#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
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.
#03Oct 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.
#04Oct 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.
#05Oct 22, 2026
cs.AI
Direct Pass@$k$ Optimization for Thought Pruning: Balancing Quality and Diversity in Test-Time Reasoning
Mahdi Salmani, Adel Javanmard, Devansh Gupta and 1 more
Test-time scaling has emerged as a key inference strategy for reasoning models, where a model generates a large number of candidate solutions in the hope of finding at least one correct solution. Running all candidate solutions to completion can be computationally demanding, so recent work prunes the candidate pool after generating only a short prefix, committing further computation only to the surviving candidates. Existing pruning strategies divide broadly into two categories: Quality-based methods assign a score to each partial solution and discard those predicted to ultimately lead to an incorrect final solution, while diversity-based methods select partial solutions that follow different reasoning trajectories and are therefore likely to cover different final solutions. The tension between these two objectives is an instance of exploration versus exploitation, yet little to no prior work on pruning exposes this trade-off directly, let alone optimizes it. In this paper, we introduce a pruning procedure that addresses this trade-off directly by optimizing pass@$k$ over the selected solution pool. In particular, it chooses the pool to maximize the probability that at least one of its partial solutions, when continued to completion, yields a correct answer. Because this objective simultaneously rewards high-quality partial solutions and penalizes redundancy among them, quality and diversity are naturally balanced by the criterion itself rather than through separate ad-hoc design choices. On eight open-weight reasoning models, our method outperforms existing quality-based and diversity-based pruning strategies. The gains are particularly pronounced when the pruning procedure keeps a moderate number of partial solutions for continued generation, highlighting the value of directly balancing quality and diversity during pruning.