Daniel Agyei Asante

Daniel Agyei Asante, Ernie Chang, Yang Li

Low-rank decomposition is a compelling approach for compressing large language models, but its effectiveness hinges on selecting which singular-vector bases to retain for a target task. Existing methods such as Basel adapt singular-value coefficients on downstream data and prune bases with small re-learned magnitudes, a heuristic that can be misaligned with task performance because it ignores the local geometry of the loss landscape. We present Basis Selection with Importance (BSI), a principled low-rank compression framework that ranks and prunes bases by directly estimating the expected loss increase incurred when each basis is removed. BSI derives a derivative-based importance score from a second-order Taylor expansion of the task loss with respect to singular values, combining first-order sensitivity and second-order curvature to quantify pruning impact. To make this criterion practical for LLMs, we develop an efficient Hessian-diagonal estimator by adapting the Hutchinson randomized-probing method to loss curvature with symmetric parameter perturbations. We provide a comprehensive theoretical analysis, including loss-increase bounds under basis pruning, explicit propagation of Hessian-diagonal estimation error into these bounds, variance characterization tied to the Hessian spectrum, high-probability sample-complexity guarantees for achieving a target estimation accuracy, and guidance on perturbation intensity. Extensive experiments on mathematical reasoning benchmarks demonstrate that BSI consistently outperforms state-of-the-art low-rank decomposition baselines, with especially strong improvements under deep compression.

Daniel Agyei Asante, Md Mokarram Chowdhury, Yang Li

Large language models (LLMs) have driven major advances across domains, yet their massive size hinders deployment in resource-constrained settings. Model compression addresses this challenge, with low-rank factorization emerging as a particularly effective method for reducing size, memory, and computation while maintaining accuracy. However, while these compressed models boast of benign performance and system-level advantages, their trustworthiness implications remain poorly understood. In this paper, we present the first comprehensive study of how low-rank factorization affects LLM trustworthiness across privacy, adversarial robustness, fairness, and ethical alignment. We evaluate multiple LLMs of different sizes and variants compressed with diverse low-rank algorithms, revealing key insights: (1) low-rank compression preserves or improves training data privacy but weakens PII protection during conversation; (2) adversarial robustness is generally preserved and often enhanced, even under deep compression; (3) ethical reasoning degrades in zero-shot settings but partially recovers with few-shot prompting; (4) fairness declines under compression. Beyond compression, we investigate how model scale and fine-tuning affect trustworthiness, as both are important in low-rank methods. To guide trustworthy compression strategies, we end our paper with a gradient-based attribution analysis to identify which layers in LLMs contribute most to adversarial robustness.

Md Mokarram Chowdhury, Daniel Agyei Asante, Ernie Chang et al.

Large language models (LLMs) achieve strong performance across many domains but are difficult to deploy in resource-constrained settings due to their size. Low-rank weight matrix compression is a popular strategy for reducing model size, typically by minimizing weight reconstruction error under the assumption that weights are low-rank. However, this assumption often does not hold in LLMs. Instead, LLM activations exhibit stronger low-rank structure-prompting a shift toward minimizing activation reconstruction error. We show that this shift alone is insufficient: activation dimensions contribute unequally to model performance, and uniform reconstruction can harm performance. We propose IMPACT, a principled framework for importance-aware activation reconstruction that links model compression decisions to their impact on model behavior. IMPACT formulates an optimization problem that considers both activation structure and gradient sensitivity, and derives a closed-form solution where the optimal reconstruction bases are the eigenvectors of an importance-weighted activation covariance matrix. This enables low-rank approximations explicitly optimized to preserve accuracy. Experiments across diverse models and tasks show that IMPACT achieves up to 48.6% greater model size reduction with accuracy comparable to state-of-the-art baselines.