Deciphering Shortcut Learning from an Evolutionary Game Theory Perspective

Shortcut learning causes deep learning models to rely on non-essential features within the data. However, its formation in deep neural network training still lacks theoretical understanding. In this paper, we provide a formal definition of core and shortcut features and employ evolutionary game theory to analyze the origins of shortcut bias by modeling data samples as players and their corresponding neural tangent features as strategies, assuming the existence of core and shortcut subnetworks. We find that gradient descent (GD) and stochastic gradient descent (SGD) lead to two distinct stochastically stable states, each corresponding to a different strategy. The former primarily optimizes the shortcut subnetwork, while the latter primarily optimizes the core subnetwork. We investigate the influence of these strategies on shortcut bias through a continuous stochastic differential equation, and reveal the impact of data noise and optimization noise on the formation of shortcut bias. In brief, our work employs evolutionary game theory to characterize the dynamics of shortcut bias formation and provides a theoretical view on its mitigation.

Make Geometry Matter for Spatial Reasoning

Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs. Nevertheless, we observe that naive token fusion followed by standard fine-tuning in this line of work often leaves such geometric cues underutilized for spatial reasoning, as VLMs tend to rely heavily on 2D visual cues. In this paper, we propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens. GeoSR introduces two key components: (1) Geometry-Unleashing Masking, which strategically masks portions of 2D vision tokens during training to weaken non-geometric shortcuts and force the model to consult geometry tokens for spatial reasoning; and (2) Geometry-Guided Fusion, a gated routing mechanism that adaptively amplifies geometry token contributions in regions where geometric evidence is critical. Together, these designs unleash the potential of geometry tokens for spatial reasoning tasks. Extensive experiments on both static and dynamic spatial reasoning benchmarks demonstrate that GeoSR consistently outperforms prior methods and establishes new state-of-the-art performance by effectively leveraging geometric information. The project page is available at https://suhzhang.github.io/GeoSR/.

Deep Learning Reforms Image Matching: A Survey and Outlook

Image matching, which establishes correspondences between two-view images to recover 3D structure and camera geometry, serves as a cornerstone in computer vision and underpins a wide range of applications, including visual localization, 3D reconstruction, and simultaneous localization and mapping (SLAM). Traditional pipelines composed of ``detector-descriptor, feature matcher, outlier filter, and geometric estimator'' falter in challenging scenarios. Recent deep-learning advances have significantly boosted both robustness and accuracy. This survey adopts a unique perspective by comprehensively reviewing how deep learning has incrementally transformed the classical image matching pipeline. Our taxonomy highly aligns with the traditional pipeline in two key aspects: i) the replacement of individual steps in the traditional pipeline with learnable alternatives, including learnable detector-descriptor, outlier filter, and geometric estimator; and ii) the merging of multiple steps into end-to-end learnable modules, encompassing middle-end sparse matcher, end-to-end semi-dense/dense matcher, and pose regressor. We first examine the design principles, advantages, and limitations of both aspects, and then benchmark representative methods on relative pose recovery, homography estimation, and visual localization tasks. Finally, we discuss open challenges and outline promising directions for future research. By systematically categorizing and evaluating deep learning-driven strategies, this survey offers a clear overview of the evolving image matching landscape and highlights key avenues for further innovation.

Shadow Wireless Intelligence: Large Language Model-Driven Reasoning in Covert Communications

Covert Communications (CC) can secure sensitive transmissions in industrial, military, and mission-critical applications within 6G wireless networks. However, traditional optimization methods based on Artificial Noise (AN), power control, and channel manipulation might not adapt to dynamic and adversarial environments due to the high dimensionality, nonlinearity, and stringent real-time covertness requirements. To bridge this gap, we introduce Shadow Wireless Intelligence (SWI), which integrates the reasoning capabilities of Large Language Models (LLMs) with retrieval-augmented generation to enable intelligent decision-making in covert wireless systems. Specifically, we utilize DeepSeek-R1, a mixture-of-experts-based LLM with RL-enhanced reasoning, combined with real-time retrieval of domain-specific knowledge to improve context accuracy and mitigate hallucinations. Our approach develops a structured CC knowledge base, supports context-aware retrieval, and performs semantic optimization, allowing LLMs to generate and adapt CC strategies in real time. In a case study on optimizing AN power in a full-duplex CC scenario, DeepSeek-R1 achieves 85% symbolic derivation accuracy and 94% correctness in the generation of simulation code, outperforming baseline models. These results validate SWI as a robust, interpretable, and adaptive foundation for LLM-driven intelligent covert wireless systems in 6G networks.

CoMatch: Dynamic Covisibility-Aware Transformer for Bilateral Subpixel-Level Semi-Dense Image Matching

This prospective study proposes CoMatch, a novel semi-dense image matcher with dynamic covisibility awareness and bilateral subpixel accuracy. Firstly, observing that modeling context interaction over the entire coarse feature map elicits highly redundant computation due to the neighboring representation similarity of tokens, a covisibility-guided token condenser is introduced to adaptively aggregate tokens in light of their covisibility scores that are dynamically estimated, thereby ensuring computational efficiency while improving the representational capacity of aggregated tokens simultaneously. Secondly, considering that feature interaction with massive non-covisible areas is distracting, which may degrade feature distinctiveness, a covisibility-assisted attention mechanism is deployed to selectively suppress irrelevant message broadcast from non-covisible reduced tokens, resulting in robust and compact attention to relevant rather than all ones. Thirdly, we find that at the fine-level stage, current methods adjust only the target view's keypoints to subpixel level, while those in the source view remain restricted at the coarse level and thus not informative enough, detrimental to keypoint location-sensitive usages. A simple yet potent fine correlation module is developed to refine the matching candidates in both source and target views to subpixel level, attaining attractive performance improvement. Thorough experimentation across an array of public benchmarks affirms CoMatch's promising accuracy, efficiency, and generalizability.

