# Fiber Fingerprints of Hidden Learning-State Dynamics

arXiv: https://arxiv.org/abs/2608.15976 · HTML: https://mlsanity.com/paper/2608.15976/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Commute Your Domains: Trajectory Optimality Criterion for Multi-Domain Learning](https://mlsanity.com/paper/2501.15556/) (2025)
- [The Geometry of Sequential Learning: Lie-Bracket Prediction of Transfer Order](https://mlsanity.com/paper/2606.24993/) (2026)
- [Optimizer Memory Makes Shuffle Order a First-Order Source of Fine-Tuning Noise](https://mlsanity.com/paper/2606.29554/) (2026)
- [Path-conditioned training: a principled way to rescale ReLU neural networks](https://mlsanity.com/paper/2602.19799/) (2026)
- [Predicting Plasticity in Deep Continual Learning: A Theoretical Perspective](https://mlsanity.com/paper/2605.09044/) (2026)
- [DynaMiCS: Fine-tuning LLMs with Performance Constraints using Dynamic Mixtures](https://mlsanity.com/paper/2605.10770/) (2026)
- [First-Order Predictable but Pairwise Fragile: Local Task Adaptation in Trained Transformers](https://mlsanity.com/paper/2607.16821/) (2026)
- [Learning reveals invisible structure in low-rank RNNs](https://mlsanity.com/paper/2605.04115/) (2026)
- [Re-Evaluating Continual Learning with Few-Shot Adaptation](https://mlsanity.com/paper/2606.03843/) (2026)
- [Hidden Gauge Controls Feature Specialization in ReLU Networks](https://mlsanity.com/paper/2608.06766/) (2026)

## Built on by (most cited first, 2 of 2)

- [Revelation Control](https://mlsanity.com/paper/2608.23860/) (2026)
- [Intrinsic-Extrinsic Coupling in Learning Dynamics](https://mlsanity.com/paper/2609.30185/) (2026)

## Abstract (arXiv)

A learning system can occupy execution states that are indistinguishable under every declared present-behavior readout yet respond differently to future training. We formalize this through fiber fingerprints: controlled future-learning response laws restricted to present-behavior equivalence classes. Prefix-compatible finite probes induce a predictive quotient functor, a Nerode-type minimal recursively sufficient representation, and a canonical set-level predictive fiber without assuming smoothness, reversibility, finite rank, or a manifold. Under an explicit finite-dimensional Hilbert realization, response decomposes into visible, visible-mode-reuse, and irreducible-new sectors; a history-reachability bridge retains only distinctions generated by natural training histories. Conditional mechanism results then identify a graph-Hodge chronology decomposition, a regular switching class with root-mean-square scale √pη3/2 and finite-scale corrections, and an exact Adam moment section whose immediate adaptive field is constant while common future gradients can reveal hidden moment differences. Frozen Transformer--LoRA--AdamW studies with Qwen2.5-7B and Mistral-7B-v0.3 support a local action backbone, longer-horizon first-return non-closure, and fresh visible-relative completion with output-range reuse and a low-rank irreducible sector. Stronger claims remain bounded by preregistered negative or mixed results: re-anchored transport is unresolved above its measurement floor; the strict finite-grid Hodge--3/2 conjunction is unmet despite prospective contraction; Qwen accessibility is not established in the frozen raw moment chart; and Mistral revelation is future-context dependent rather than bank invariant. Within these support-, scale-, metric-, and context-resolved boundaries, present behavior is not a sufficient statistic for declared future learning.