In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in ℓ2, ℓ1, and ℓ norms. Notably, this framework includes the important case where the function outputs are symmetric matrices, and sensitivity is measured in the Frobenius, nuclear, or spectral norm. We further derive private algorithms for solving symmetric cone programs under various settings, using a combination of the multiplicative weights update method and our generic Gaussian mechanism. As an application, we present differentially private algorithms for semidefinite programming, resolving a major open question posed by [Hsu, Roth, Roughgarden, and Ullman, ICALP 2014].

Point cloud completion is essential for robust 3D perception in safety-critical applications such as robotics and augmented reality. However, existing models perform static inference and rely heavily on inductive biases learned during training, limiting their ability to adapt to novel structural patterns and sensor-induced distortions at test time. To address this limitation, we propose PointMAC, a meta-learned framework for robust test-time adaptation in point cloud completion. It enables sample-specific refinement without requiring additional supervision. Our method optimizes the completion model under two self-supervised auxiliary objectives that simulate structural and sensor-level incompleteness.

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior knowledge in non-hybrid settings, overlooking the crucial integration of observational data, and are frequently limited to linear systems, unlike the prevalent nonlinear nature of many real-world applications. To address these limitations, we introduce a unified residual form that unifies collocation and variational methods, enabling the incorporation of incomplete and complex physical constraints in hybrid learning settings. Within this formulation, we establish that the generalization performance of physics-informed regression in such hybrid settings is governed by the dimension of the affine variety associated with the physical constraint, rather than by the number of parameters. This enables a unified analysis that is applicable to both linear and nonlinear equations. We also present a method to approximate this dimension and provide experimental validation of our theoretical findings.

Out-of-distribution (OOD) detection is crucial for ensuring the reliability and safety of machine learning models in real-world applications, where they frequently face data distributions unseen during training. Despite progress, existing methods are often vulnerable to spurious correlations that mislead models and compromise robustness. To address this, we propose SPROD, a novel prototype-based OOD detection approach that explicitly addresses the challenge posed by unknown spurious correlations. Our post-hoc method refines class prototypes to mitigate bias from spurious features without additional data or hyperparameter tuning, and is broadly applicable across diverse backbones and OOD detection settings. We conduct a comprehensive spurious correlation OOD detection benchmarking, comparing our method against existing approaches and demonstrating its superior performance across challenging OOD datasets, such as CelebA, Waterbirds, UrbanCars, Spurious Imagenet, and the newly introduced Animals MetaCoCo. On average, SPROD improves AUROC by 4.8% and FPR@95 by 9.4% over the second best.

Cyclic peptides exhibit better binding affinity and proteolytic stability compared to their linear counterparts. However, the development of cyclic peptide design models is hindered by the scarcity of data. To address this, we introduce CPSea(Cyclic Peptide Sea), a dataset of 2.71 million cyclic peptide-receptor complexes, curated through systematic mining of the AlphaFold Database (AFDB). Our pipeline extracts compact domains from AFDB, identifies cyclization sites using the β-carbon (Cβ) distance thresholds, and applies multi-stage filtering to ensure structure fidelity and binding compatibility. Compared with experimental data of cyclic peptides, CPSea shows similar distributions in metrics on structure fidelity and wet-lab compatibility. To our knowledge, CPSea is the largest cyclic peptide-receptor dataset to date, enabling end-to-end model training for the first time.

The ability to selectively remove knowledge from LLMs is highly desirable. However, existing methods often struggle with balancing unlearning efficacy and retain model utility, and lack controllability at inference time to emulate base model behavior as if it had never seen the unlearned data. In this paper, we propose LUNAR, a novel unlearning method grounded in the Linear Representation Hypothesis and operates by redirecting the representations of unlearned data to activation regions that expresses its inability to answer. We show that contrastive features are not a prerequisite for effective activation redirection, and LUNARachieves state-of-the-art unlearning performance and superior controllability. Specifically, LUNARachieves between 2.9 and 11.7 improvement in the combined unlearning efficacy and model utility score (Deviation Score) across various base models and generates coherent, contextually appropriate responses post-unlearning. Moreover, LUNAR effectively reduces parameter updates to a single down-projection matrix, a novel design that significantly enhances efficiency by 20 and robustness. Finally, we demonstrate that LUNARis robust to white-box adversarial attacks and versatile in real-world scenarios, including handling sequential unlearning requests.

The sensitivity of optimal transport (OT) to noise has motivated the study of robust variants. In this paper, we study two such formulations of semi-discrete OT in Rd: (i) the α-optimal partial transport, which minimizes the cost of transporting a mass of α; and (ii) the λ-robust optimal transport, which regularizes the OT problem using the total variation (TV) distance. First, we provide a novel characterization of the optimal solutions in these settings, showing they can be represented as a restricted Laguerre diagram. Second, we exploit this characterization to establish a strong algorithmic connection between the two problems, showing that any solver for one can be adapted to solve the other with comparable precision. Third, we overcome key challenges posed in extending the cost-scaling paradigm to compute these variants of OT and present an algorithm that computes the exact solution up to log(1/ε) bits of precision in nO(d) log(1/ε) time, where nis the support size of the discrete distribution.

Gradient-based data attribution methods, such as influence functions, are critical for understanding the impact of individual training samples without requiring repeated model retraining. However, their scalability is often limited by the high computational and memory costs associated with per-sample gradient computation. In this work, we propose GRASS, a novel gradient compression algorithm and its variants FACTGRASS for linear layers specifically, that explicitly leverage the inherent sparsity of per-sample gradients to achieve sub-linear space and time complexity. Extensive experiments demonstrate the effectiveness of our approach, achieving substantial speedups while preserving data influence fidelity. In particular, FACTGRASS achieves up to 165% faster throughput on billion-scale models compared to the previous state-of-the-art baselines.

Interpreting deep neural networks through concept-based explanations offers a bridge between low-level features and high-level human-understandable semantics. However, existing automatic concept discovery methods often fail to align these extracted concepts with the model's true decision-making process, thereby compromising explanation faithfulness. In this work, we propose FACE (Faithful Automatic Concept Extraction), a novel framework that augments Non-negative Matrix Factorization (NMF) with a Kullback-Leibler (KL) divergence regularization term to ensure alignment between the model's original and concept-based predictions. Unlike prior methods that operate solely on encoder activations, FACE incorporates classifier supervision during concept learning, enforcing predictive consistency and enabling faithful explanations. We provide theoretical guarantees showing that minimizing the KL divergence bounds the deviation in predictive distributions, thereby promoting faithful local linearity in the learned concept space. Systematic evaluations on ImageNet, COCO, and CelebA datasets demonstrate that FACE outperforms existing methods across faithfulness and sparsity metrics.

The empirical emergence of neural collapse--a surprising symmetry in the feature representations of the training data in the penultimate layer of deep neural networks--has spurred a line of theoretical research aimed at its understanding. However, existing work focuses on data-agnostic models or, when data structure is taken into account, it remains limited to multi-layer perceptrons. Our paper fills both these gaps by analyzing modern architectures in a data-aware regime: we prove that global optima of deep regularized transformers and residual networks (ResNets) with LayerNorm trained with cross entropy or mean squared error loss are approximately collapsed, and the approximation gets tighter as the depth grows. More generally, we formally reduce any end-to-end large-depth ResNet or transformer training into an equivalent unconstrained features model, thus justifying its wide use in the literature even beyond data-agnostic settings. Our theoretical results are supported by experiments on computer vision and language datasets showing that, as the depth grows, neural collapse indeed becomes more prominent.