While the continuous Entropic Optimal Transport (EOT) field has been actively developing in recent years, it became evident that the classic EOT problem is prone to different issues like the sensitivity to outliers and imbalance of classes in the source and target measures. This fact inspired the development of solvers that deal with the *unbalanced* EOT (UEOT) problem $-$ the generalization of EOT allowing for mitigating the mentioned issues by relaxing the marginal constraints. Surprisingly, it turns out that the existing solvers are either based on heuristic principles or heavy-weighted with complex optimization objectives involving several neural networks. We address this challenge and propose a novel theoretically-justified, lightweight, unbalanced EOT solver. Our advancement consists of developing a novel view on the optimization of the UEOT problem yielding tractable and a non-minimax optimization objective. We show that combined with a light parametrization recently proposed in the field our objective leads to a fast, simple, and effective solver which allows solving the continuous UEOT problem in minutes on CPU. We prove that our solver provides a universal approximation of UEOT solutions and obtain its generalization bounds. We give illustrative examples of the solver's performance.

Symmetries are prevalent in deep learning and can significantly influence the learning dynamics of neural networks. In this paper, we examine how exponential symmetries -- a broad subclass of continuous symmetries present in the model architecture or loss function -- interplay with stochastic gradient descent (SGD). We first prove that gradient noise creates a systematic motion (a ``Noether flow) of the parameters $\theta$ along the degenerate direction to a unique initialization-independent fixed point $\theta^*$. These points are referred to as the noise equilibria because, at these points, noise contributions from different directions are balanced and aligned. Then, we show that the balance and alignment of gradient noise can serve as a novel alternative mechanism for explaining important phenomena such as progressive sharpening/flattening and representation formation within neural networks and have practical implications for understanding techniques like representation normalization and warmup.

Diffusion models have demonstrated significant promise in various generative tasks; however, they often struggle to satisfy challenging constraints.

In this paper, we reconstruct naturalistic images directly from macaque brain signals using a convolutional neural network (CNN) based decoder. We investigate the ability of this CNN-based decoding technique to differentiate among neuronal populations from areas V1, V4, and IT, revealing distinct readout characteristics for each. This research marks a progression from low-level to high-level brain signals, thereby enriching the existing framework for utilizing CNN-based decoders to decode brain activity. Our results demonstrate high-precision reconstructions of naturalistic images, highlighting the efficiency of CNN-based decoders in advancing our knowledge of how the brain's representations translate into pixels. Additionally, we present a novel space-time-resolved decoding technique, demonstrating how temporal resolution in decoding can advance our understanding of neural representations. Moreover, we introduce a learned receptive field layer that sheds light on the CNN-based model's data processing during training, enhancing understanding of its structure and interpretive capacity.

Thus, weaker models which give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle. We design and analyze practical algorithms which only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty oracles, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems.

LiDAR data exhibits significant domain gaps due to variations in sensors, vehicles, and driving environments, creating "language barriers" that limit the effective use of data across domains and the scalability of LiDAR perception models. To address these challenges, we introduce the LiDAR Translator (LiT), a framework that directly translates LiDAR data across domains, enabling both cross-domain adaptation and multi-domain joint learning. LiT integrates three key components: a scene modeling module for precise foreground and background reconstruction, a LiDAR modeling module that models LiDAR rays statistically and simulates ray-drop, and a fast, hardware-accelerated ray casting engine. LiT enables state-of-the-art zero-shot and unified domain detection across diverse LiDAR datasets, marking a step toward data-driven domain unification for autonomous driving systems. Source code and demos are available at: https://yxlao.github.io/lit.

The spatio-temporal relations of impacts of extreme events and their drivers in climate data are not fully understood and there is a need of machine learning approaches to identify such spatio-temporal relations from data. The task, however, is very challenging since there are time delays between extremes and their drivers, and the spatial response of such drivers is inhomogeneous. In this work, we propose a first approach and benchmarks to tackle this challenge. Our approach is trained end-to-end to predict spatio-temporally extremes and spatio-temporally drivers in the physical input variables jointly. By enforcing the network to predict extremes from spatio-temporal binary masks of identified drivers, the network successfully identifies drivers that are correlated with extremes. We evaluate our approach on three newly created synthetic benchmarks, where two of them are based on remote sensing or reanalysis climate data, and on two real-world reanalysis datasets. The source code and datasets are publicly available at the project page https://hakamshams.github.io/IDE.

Vanilla pixel-level classifiers for semantic segmentation are based on a certain paradigm, involving the inner product of fixed prototypes obtained from the training set and pixel features in the test image. This approach, however, encounters significant limitations, i.e., feature deviation in the semantic domain and information loss in the spatial domain. The former struggles with large intra-class variance among pixel features from different images, while the latter fails to utilize the structured information of semantic objects effectively. This leads to blurred mask boundaries as well as a deficiency of fine-grained recognition capability. In this paper, we propose a novel Semantic and Spatial Adaptive Classifier (SSA-Seg) to address the above challenges. Specifically, we employ the coarse masks obtained from the fixed prototypes as a guide to adjust the fixed prototype towards the center of the semantic and spatial domains in the test image. The adapted prototypes in semantic and spatial domains are then simultaneously considered to accomplish classification decisions. In addition, we propose an online multi-domain distillation learning strategy to improve the adaption process. Experimental results on three publicly available benchmarks show that the proposed SSA-Seg significantly improves the segmentation performance of the baseline models with only a minimal increase in computational cost.

The spurious correlation between the background features of the image and its label arises due to that the samples labeled with the same class in the training set often co-occurs with a specific background, which will cause the encoder to extract non-semantic features for classification, resulting in poor out-of-distribution generalization performance. Although many studies have been proposed to address this challenge, the semantic and spurious features are still difficult to accurately decouple from the original image and fail to achieve high performance with deep learning models. This paper proposes a novel perspective inspired by neural collapse to solve the spurious correlation problem through the alternate execution of environment partitioning and learning semantic masks. Specifically, we propose to assign an environment to each sample by learning a local model for each environment and using maximum likelihood probability. At the same time, we require that the learned semantic mask neurally collapses to the same simplex equiangular tight frame (ETF) in each environment after being applied to the original input. We conduct extensive experiments on four datasets, and the results demonstrate that our method significantly improves out-of-distribution performance.

Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics.We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems.We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.