Organizations: University of South Florida, Tampa, FL, USA · Brandeis University, Waltham, MA, USA
Abstract
Understanding which parameters are influential in Large Language Models (LLMs) is central to improving their efficiency, reliability, and interpretability. We introduce Weight-Adjusted Gradients (WAG), a simple yet effective approach for estimating parameter importance that explicitly captures the interaction between model weights and first-order gradient information and identifies parameters that disproportionately influence model behavior, such as those responsible for collapse phenomena in LLMs. Across a range of models and settings, we show that WAG surfaces a tiny but critical subset of parameters whose modification leads to dramatic degradation in performance, a failure mode that existing importance metrics overlook. These findings reveal a previously underexplored interplay between weights and gradients, suggesting that parameter importance cannot be fully understood through either signal alone. The surprising effectiveness of WAG points to fundamental structural properties of trained networks and motivates new open questions about the role of zeroth-order and first-order information in deep learning. We demonstrate the practical utility of WAG across multiple applications, including expert allocation in mixture-of-expert architectures, parameter-specific unlearning, mixed-precision quantization, and layer selection for knowledge editing. Our results position WAG as a unified approach for analyzing, debugging, and controlling LLMs, and opens new directions for principled model-level interpretation.
Recent work identified Super Weights, individual parameters whose removal degrades model performance by orders of magnitude. We show that this degradation due to pruning Super Weights does not universally apply to all LLMs. Furthermore, if these parameters are so important, Super Weight-aware training should be effective. We show the opposite. Training Super Weights in isolation (100 to 8,192 parameters) drops accuracy to random-guessing levels on both OLMo-1B and OLMo-7B, and expanding to local neighborhoods of up to 36K parameters provides no improvement. The failure is specific to Super Weight coordinates: training an equal number of randomly chosen positions in the same down_proj layers instead improves over the baseline, so the collapse comes from targeting Super Weights, not from sparsity itself. Vanilla LoRA, updating every position in attention weight matrices through low-rank structure, succeeds with only 0.16% of parameters, and applying the same low-rank update to down_proj succeeds as well. A 10-seed ablation confirms that constraining LoRA updates at positions corresponding to Super Weight coordinates yields statistically indistinguishable results. These findings establish that parameter importance does not imply parameter trainability in isolation, and that effective fine-tuning relies on structured decompositions over entire layers rather than targeting individually important weights.
Large Language Models (LLMs) are increasingly deployed across diverse applications, raising critical questions for governance, accountability, and data provenance. Understanding which training data most influenced a model's output remains a fundamental open problem. We address this challenge through training data attribution (TDA) for auto-regressive LLMs by expanding upon the inverse formulation: How would training data be affected if the model had seen the generated output during training? Our method perturbs the base model using bidirectional gradient optimization (gradient ascent and descent) on a generated text sample and measures the resulting change in loss across training samples. Our framework supports attribution at arbitrary data granularity, enabling both factual and stylistic attribution. We evaluate our method against baselines on pretrained models with known datasets, and show that it outperforms previous work on influence metrics, thereby enhancing model interpretability, an essential requirement for accountable AI systems.
Frédéric Berdoz, Luca A. Lanzendörfer, Kaan Bayraktar +1
Continual post-training enables models to absorb emerging knowledge after deployment, but repeatedly updating shared parameters can accumulate weight drift, potentially causing catastrophic forgetting and degrading general capabilities. Retrieval-augmented generation avoids such parameter drift, yet often lacks the depth of parametric knowledge integration. In this paper, we propose ReGrad (Retrievable Gradients), a new paradigm that treats gradients as retrievable units of knowledge. ReGrad pre-computes document-specific gradients offline, stores them in an indexed Gradient Bank, and retrieves only query-relevant gradients at inference time for temporary weight adaptation. However, raw language-modeling gradients are optimized for token-level document reconstruction rather than for query-driven knowledge use. We therefore introduce a bi-level meta-learning objective that reshapes document-derived gradients into generalizable adaptation signals for downstream tasks. Experiments across general and domain-specific settings show that \textsc{ReGrad} outperforms CPT and RAG baselines, enabling scalable and reversible parametric knowledge injection without accumulating weight drift.