arXiv subjects

Alex Mulrooney

Publications and source records attributed to Alex Mulrooney.

3 recordsLinked to original sources

arXiv2026

Generalized Canonical Polyadic Tensor Decompositions with General Symmetry

Canonical Polyadic (CP) tensor decomposition is a workhorse algorithm for discovering underlying low-dimensional structure in tensor data. This is accomplished in conventional CP decomposition by fitting a low-rank tensor to data with respect to the least-squares loss. Generalized CP (GCP) decompositions generalize this approach by allowing general loss functions that can be more appropriate, e.g., to model binary and count data or to improve robustness to outliers. However, GCP decompositions do not explicitly account for any symmetry in the tensors, which commonly arises in modern applications. For example, a tensor formed by stacking the adjacency matrices of a dynamic graph over time will naturally exhibit symmetry along the two modes corresponding to the graph nodes. In this paper, we develop a symmetric GCP (SymGCP) decomposition that allows for general forms of symmetry, i.e., symmetry along any subset of the modes. SymGCP accounts for symmetry by enforcing the corresponding symmetry in the decomposition. We derive gradients for SymGCP that enable its efficient computation via all-at-once optimization with existing tensor kernels. The form of the gradients also leads to various stochastic approximations that enable us to develop stochastic SymGCP algorithms that can scale to large tensors. We demonstrate the utility of the proposed SymGCP algorithms with a variety of experiments on both synthetic and real data.

math.NA↗

arXiv2025

Memory-Efficient Differentially Private Training with Gradient Random Projection

Differential privacy (DP) protects sensitive data during neural network training, but standard methods like DP-Adam suffer from high memory overhead due to per-sample gradient clipping, limiting scalability. We introduce DP-GRAPE (Gradient RAndom ProjEction), a DP training method that significantly reduces memory usage while maintaining utility on par with first-order DP approaches. DP-GRAPE is motivated by our finding that privatization flattens the gradient singular value spectrum, making SVD-based projections (as in GaLore (Zhao et al., 2024)) unnecessary. Consequently, DP-GRAPE employs three key components: (1) random Gaussian matrices replace SVD-based subspaces, (2) gradients are privatized after projection, and (3) projection is applied during backpropagation. These contributions eliminate the need for costly SVD computations, enable substantial memory savings, and lead to improved utility. Despite operating in lower-dimensional subspaces, our theoretical analysis shows that DP-GRAPE achieves a privacy-utility tradeoff comparable to DP-SGD. Our extensive empirical experiments show that DP-GRAPE can significantly reduce the memory footprint of DP training without sacrificing accuracy or training time. In particular, DP-GRAPE reduces memory usage by over 63% when pre-training Vision Transformers and over 70% when fine-tuning RoBERTa-Large as compared to DP-Adam, while achieving similar performance. We further demonstrate that DP-GRAPE scales to fine-tuning large models such as OPT with up to 6.7 billion parameters, a scale at which DP-Adam fails due to memory constraints. Our code is available at https://github.com/alexmul1114/DP_GRAPE.

cs.LG↗

arXiv2024

Contrastive Learning to Fine-Tune Feature Extraction Models for the Visual Cortex

Predicting the neural response to natural images in the visual cortex requires extracting relevant features from the images and relating those feature to the observed responses. In this work, we optimize the feature extraction in order to maximize the information shared between the image features and the neural response across voxels in a given region of interest (ROI) extracted from the BOLD signal measured by fMRI. We adapt contrastive learning (CL) to fine-tune a convolutional neural network, which was pretrained for image classification, such that a mapping of a given image's features are more similar to the corresponding fMRI response than to the responses to other images. We exploit the recently released Natural Scenes Dataset (Allen et al., 2022) as organized for the Algonauts Project (Gifford et al., 2023), which contains the high-resolution fMRI responses of eight subjects to tens of thousands of naturalistic images. We show that CL fine-tuning creates feature extraction models that enable higher encoding accuracy in early visual ROIs as compared to both the pretrained network and a baseline approach that uses a regression loss at the output of the network to tune it for fMRI response encoding. We investigate inter-subject transfer of the CL fine-tuned models, including subjects from another, lower-resolution dataset (Gong et al., 2023). We also pool subjects for fine-tuning to further improve the encoding performance. Finally, we examine the performance of the fine-tuned models on common image classification tasks, explore the landscape of ROI-specific models by applying dimensionality reduction on the Bhattacharya dissimilarity matrix created using the predictions on those tasks (Mao et al., 2024), and investigate lateralization of the processing for early visual ROIs using salience maps of the classifiers built on the CL-tuned models.

cs.CV↗