Supply chains are integral to global economic stability, yet disruptions can swiftly propagate through interconnected networks, resulting in substantial economic impacts. Accurate and timely inference of supply chain resilience--the capability to maintain core functions during disruptions--is crucial for proactive risk mitigation and robust network design. However, existing approaches lack effective mechanisms to infer supply chain resilience without explicit system dynamics and struggle to represent the higher-order, multi-entity dependencies inherent in supply chain networks. These limitations motivate the definition of a novel problem and the development of targeted modeling solutions. To address these challenges, we formalize a novel problem: Supply Chain Resilience Inference (SCRI), defined as predicting supply chain resilience using hypergraph topology and observed inventory trajectories without explicit dynamic equations. To solve this problem, we propose the Supply Chain Resilience Inference Hypergraph Network (SC-RIHN), a novel hypergraph-based model leveraging set-based encoding and hypergraph message passing to capture multi-party firm-product interactions. Comprehensive experiments demonstrate that SC-RIHN significantly outperforms traditional MLP, representative graph neural network variants, and ResInf baselines across synthetic benchmarks, underscoring its potential for practical, early-warning risk assessment in complex supply chain systems.

Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attacks is still not quite clear. In this paper, we investigate the adversarial learning from the perturbation analysis point of view. We characterize the robustness of learning models through the calmness of the solution mapping. In the case of convex clustering models, we identify the conditions under which the clustering results remain the same under perturbations. When the noise level is large, it leads to an attack. Therefore, we propose two bilevel models for adversarial learning where the effect of adversarial learning is measured by some deviation function. Specifically, we systematically study the so-called $δ$-measure and show that under certain conditions, it can be used as a deviation function in adversarial learning for convex clustering models. Finally, we conduct numerical tests to verify the above theoretical results as well as the efficiency of the two proposed bilevel models.

The LogSumExp function, also known as the free energy, plays a central role in many important optimization problems, including entropy-regularized optimal transport and distributionally robust optimization (DRO). It is also the dual to the Kullback-Leibler (KL) divergence, which is widely used in machine learning. In practice, when the number of exponential terms inside the logarithm is large or infinite, optimization becomes challenging since computing the gradient requires differentiating every term. Previous approaches that replace the full sum with a small batch introduce significant bias. We propose a novel approximation to LogSumExp that can be efficiently optimized using stochastic gradient methods. This approximation is rooted in a sound modification of the KL divergence in the dual, resulting in a new $f$-divergence called the safe KL divergence. The accuracy of the approximation is controlled by a tunable parameter and can be made arbitrarily small. Like the LogSumExp, our approximation preserves convexity. Moreover, when applied to an $L$-smooth function bounded from below, the smoothness constant of the resulting objective scales linearly with $L$. Experiments in DRO and continuous optimal transport demonstrate the advantages of our approach over state-of-the-art baselines and the effective treatment of numerical issues associated with the standard LogSumExp and KL.

We introduce the Similarity-Distance-Magnitude (SDM) activation function, a more robust and interpretable formulation of the standard softmax activation function, adding Similarity (i.e., correctly predicted depth-matches into training) awareness and Distance-to-training-distribution awareness to the existing output Magnitude (i.e., decision-boundary) awareness, and enabling interpretability-by-exemplar via dense matching. We further introduce the SDM estimator, based on a data-driven partitioning of the class-wise empirical CDFs via the SDM activation, to control the class- and prediction-conditional accuracy among selective classifications. When used as the final-layer activation over pre-trained language models for selective classification, the SDM estimator is more robust to co-variate shifts and out-of-distribution inputs than existing calibration methods using softmax activations, while remaining informative over in-distribution data.

The Information Contrastive (I-Con) framework revealed that over 23 representation learning methods implicitly minimize KL divergence between data and learned distributions that encode similarities between data points. However, a KL-based loss may be misaligned with the true objective, and properties of KL divergence such as asymmetry and unboundedness may create optimization challenges. We present Beyond I-Con, a framework that enables systematic discovery of novel loss functions by exploring alternative statistical divergences. Key findings: (1) on unsupervised clustering of DINO-ViT embeddings, we achieve state-of-the-art results by modifying the PMI algorithm to use total variation (TV) distance; (2) supervised contrastive learning with Euclidean distance as the feature space metric is improved by replacing the standard loss function with Jenson-Shannon divergence (JSD); (3) on dimensionality reduction, we achieve superior qualitative results and better performance on downstream tasks than SNE by replacing KL with a bounded $f$-divergence. Our results highlight the importance of considering divergence choices in representation learning optimization.

