mappings.
#05Oct 22, 2026
cs.SE
VERA: A Responsible AI Dashboard for Assessing LLM Deployments in Light of the EU AI Act
Robin Quériaux, Solveig Bachellery, Léa Déléris and 4 more
Institutions that deploy large language models in regulated settings often need technical evidence of responsible AI practices before approving a deployment. COMPL-AI provides a technical interpretation of the EU AI Act that organises this evidence under six principle groups and eighteen technical requirements, twelve of which current benchmarks can measure. The benchmark suites that produce this evidence are typically operated from a command line, while the staff who approve deployments are non-engineers. We present VERA, an open-source self-hosted dashboard deployed to facilitate responsible AI processes within a large European bank. A reviewer selects a model and runs public benchmarks against it. VERA scores the twelve requirements that current benchmarks can measure and instruments the energy consumed by each evaluation, adding run-level evidence for environmental impact. We run four served open-weight models through the requirement pipeline, and the dashboard displays a score for each measurable requirement. A within-subject study then compares how participants read these benchmark results: from the raw output files in one condition, and through the VERA dashboard in the other. The dashboard reduced the time needed to perform the responsible AI assessment, reducing the time required from 56 seconds using raw files to 30 seconds using our dashboard, on average. Our dashboard scored highly (4.36 out of 5) on usefulness in the survey conducted within the organization. The dashboard and the study material are released publicly to promote replicability and reproducibility in different organisational contexts.