6arXiv cs.LG (Machine Learning)·
Super Weights in LLMs are not selectively trainable despite high importance
A new arXiv paper investigates Super Weights — individual LLM parameters whose removal catastrophically degrades performance — and finds that their apparent importance does not translate into trainability. Training Super Weights in isolation (100 to 8,192 parameters) collapses accuracy to random-guessing on OLMo-1B and OLMo-7B, while training an equal number of randomly chosen parameters in the same layers improves over baseline. LoRA, which applies structured low-rank updates across entire layers, succeeds with only 0.16% of parameters, and constraining LoRA updates at Super Weight coordinates yields no benefit. The findings challenge the assumption that parameter importance implies parameter trainability and suggest effective fine-tuning requires structured decompositions over full layers rather than targeted sparse updates.
Related guides (3)
Related events (8)
Local linear structures in LLM weights and activations are dynamic, not fixed global directions
A new arXiv paper investigates the nature of linear structures in transformer weights and activations, finding strong local low-rank task-gradient structure but rejecting the hypothesis that fixed task planes exist. The authors show that useful bases drift substantially within 100 optimization steps, yet early recovery updates form a trajectory-prefix basis capturing 77% of LoRA recovery displacement. They also establish a formal connection between parameter perturbations and activation steering, finding a 0.58 cosine similarity between gradient-step-induced activation shifts and CAA steering vectors, suggesting linear structures are evolving local geometries rather than stable global task directions.
PC Layer: Polynomial weight preconditioning for stable LLM pre-training
Researchers propose a PC (preconditioning) layer that applies polynomial preconditioning to reshape the singular-value spectrum of weight matrices during LLM training, improving conditioning stability. The preconditioned weights merge back into the original architecture at inference time with no overhead. Experiments on Llama-1B pre-training show advantages over standard transformers for both AdamW and Muon optimizers, with theoretical convergence guarantees for deep linear networks.
PALS: Percentile-aware per-layer sparsity improves LLM pruning on LLaMA-2 but not universally
PALS (Percentile-Aware Layerwise Sparsity) is a one-shot pruning method that assigns per-layer sparsity ratios based on the 99th percentile of activation magnitudes, bounded within ±5% of a target ratio. On LLaMA-2-7B at 50% sparsity, PALS achieves perplexity of 10.96 vs. 12.92 for uniform Wanda, a statistically significant improvement requiring no fine-tuning. However, gains are architecture-dependent: LLaMA-3-8B shows marginal improvement and Mistral-7B shows none. A notable negative finding is that gradient-based allocation performs worse than random, suggesting gradient magnitude is a poor proxy for the impact of discrete weight removal.
LACUNA testbed introduces ground-truth parameter-level evaluation for LLM unlearning
Researchers introduce LACUNA, the first unlearning testbed with ground-truth parameter-level localization, designed to evaluate whether LLM unlearning methods truly erase knowledge from model weights or merely suppress it at the output level. The testbed injects PII of synthetic individuals into predefined parameters of 1B and 7B OLMo-based models via masked continual pretraining, enabling direct measurement of localization precision. Benchmarking current SOTA unlearning methods reveals they are highly imprecise and vulnerable to resurfacing attacks despite strong output-level performance, while successful localization enables even simple gradient-based methods to achieve robust erasure. The work addresses a critical gap in unlearning evaluation methodology relevant to privacy compliance and AI safety.
Quantifying Hyperparameter Transfer: Embedding Layer Learning Rate as Key Driver of μP Benefits
This paper develops a three-metric framework to quantify hyperparameter transfer quality across model scales, targeting the problem of extrapolating optimal hyperparameters from small to large LLMs. The central empirical finding is that the well-known advantage of Maximal Update Parameterization (μP) over standard parameterization (SP) with AdamW largely reduces to a single factor: the embedding layer learning rate. In SP, the embedding layer acts as a training bottleneck causing instabilities; scaling its learning rate by model width to match μP substantially stabilizes training and improves transfer. The paper also characterizes how weight decay affects scaling law fit quality versus extrapolation robustness in opposite directions.
Parametric Memory Law for LoRA Finetuning: Quantifying LLM Memory Capacity
This paper introduces the Parametric Memory Law, a power-law relationship linking loss reduction to effective parameters and sequence length during LoRA-based LLM finetuning. The authors identify a phase transition at the token level where prediction probability p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Building on these findings, they propose MemFT, a threshold-guided optimization strategy that dynamically reallocates training budget toward sub-threshold tokens, improving memory fidelity and efficiency.
Analysis-driven transformer linearization outperforms prior baselines on LLaMA and Qwen up to 32B
A new arXiv paper analyzes why post-hoc linearization of causal self-attention degrades model quality, identifying key-dependent rank-1 orthogonal projections as the mechanism softmax relies on and explaining why delta-style networks outperform gated accumulation. The authors introduce structural interventions—sink tokens, short convolutions, and fixed-budget cache routing—applied in a frozen-backbone regime. Scaling across LLaMA and Qwen models up to 32B parameters, the approach outperforms prior post-hoc linearization baselines on MMLU and matches long-context retrieval of adaptive-caching frameworks.
RELEX: Extrapolating LLM RLVR Training via Rank-1 Parameter Trajectories
This paper demonstrates that RLVR weight update trajectories are extremely low-rank and near-linearly predictable, with a rank-1 approximation capturing most downstream performance gains. The authors propose RELEX, a compute-efficient method that observes a short training window, estimates the rank-1 subspace, and extrapolates future checkpoints via linear regression—requiring no additional training. Evaluated on Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base, RELEX matches or exceeds full RLVR performance using as few as 15% of training steps, and can extrapolate up to 10–20× beyond the observed prefix. The authors attribute the method's effectiveness to a denoising effect from rank-1 projection that discards stochastic optimization noise.