#01Nov 9, 2026
cs.LG
Inversion-Free High-Dimensional Counterfactual Inference
Saketh Vishnubhatla, Pingchuan Ma, Shu Wan and 4 more
Counterfactual inference is the task of answering hypothetical "what-if" queries about a unit, given an observational dataset, modeling assumptions, and a causal graph. This enables a modeler to reason about hypothetical scenarios that cannot otherwise be answered without assumptions or a causal graph. The simpler case involves a causal graph with scalar 1-D variables that denote different attributes in the data-generation process. While the literature is clear in the 1-D case, extending this to settings with high-dimensional nodes (e.g., images) remains challenging. Conventionally, in the literature, methods recover the latent state from the factual image (inversion), generate counterfactual attributes from the graph, and render the counterfactual image from the latent state using the updated attributes. In our work, we investigate the necessity of the inversion step in computing high-dimensional counterfactuals. We first discuss moving from the scalar 1-D case to the higher-dimensional case. Secondly, we discuss the relevance of the inversion step and evaluate an inversion-free counterpart repurposed from the image-editing literature. Finally, on image datasets such as CelebA and ADNI, we benchmark our approach using two measures: namely, effectiveness and identity preservation. While effectiveness is a measure of how faithfully the counterfactual attribute is rendered, identity preservation measures whether the same unit (image) is being rendered, both of which are crucial for high-dimensional counterfactual inference. We present the tradeoffs of using inversion-based and inversion-free approaches in our work.
#02Nov 9, 2026
cs.LG
Guiding Data Allocation for Robust Subpopulation Generalization
Zhaoying Pan, Yipei Wang, Shenyu Lu and 1 more
Machine learning models often achieve high average accuracy in the training data while performing poorly on test data due to subpopulation shift. A common data-centric solution is to enforce balanced subgroup proportions, but full balance can be costly, infeasible, and not always necessary. In this work, we study whether balanced training data is the unique optimal configuration for robust subpopulation generalization. We extend a Gaussian feature-model framework to theoretically characterize the performance landscape across general training subgroup distributions. We show that multiple configurations, including substantially imbalanced ones, can perform comparably to the balanced one. We further derive gradient-based directions for adjusting subgroup proportions to improve adjusted accuracy and worst-group accuracy more efficiently. These findings suggest that strategically allocating data offers a more flexible and principled path to robust performance than simple balancing. The code is available at https://github.com/zhaoyingpan/subpop-data-allocation.
#03Nov 9, 2026
cs.CV
What kills $v$-prediction? A Patch-wise PCA Perspective on Pixel-Space Flow Matching
Tianze Luo, Haofeng Huang, Yuan Yao
Latent Diffusion Models dominate generative modeling but face two-stage training complexity and the inherent reconstruction limits of pre-trained autoencoders. Pixel-space Flow Matching offers a simplified end-to-end alternative yet often encounters training difficulties when using the standard $v$-prediction objective. Recent research attributes this difficulty to the off-manifold nature of noised targets, motivating a shift toward $x$-prediction. In this paper, we investigate this explanation through patch-wise Principal Component Analysis (PCA) and identify a bandwidth bottleneck. The velocity in minor components is largely determined by the raw noisy input, requiring deep backbones to preserve information that competes with principal-component modeling. Through controlled experiments and representation analysis, we further examine why $x$-prediction remains effective: its parameterization provides a raw-input bypass, while its learned input representation can spontaneously concentrate on principal directions. Under low-rank observations, our analysis of the induced flow characterizes $x$-prediction as an implicit conditional-mean decoder, reconstructing discarded components from the retained information. These observations motivate the Raw-injected Transformer (RiT), which combines a lightweight raw-conditioned decoder with an output-side shortcut to separate semantic modeling from raw-state propagation. Our method restores effective $v$-prediction and achieves competitive performance on ImageNet $256\times256$, providing a perspective on the interaction between prediction objectives and architectural bandwidth.
#04Nov 9, 2026
math.OC
Learning Rate Decay Can Exponentially Accelerate SGD for Global Optimization of Nonconvex Functions
Guneykan Ozgul, Dylan Herman, Junhyung Lyle Kim and 2 more
Stochastic Gradient Descent (SGD) is a workhorse algorithm for continuous optimization. It is a folk belief among deep learning practitioners that learning rate decay in SGD substantially improves performance. However, it has remained unclear whether learning rate decay offers an asymptotic advantage for global nonconvex optimization. We answer this question in the affirmative by demonstrating a natural class of nonconvex functions for which, we prove that SGD with learning rate decay requires exponentially fewer gradient queries for global optimization than SGD with any fixed learning rate in the small-step size regime. To the best of our knowledge, this is the first exponential advantage that has been demonstrated for learning rate decay. The class of functions we consider includes many popular benchmark nonconvex functions. Our results provide a robust explanatory theory for the empirically observed benefits of learning rate decay for global optimization. We show that annealing performs the non-logconcave sampling task associated to the optimization problem in polynomial time, via a novel application of weak Poincaré inequalities.
#05Nov 9, 2026
cs.LG
Adaptive Quantization Preserves Fast Rates for TD Learning over Rate-Limited Channels
Sreejeet Maity, Aritra Mitra
Motivated by reinforcement learning subject to communication constraints, we study a policy evaluation problem with linear function approximation over a rate-limited channel. In our setup, an agent interacting with an unknown environment (modeled as a Markov Decision Process) transmits quantized estimates of a temporal-difference (TD) learning update direction to a server over a finite-capacity channel. Our goal is to investigate to what extent one can preserve the statistical convergence rates achievable when the channel has infinite capacity. To that end, we propose a new algorithm called Batched Adaptively Quantized TD (BAQ-TD), which uses batching to reduce the variance of the transmitted information, and adaptive quantization to encode innovations. We prove a high-probability finite-time error bound for BAQ-TD, and show that, above a certain finite channel capacity, BAQ-TD preserves the convergence rate of unquantized TD up to logarithmic factors. Specifically, for a $d$-dimensional value function parameter, we establish that transmitting a total of $\mathcal{O}(d \log(T))$ bits over a horizon of length $T$ suffices to achieve the order-optimal rate of $\tilde{\mathcal{O}}(1/T)$, marking an exponential improvement in communication-complexity over prior work.