#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.LG
Shift-aware score transport for privacy auditing without retraining
Yaohong Yang, Gauri Pradhan, Qi Chen and 2 more
Privacy auditing empirically assesses privacy leakage by using membership inference attacks to establish lower bounds on privacy loss. We consider an observational auditing setting in which the auditor cannot insert canaries, control data inclusion, or retrain the target model, and must instead rely on fixed sets of known members and non-members. This setting is relevant for large deployed models or when retraining is restricted by computational or access constraints. In this case, non-members available for auditing may differ in distribution from the training data, causing membership-inference scores to be skewed due to the distribution shift. We address this problem by estimating the counterfactual in-distribution non-member score distribution using the available out-of-distribution (OOD) non-members. Our proposed method learns the relationship between data representations and membership-inference scores from OOD non-members and transports it to the target covariate distribution. Because this transport may become unreliable under extrapolation or imperfect conditional invariance, we further introduce a conservative correction calibrated directly to the nominal transported privacy level. We construct controlled calibration tasks from the available non-member data to estimate how representation-space displacement inflates the audit, and use this estimate to correct the transport-induced audit error. Across multiple datasets with distribution shifts, our method yields substantially more stable privacy estimates while retaining tighter lower bounds than baselines.
#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.LG
Questioning Instrumental Convergence in RLVR: Checkpoint Evidence from OLMo-3
Barış Alparslan, Sandy Tanwisuth, Caleb Petterson
Instrumental convergence is often invoked as a general reason to expect capable agents to acquire or express power-seeking subgoals: self-preservation, resource acquisition, deception, or resistance to oversight which poses an important threat to the society. For LLMs, reinforcement learning is the first stage of post-training that directly optimizes behavior against an objective; therefore, it is the stage where convergent instrumental behavior, on IC grounds, likely to appear. Does reinforcement learning with verifiable rewards (RLVR) make a model more likely to express instrumental-convergence behavior, or does this depend on the training regime, evaluation frame, and stage of post-training? We study this question as a checkpoint-conditioned behavioral trajectory rather than as a single before/after safety score. Using InstrumentalEval, we evaluate OLMo-3-7B-Think across SFT, DPO, 13 intermediate RLVR checkpoints, and the final RLVR model. The trajectory is nonmonotonic: instrumental rate rises from 25.0% at SFT to 46.1% near RLVR step 200, then falls to 11.8% at the final checkpoint. Paired item-level tests and step-wise regression support the final SFT-to-RLVR reduction. Prompt framing does not explain this pattern: a harmful-prompt indicator combined with other framing effects explains only 15% of within-checkpoint score variance on average, and Iterative Null-space Projection (INLP) removes a detectable framing direction without changing the SFT-to-final-RLVR gap. Together with preliminary 32B endpoint results (35.53% SFT to 22.37% RLVR final), these findings indicate that RLVR does not monotonically increase instrumental behavior in this setting: the rate rises early, then falls below the SFT baseline. The result is specific to this model family and benchmark, and judge agreement is moderate, so absolute rates should be read cautiously.