Learning-Based TSP-Solvers Tend to Be Overly Greedy

Deep learning has shown significant potential in solving combinatorial optimization problems such as the Euclidean traveling salesman problem (TSP). However, most training and test instances for existing TSP algorithms are generated randomly from specific distributions like uniform distribution. This has led to a lack of analysis and understanding of the performance of deep learning algorithms in out-of-distribution (OOD) generalization scenarios, which has a close relationship with the worst-case performance in the combinatorial optimization field. For data-driven algorithms, the statistical properties of randomly generated datasets are critical. This study constructs a statistical measure called nearest-neighbor density to verify the asymptotic properties of randomly generated datasets and reveal the greedy behavior of learning-based solvers, i.e., always choosing the nearest neighbor nodes to construct the solution path. Based on this statistical measure, we develop interpretable data augmentation methods that rely on distribution shifts or instance perturbations and validate that the performance of the learning-based solvers degenerates much on such augmented data. Moreover, fine-tuning learning-based solvers with augmented data further enhances their generalization abilities. In short, we decipher the limitations of learning-based TSP solvers tending to be overly greedy, which may have profound implications for AI-empowered combinatorial optimization solvers.

Towards understanding how attention mechanism works in deep learning

Attention mechanism has been extensively integrated within mainstream neural network architectures, such as Transformers and graph attention networks. Yet, its underlying working principles remain somewhat elusive. What is its essence? Are there any connections between it and traditional machine learning algorithms? In this study, we inspect the process of computing similarity using classic metrics and vector space properties in manifold learning, clustering, and supervised learning. We identify the key characteristics of similarity computation and information propagation in these methods and demonstrate that the self-attention mechanism in deep learning adheres to the same principles but operates more flexibly and adaptively. We decompose the self-attention mechanism into a learnable pseudo-metric function and an information propagation process based on similarity computation. We prove that the self-attention mechanism converges to a drift-diffusion process through continuous modeling provided the pseudo-metric is a transformation of a metric and certain reasonable assumptions hold. This equation could be transformed into a heat equation under a new metric. In addition, we give a first-order analysis of attention mechanism with a general pseudo-metric function. This study aids in understanding the effects and principle of attention mechanism through physical intuition. Finally, we propose a modified attention mechanism called metric-attention by leveraging the concept of metric learning to facilitate the ability to learn desired metrics more effectively. Experimental results demonstrate that it outperforms self-attention regarding training efficiency, accuracy, and robustness.

OTAD: An Optimal Transport-Induced Robust Model for Agnostic Adversarial Attack

Deep neural networks (DNNs) are vulnerable to small adversarial perturbations of the inputs, posing a significant challenge to their reliability and robustness. Empirical methods such as adversarial training can defend against particular attacks but remain vulnerable to more powerful attacks. Alternatively, Lipschitz networks provide certified robustness to unseen perturbations but lack sufficient expressive power. To harness the advantages of both approaches, we design a novel two-step Optimal Transport induced Adversarial Defense (OTAD) model that can fit the training data accurately while preserving the local Lipschitz continuity. First, we train a DNN with a regularizer derived from optimal transport theory, yielding a discrete optimal transport map linking data to its features. By leveraging the map's inherent regularity, we interpolate the map by solving the convex integration problem (CIP) to guarantee the local Lipschitz property. OTAD is extensible to diverse architectures of ResNet and Transformer, making it suitable for complex data. For efficient computation, the CIP can be solved through training neural networks. OTAD opens a novel avenue for developing reliable and secure deep learning systems through the regularity of optimal transport maps. Empirical results demonstrate that OTAD can outperform other robust models on diverse datasets.

Analytical Solution of a Three-layer Network with a Matrix Exponential Activation Function

In practice, deeper networks tend to be more powerful than shallow ones, but this has not been understood theoretically. In this paper, we find the analytical solution of a three-layer network with a matrix exponential activation function, i.e., $$ f(X)=W_3\exp(W_2\exp(W_1X)), X\in \mathbb{C}^{d\times d} $$ have analytical solutions for the equations $$ Y_1=f(X_1),Y_2=f(X_2) $$ for $X_1,X_2,Y_1,Y_2$ with only invertible assumptions. Our proof shows the power of depth and the use of a non-linear activation function, since one layer network can only solve one equation,i.e.,$Y=WX$.

Progressive Feedforward Collapse of ResNet Training

Neural collapse (NC) is a simple and symmetric phenomenon for deep neural networks (DNNs) at the terminal phase of training, where the last-layer features collapse to their class means and form a simplex equiangular tight frame aligning with the classifier vectors. However, the relationship of the last-layer features to the data and intermediate layers during training remains unexplored. To this end, we characterize the geometry of intermediate layers of ResNet and propose a novel conjecture, progressive feedforward collapse (PFC), claiming the degree of collapse increases during the forward propagation of DNNs. We derive a transparent model for the well-trained ResNet according to that ResNet with weight decay approximates the geodesic curve in Wasserstein space at the terminal phase. The metrics of PFC indeed monotonically decrease across depth on various datasets. We propose a new surrogate model, multilayer unconstrained feature model (MUFM), connecting intermediate layers by an optimal transport regularizer. The optimal solution of MUFM is inconsistent with NC but is more concentrated relative to the input data. Overall, this study extends NC to PFC to model the collapse phenomenon of intermediate layers and its dependence on the input data, shedding light on the theoretical understanding of ResNet in classification problems.