#01Oct 30, 2026
stat.ML
Regret-Optimal Wasserstein-Robust Linear Regression
Sloan Nietert, Daniel Kuhn
Distributionally robust optimization (DRO) minimizes worst-case risk under distributional uncertainty, but its decisions can be suboptimal in terms of their excess risk, or regret. We study this gap for multivariate least-squares regression, assuming that the observed source law and unknown target law differ by an adversarial 2-Wasserstein perturbation of size $\varepsilon$. We first identify the asymptotic complexity of robust decision-making in the $\varepsilon \to 0$ limit, characterized by a problem-specific condition number $κ$. Here, a wide spectrum of simple algorithms, including DRO, achieve the instance-optimal rate of $O(κ\varepsilon^2)$. For fixed $\varepsilon > 0$, we prove that DRO still achieves the minimax rate if the problem has bounded residual effective rank. On the other hand, we identify significant failure modes where DRO is provably suboptimal by dimension-dependent factors. Fortunately, we prove that two alternative procedures, minimax regret optimization (MRO) and spectral-norm regularization (SNR), attain the minimax rate. We derive an exact convex reformulation of MRO and an accelerated proximal algorithm for SNR, along with high-probability finite-sample guarantees. We support these theoretical results with numerical experiments separating the performance of MRO and SNR from DRO.
#02Oct 30, 2026
cs.LG
Less Loss, Fixed Weights: Logit Corrections for Forgetting
Hanyu Yang
When a language model is fine-tuned to follow instructions, or further pretrained on a new subject, it often gets worse at predicting standard web text. This is known as "forgetting." We ask whether this loss can be undone by simple, fixed adjustments to the model's final token predictions. Across 14 pairs of base and derived models, from 1B to 7B parameters, we fitted a fixed bonus or penalty for each token (a vocabulary bias), alone or together with a temperature. On text held out from correction fitting, the largest top-4K bias recovery estimate is under 10%, with loss conditional on the retained vocabulary. Combining the bias with a temperature recovers up to 36%. Models further pretrained on math lose the most and recover almost nothing. Finally, in a controlled simulation where a model is damaged at random, with no planted bias or temperature change, the bias-plus-temperature fix still recovers 29%. Most of the real-model loss increase stays out of reach of our restricted fits.
#03Oct 30, 2026
cs.LG
When Does Jacobian Fine-Tuning Stabilize Neural PDE Emulators?
Shreeyam Bangera, Manya Gupta
Neural emulators of chaotic PDEs are trained on one-step prediction but deployed autoregressively, where their errors compound. Jacobian-based regularisers aim to curb this growth, but in a chaotic system part of the growth is physical and cannot be trained away. We separate the two sources of this error with a first-order decomposition. We compare the emulator's error with a counterfactual that propagates the same one-step mistakes through the solver's Jacobian, giving an amplification ratio: the factor by which the model's own dynamics amplify its errors. We study 21 configurations across four PDEs, five architectures and two model sizes (8-10k and 33k parameters), with errors measured at one Lyapunov time. Jacobian fine-tuning reduced the error by more than 10% for 1 of 34 seeds whose amplification ratio was at most 1.25, and for all 20 seeds whose ratio was at least four; for the latter, the error fell by a factor of 8 (small models) and 55 (33k models) in geometric mean over seeds. The gain approximately equals the one-step accuracy cost of fine-tuning divided by the amplification ratio. Matching the solver's Jacobian along the model's own error direction (EDJM) outperformed random directions at the same cost on 28 of 35 seeds; input-noise injection performed comparably to EDJM.
#04Oct 30, 2026
cs.LG
Counting on Dummies: Privacy Amplification with Observable Counts and Truncated Batches
Vitaly Feldman, Audra McMillan, Kunal Talwar
In many practical deployments of Differentially Private Stochastic Gradient Descent (DP-SGD), the server processes data in batches. Randomly sampling these batches allows for better privacy bounds via privacy amplification results. Most sampling schemes with provable privacy amplification, including Poisson sampling and random allocation, result in variable batch sizes. The privacy guarantee of these schemes requires that the batch sizes are not revealed. In distributed settings, the server performing the aggregation or any party observing the communication traffic may learn these batch sizes. Furthermore, in both centralized and distributed settings, memory and computation constraints may require each batch to be of some maximum size $s$, necessitating truncation of the batch when it exceeds this limit. It is known that this truncation can result in a significant increase in privacy loss. In this work, we address both of these challenges via a simple mechanism that uses a random number of \emph{dummy points} to privatize the batch size and maintain the privacy guarantee even under truncation. We demonstrate that our mechanism is easy to implement in a distributed setting, and provide a general analysis of this mechanism for both Poisson sampling and random allocation. Our analysis is designed to support efficient and relatively tight privacy accounting. It also effectively amplifies the privacy of the count releases by subsampling, making the expected number of dummy points asymptotically smaller than what is needed to directly privatize the (sensitivity-one) batch sizes with non-negative noise. For Poisson sampling with truncated batches, we demonstrate empirically that our mechanism achieves better privacy--efficiency tradeoffs than the direct accounting for truncation recently given by (Ganesh, 2025).
#05Oct 30, 2026
eess.SY
A Neural Network Approach towards Real-Time Knot Point Density Estimates for the Nonlinear Quadrotor
Jasmine Ratchford, Raffaele Romagnoli, Mark H. Klein
Spline representations provide a compact way to approximate continuous trajectories using a finite number of parameters. When approximating trajectories generated by dynamical systems, the efficiency of a spline representation depends strongly on the placement of knot points. Uniform knot distributions often lead to inefficient representations, requiring either unnecessary control points or producing poor approximations in regions where the trajectory varies rapidly. In this work we propose a learning-based method for adaptive knot placement in B-spline approximations of trajectories generated by ordinary differential equations. A neural network learns a mapping from the initial condition of the system to quantities that characterize the local variation of the resulting trajectory. These estimates are used to construct nonuniform knot distributions that approximately equidistribute a local error indicator, reducing the number of control points needed to meet a prescribed accuracy.