Modes of Sequence Models and Learning Coefficients

• URL: http://arxiv.org/abs/2504.18048v1
• Date: Fri, 25 Apr 2025 03:38:10 GMT
• Title: Modes of Sequence Models and Learning Coefficients
• Authors: Zhongtian Chen, Daniel Murfet,
• Abstract summary: We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks.<n>We show theoretically that Local Learning Coefficient estimates are insensitive to modes below a data-dependent threshold.<n>This insight clarifies why reliable LLC estimates can be obtained even when a network parameter is not a strict minimiser of the population loss.
• Score: 0.6906005491572401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks. First, we cast conditional sequence distributions into a Hilbert-space framework and apply tensor decompositions to identify their principal modes. Truncating the small-amplitude modes yields an effective data distribution that preserves dominant structure while discarding statistical detail. Second, we show theoretically that Local Learning Coefficient (LLC) estimates are insensitive to modes below a data-dependent threshold. Consequently, the LLC calculated in practice characterises the geometry of the effective rather than the true distribution. This insight clarifies why reliable LLC estimates can be obtained even when a network parameter is not a strict minimiser of the population loss, and it highlights how the inverse temperature in SGLD acts as a resolution dial on the landscape structure.

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