fallrisk-ai
Published March 20, 2026 | Version v1
Preprint Open

Where Identity Comes From — Path Sensitivity and Endpoint Underdetermination in Neural Network Training

Authors/Creators

  • 1. Fall Risk Research

Description

Structural identity — the geometric fingerprint that makes a neural network this specific model rather than any other — can be measured, survives routine deformation, resists adversarial erasure, and composes with standard verification infrastructure. It cannot, in the tested regime, be recovered from endpoint weight statistics or architecture descriptors alone. These two facts together force a question the measurement program has not yet answered: if identity is real but not readable from the final artifact, then where in the training process did it form, and what determined which identity formed rather than another?
 
This paper presents the first empirical study of structural identity formation during neural network pretraining. Using dense checkpoint trajectories and seed-controlled training runs in the Pythia observatory suite, we show three results. First, the structural observable follows a characteristic three-phase identity emergence profile — an early rise in geometric spread, a long compression, and a late plateau where identity stabilizes while functional training continues. Second, models trained with the same architecture, the same data, and the same hyperparameters but different random seeds produce structurally distinguishable fingerprints far beyond measurement noise — a property we call path sensitivity — with the divergence traceable to differential structural response during the learning-rate warmup regime. Third, a panel of endpoint weight statistics varies across seeds but does not predict which structural identity formed — a condition we call endpoint underdetermination. Together, these results recast structural identity as a developmental property of training history rather than a static property legible from final artifacts alone.
 
Supplementary Material

This paper is accompanied by HistoricalIdentity.v, a Coq proof file that formalizes two consequences of the formation data described in §§3–5: trajectory non-recovery (no decision procedure restricted to the tested endpoint summary panel can be both sound and complete for claims about the formative training-history class that produced a model's structural identity) and lock boundary source exclusion (if structural divergence between two specification-identical models is already present at the lock boundary, no intervention applied after that boundary can be its source). The file contains 4 empirical axioms grounded in the measurements of §§3–5, 4 theorems, 1 corollary, and 0 unresolved obligations (Admitted). It compiles cleanly under the Rocq Prover 9.1.1 (the current release of the Coq proof assistant, compiled with OCaml 5.4.0). It is available for download as a supplementary file attached to this record.

 

The Neural Network Identity Series — Mathematical foundations, empirical validation, and governance frameworks for verifying which model is running

Newest addition:

Technical Note: The Disappearing Window — AI Logprob Access Withdrawal and the Structural Verifiability of Frontier Model Contracts (DOI: 10.5281/zenodo.20362098)

  1. Paper 1: The δ-Gene: Inference-Time Physical Unclonable Functions from Architecture-Invariant Output Geometry (DOI: 10.5281/zenodo.18704275)

  2. Paper 2: Template-Based Endpoint Verification via Logprob Order-Statistic Geometry (DOI: 10.5281/zenodo.18776711)

  3. Paper 3: The Geometry of Model Theft: Distillation Forensics, Adversarial Erasure, and the Illusion of Spoofing (DOI: 10.5281/zenodo.18818608)

  4. Paper 4: Provenance Generalization and Verification Scaling for Neural Network Forensics (DOI: 10.5281/zenodo.18872071)

  5. Paper 5: Beneath the Character: The Structural Identity of Neural Networks — Mathematical Evidence for a Non-Narrative Layer of AI Identity (DOI: 10.5281/zenodo.18907292)

  6. Paper 6: Which Model Is Running?: Structural Identity as a Prerequisite for Trustworthy Zero-Knowledge Machine Learning (DOI: 10.5281/zenodo.19008116)

  7. Paper 7: The Deformation Laws of Neural Identity (DOI: 10.5281/zenodo.19055966) 

  8. Paper 8: What Counts as Proof? — Admissible Evidence for Neural Network Identity Claims (DOI: 10.5281/zenodo.19058540)

  9. Paper 9: Composable Model Identity — Formal Hardening of Structural Attestations in the Enterprise Identity Stack (DOI: 10.5281/zenodo.19099911) 

  10. Paper 10:Where Identity Comes From: Path Sensitivity and Endpoint Underdetermination in Neural Network Training (DOI: 10.5281/zenodo.19118807)

  11. Paper 11: Post-Hoc Disclosure Is Not Runtime Proof: Model Identity at Frontier Scale (DOI: 10.5281/zenodo.19216634)

  12. Paper 12: Family-Dependent Response to Reasoning Distillation Across Structural and Functional Identity Layers (DOI: 10.5281/zenodo.19298857)
  13. Paper 13: Safety-Alignment Removal as a Model-Identity Failure — Structural Evidence from Published Weight-Level Mutation Checkpoints (DOI: 10.5281/zenodo.19383019)

Copyright (c) 2026 Anthony Ray Coslett / Fall Risk AI, LLC. All Rights Reserved.

Confidential and Proprietary.

Patent Pending (Applications 63/982,893, 63/990,487, 63/996,680, 64/003,244).

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Additional details

Identifiers

URL
https://fallrisk.ai

Continues
Preprint: 10.5281/zenodo.18704275 (DOI)
Preprint: 10.5281/zenodo.18818608 (DOI)
Preprint: 10.5281/zenodo.18872071 (DOI)
Preprint: 10.5281/zenodo.18907293 (DOI)
Preprint: 10.5281/zenodo.19008116 (DOI)
Preprint: 10.5281/zenodo.19055966 (DOI)
Preprint: 10.5281/zenodo.19058540 (DOI)
Preprint: 10.5281/zenodo.19099911 (DOI)
Preprint: 10.5281/zenodo.18704275 (DOI)
Is continued by
Preprint: 10.5281/zenodo.19216634 (DOI)
Preprint: 10.5281/zenodo.19298857 (DOI)
Technical note: 10.5281/zenodo.19342848 (DOI)
Preprint: 10.5281/zenodo.19383019 (DOI)
Is supplemented by
Software: 10.5281/zenodo.18930621 (DOI)
Technical note: 10.5281/zenodo.19240883 (DOI)
Technical note: 10.5281/zenodo.19275524 (DOI)
Technical note: 10.5281/zenodo.20019127 (DOI)

Software

Repository URL
https://github.com/fallrisk-ai/trustfall-lite
Development Status
Active