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arxiv 2509.25359 v2 pith:FH3PEACH submitted 2025-09-29 cs.CL cs.AI

Geometric Metrics and LLMs: What They Measure and When They Work

classification cs.CL cs.AI
keywords metricsgeometrictextstatisticstheyeightintrinsic-dimensionalitylength
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We present a systematic stress-test of geometric metrics for LLM evaluation. Rank-based geometric properties of internal representations have shown promise as reference-free quality signals, but the conditions under which they are reliable remain unclear. We evaluate eight commonly-used metrics: intrinsic-dimensionality estimators, spectral norms, and related quantities across six tester models (0.5-8B) and eight generators on contrasting tasks, separating genuine geometric signal from text-length effects and from what standard text statistics already capture. Three findings emerge. First, some metrics (notably Schatten Norm and MOM) mainly reflect output length, and their apparent discriminative power collapses once length is controlled. Second, geometric metrics add modest but real information beyond text statistics: combined with them, a classifier reaches 78% accuracy on 6-way generator identification versus 69% for text statistics alone. Third, rather than tracking a general notion of text quality, the metrics demonstrate only moderate association between the intrinsic-dimensionality and lexical diversity (RTTR). We give use-case-specific recommendations and identify failure detection as the most promising near-term application.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Bug or Feature$^2$: Weight Drift, Activation Sparsity and Spikes

    cs.LG 2026-05 accept novelty 7.0

    Standard losses induce negative weight drift with positive-biased activations, producing up to 90% sparsity in GPT-nano and an accuracy cliff above ~70% sparsity; clipped ReLU² and GELU² improve the tradeoff.

  2. Bug or Feature$^2$: Weight Drift, Activation Sparsity and Spikes

    cs.LG 2026-05 accept novelty 7.0

    The paper proves negative weight drift at initialization under MSE or cross-entropy with asymmetric activations, links it to up to 90% sparsity in GPT-nano, maps the sparsity-accuracy cliff across 79 configurations, a...