Low-rank LLM compression usually allocates rank per layer by hand, so FermiGrad turns it into a differentiable optimisation and adds a domain-targeted mode
AspireAI community · arXiv (cs.LG)
FermiGrad formulates global layer-wise rank allocation as a differentiable problem by replacing discrete singular-value truncation with continuous Fermi gates, and optimises only rank parameters over precomputed low-rank factors, which avoids repeated activation decompositions and backpropagation through the SVD. A task-specific variant directs limited capacity at a chosen domain: at 60 percent parameter density for Llama-3.1-8B-Instruct, SciQ-targeted compression reached 60 percent MMLU accuracy, 10 percentage points above the reported quantized Dobi-SVD result, while deliberately trading away performance on unrelated tasks. The framework also compresses Llama-3.3-70B-Instruct to 50 percent parameter density.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.