Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget.

Fraudulent activities have caused substantial negative social impacts and are exhibiting emerging characteristics such as intelligence and industrialization, posing challenges of high-order interactions, intricate dependencies, and the sparse yet concealed nature of fraudulent entities. Existing graph fraud detectors are limited by their narrow "receptive fields", as they focus only on the relations between an entity and its neighbors while neglecting longer-range structural associations hidden between entities. To address this issue, we propose a novel fraud detector based on Graph Path Aggregation (GPA). It operates through variable-length path sampling, semantic-associated path encoding, path interaction and aggregation, and aggregation-enhanced fraud detection. To further facilitate interpretable association analysis, we synthesize G-Internet, the first benchmark dataset in the field of internet fraud detection. Extensive experiments across datasets in multiple fraud scenarios demonstrate that the proposed GPA outperforms mainstream fraud detectors by up to +15% in Average Precision (AP). Additionally, GPA exhibits enhanced robustness to noisy labels and provides excellent interpretability by uncovering implicit fraudulent patterns across broader contexts.

In this manuscript, we analyze a solvable model of flow or diffusion-based generative model. We consider the problem of learning a model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a highdimensional target density with an underlying low-dimensional manifold structure. We derive a tight asymptotic characterization of low-dimensional projections of the distribution of samples generated by the learned model, ascertaining in particular its dependence on the number of training samples. Building on this analysis, we discuss how mode collapse can arise, and lead to model collapse when the generative model is re-trained on generated synthetic data.

Ensemble learning is a popular technique to improve the accuracy of machine learning models. It traditionally hinges on the rationale that aggregating multiple weak models can lead to better models with lower variance and hence higher stability, especially for discontinuous base learners. In this paper, we provide a new perspective on ensembling. By selecting the most frequently generated model from the base learner when repeatedly applied to subsamples, we can attain exponentially decaying tails for the excess risk, even if the base learner suffers from slow (i.e., polynomial) decay rates. This tail enhancement power of ensembling applies to base learners that have reasonable predictive power to begin with and is stronger than variance reduction in the sense of exhibiting rate improvement. We demonstrate how our ensemble methods can substantially improve out-of-sample performances in a range of numerical examples involving heavy-tailed data or intrinsically slow rates.

A reliable estimate of the full conditional distribution of a multivariate response given a set of covariates is essential in many decision-making applications. However, misspecified or miscalibrated models can lead to poor approximations of the joint distribution, resulting in unreliable predictions and suboptimal decisions. Standard recalibration methods are largely restricted to univariate settings, and while conformal prediction techniques yield multivariate regions with coverage guarantees, they do not provide an explicit form of the underlying probability distribution. We address this gap by first introducing a novel notion of latent calibration, which assesses probabilistic calibration in the latent space of conditional invertible generative models such as normalizing flows and flow matching. Second, we propose latent recalibration (LR), a post-hoc model recalibration method that learns a transformation of the latent space with finite-sample bounds on latent calibration. Unlike existing recalibration methods, LR produces a recalibrated distribution with an explicit multivariate density function while remaining computationally efficient. Extensive experiments on both tabular and image datasets show that LR consistently improves latent calibration error and the negative log-likelihood of the recalibrated models.

We study the robust geometric median problem in Euclidean space Rd, with a focus on coreset construction. A coreset is a compact summary of a dataset P of size n that approximates the robust cost for all centers c within a multiplicative error ε.

What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained from small initialization. Prior works have shown that gradient flow in this regime exhibits a staircase-like loss curve, alternating between plateaus where neurons slowly align to useful directions and sharp drops where neurons rapidly grow in norm. AGF approximates this behavior as an alternating two-step process: maximizing a utility function over dormant neurons and minimizing a cost function over active ones. AGF begins with all neurons dormant.

Large language models (LLMs) suffer from forgetting of upstream knowledge when fine-tuned. Despite efforts on mitigating forgetting, few have investigated how forgotten upstream examples are dependent on newly learned tasks. Insights on such dependencies enable efficient and targeted mitigation of forgetting. In this paper, we empirically analyze forgetting that occurs in N upstream examples of language modeling or instruction-tuning after fine-tuning LLMs on one of M new tasks, visualized in M N matrices. We show that the matrices are often well-approximated with low-rank matrices, indicating the dominance of simple associations between the learned tasks and forgotten upstream examples. Leveraging the analysis, we predict forgetting of upstream examples when fine-tuning LLMs on unseen tasks with matrix completion over the empirical associations. This enables fast identification of most forgotten examples without expensive inference on the entire upstream data. Despite simplicity, the approach outperforms prior approaches that learn semantic relationships of learned tasks and upstream examples with LMs. We demonstrate the practical utility of our analysis by showing statistically significantly reduced forgetting as we upweight predicted examples for replay during fine-tuning.

Predicting interactions between biochemical entities is a core challenge in drug discovery and systems biology, often hindered by limited data and poor generalization to unseen entities. Traditional discriminative models frequently underperform in such settings. We propose BioCG (Biochemical Constrained Generation), a novel framework that reformulates interaction prediction as a constrained sequence generation task. BioCG encodes target entities as unique discrete sequences via Iterative Residual Vector Quantization (I-RVQ) and trains a generative model to produce the sequence of an interacting partner given a query entity. A trie-guided constrained decoding mechanism, built from a catalog of valid target sequences, concentrates the model's learning on the critical distinctions between valid biochemical options, ensuring all outputs correspond to an entity within the pre-defined target catalog. An information-weighted training objective further focuses learning on the most critical decision points. BioCG achieves state-of-the-art (SOTA) performance across diverse tasks, Drug-Target Interaction (DTI), Drug-Drug Interaction (DDI), and Enzyme-Reaction Prediction, especially in data-scarce and cold-start conditions.

This paper studies the problem of learning hash codes from noisy supervision, which is a practical yet challenging task. This problem is important in extensive real-world applications such as image retrieval and cross-modal retrieval. However, most of the existing methods focus on label denoising to address this problem, but ignore the geometric structure of the hash space, which is critical for learning stable hash codes. Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. Specifically, we first learn dynamic class prototypes as semantic anchors and cluster hash embeddings around these prototypes to keep structural stability. We then leverage both the energy of predicted distributions and structure-based divergence to estimate the uncertainty of instances and calibrate the supervision in a soft manner. Moreover, we introduce structure-aware interpolation to improve the class boundaries. To verify the effectiveness of our design, we give the theoretical analysis for the proposed framework. Experiments on a range of widely-used retrieval datasets justify the superiority of our SEGA over extensive strong baselines under noisy supervision.