Visual geo-localization for drones faces critical degradation under weather perturbations, \eg, rain and fog, where existing methods struggle with two inherent limitations: 1) Heavy reliance on limited weather categories that constrain generalization, and 2) Suboptimal disentanglement of entangled scene-weather features through pseudo weather categories. We present WeatherPrompt, a multi-modality learning paradigm that establishes weather-invariant representations through fusing the image embedding with the text context. Our framework introduces two key contributions: First, a Training-free Weather Reasoning mechanism that employs off-the-shelf large multi-modality models to synthesize multi-weather textual descriptions through human-like reasoning. It improves the scalability to unseen or complex weather, and could reflect different weather strength. Second, to better disentangle the scene and weather feature, we propose a multi-modality framework with the dynamic gating mechanism driven by the text embedding to adaptively reweight and fuse visual features across modalities. The framework is further optimized by the cross-modal objectives, including image-text contrastive learning and image-text matching, which maps the same scene with different weather conditions closer in the respresentation space. Extensive experiments validate that, under diverse weather conditions, our method achieves competitive recall rates compared to state-of-the-art drone geo-localization methods. Notably, it improves Recall@1 by +13.37\% under night conditions and by 18.69\% under fog and snow conditions.

Accurate short-term electricity price forecasting is crucial for strategically scheduling demand and generation bids in day-ahead markets. While data-driven techniques have shown considerable prowess in achieving high forecast accuracy in recent years, they rely heavily on the quality of input covariates. In this paper, we investigate whether asynchronously published prices as a result of differing gate closure times (GCTs) in some bidding zones can improve forecasting accuracy in other markets with later GCTs. Using a state-of-the-art ensemble of models, we show significant improvements of 22% and 9% in forecast accuracy in the Belgian (BE) and Swedish bidding zones (SE3) respectively, when including price data from interconnected markets with earlier GCT (Germany-Luxembourg, Austria, and Switzerland). This improvement holds for both general as well as extreme market conditions. Our analysis also yields further important insights: frequent model recalibration is necessary for maximum accuracy but comes at substantial additional computational costs, and using data from more markets does not always lead to better performance - a fact we delve deeper into with interpretability analysis of the forecast models. Overall, these findings provide valuable guidance for market participants and decision-makers aiming to optimize bidding strategies within increasingly interconnected and volatile European energy markets.

Neighbor-based methods are a natural alternative to linear prediction for tabular data when relationships between inputs and targets exhibit complexity such as nonlinearity, periodicity, or heteroscedasticity. Yet in deep learning on unstructured data, nonparametric neighbor-based approaches are rarely implemented in lieu of simple linear heads. This is primarily due to the ability of systems equipped with linear regression heads to co-learn internal representations along with the linear head's parameters. To unlock the full potential of neighbor-based methods in neural networks we introduce SoftStep, a parametric module that learns sparse instance-wise similarity measures directly from data. When integrated with existing neighbor-based methods, SoftStep enables regression models that consistently outperform linear heads across diverse architectures, domains, and training scenarios. We focus on regression tasks, where we show theoretically that neighbor-based prediction with a mean squared error objective constitutes a metric learning algorithm that induces well-structured embedding spaces. We then demonstrate analytically and empirically that this representational structure translates into superior performance when combined with the sparse, instance-wise similarity measures introduced by SoftStep. Beyond regression, SoftStep is a general method for learning instance-wise similarity in deep neural networks, with broad applicability to attention mechanisms, metric learning, representational alignment, and related paradigms.

Recent advancements in machine learning have improved performance while also increasing computational demands. While federated and distributed setups address these issues, their structures remain vulnerable to malicious influences. In this paper, we address a specific threat: Byzantine attacks, wherein compromised clients inject adversarial updates to derail global convergence. We combine the concept of trust scores with trial function methodology to dynamically filter outliers. Our methods address the critical limitations of previous approaches, allowing operation even when Byzantine nodes are in the majority. Moreover, our algorithms adapt to widely used scaled methods such as Adam and RMSProp, as well as practical scenarios, including local training and partial participation. We validate the robustness of our methods by conducting extensive experiments on both public datasets and private ECG data collected from medical institutions. Furthermore, we provide a broad theoretical analysis of our algorithms and their extensions to the aforementioned practical setups. The convergence guaranties of our methods are comparable to those of classical algorithms developed without Byzantine interference.

Cross-entropy (CE) training loss dominates deep learning practice, yet existing theory often relies on simplifications, either replacing it with squared loss or restricting to convex models, that miss essential behavior. CE and squared loss generate fundamentally different dynamics, and convex linear models cannot capture the complexities of non-convex optimization. We provide an in-depth characterization of multi-class CE optimization dynamics beyond the convex regime by analyzing a canonical two-layer linear neural network with standard-basis vectors as inputs: the simplest non-convex extension for which the implicit bias remained unknown. This model coincides with the unconstrained features model used to study neural collapse, making our work the first to prove that gradient flow on CE converges to the neural collapse geometry. We construct an explicit Lyapunov function that establishes global convergence, despite the presence of spurious critical points in the non-convex landscape. A key insight underlying our analysis is an inconspicuous finding: Hadamard Initialization diagonalizes the softmax operator, freezing the singular vectors of the weight matrices and reducing the dynamics entirely to their singular values. This technique opens a pathway for analyzing CE training dynamics well beyond our specific setting considered here.