Artificial Intelligence

2609 Submissions

[2] ai.viXra.org:2609.0005 [pdf] submitted on 2026-09-03 23:03:35

Arnold’s Bifurcation Principle Applied to Large-Scale AI Training: Real-Time Hardware Prediction of Loss Divergence Using Hessian-Free Eigenvalue Tracking

Authors: Prakash Vaithyanathan
Comments: 7 Pages. CC BY-NC-ND 4.0

When a very large AI model is trained, the training sometimes breaks on its own. The loss suddenly jumps up, the numbers inside the model become too large or too small to handle correctly, and the run has to be stopped and restarted from an older saved copy. This is called training instability, and on a large training run it can waste a very large amount of computer time and money. Earlier work in machine learning has shown that this kind of breakdown is closely tied to a single number: the sharpness of the loss surface, which is the largest eigenvalue of the Hessian matrix of the loss function. When this number grows too large compared to the learning rate, the training stops behaving smoothly. The problem is that for a model with a billion or more parameters, the full Hessian matrix cannot be built or stored by any realmachine: it would need far more numbers than there are atoms within reach. We show that this is not actually needed. A small hardware block can track the same leading eigenvalue using only the gradient vectors that the training hardware is already computing at every step, through a standard numerical method called power iteration, combined with the well-known fact that a Hessian-vector product can be estimated from the difference between two gradients without ever building the Hessian itself. We also show that watching a small, carefully chosen part of the model, rather than the whole thing, is often enough to catch the problem early. We describe a domain-blind hardware controller that watches this shrinking safety margin every single step and estimates how many steps remain before the run is expected to become unstable, so that a corrective action can be taken before the run actually fails rather than after.
Category: Artificial Intelligence

[1] ai.viXra.org:2609.0003 [pdf] submitted on 2026-09-02 18:16:51

Structural Trust: An Uncertainty-Typed Property Hypergraph for Agent Memory

Authors: Raymond Deiotte
Comments: 42 Pages.

Agent-facing knowledgebases compute confidence and provenance at answer time, as properties of the re- sponse. This paper argues that is too late, and that the argument is not a matter of engineering quality: information about whether a claim is true enters through the primary record, and every later stage is a rendering of that record, so no downstream scoring can add a bit that the record did not already carry. Confidence computed from the exhibit has an evidential ceiling fixed before it runs.We describe the store that follows from taking that seriously. The substrate is an uncertainty-typed property hypergraph: every unit carries the same five fields, a knowledge type, provenance graded on a four-valued lattice and carrying a validity horizon, the condition under which the entry held, a version with its conflict history, and a confidence separated into write-time and serving-time quantities, and relations are hyperedges because the relations that matter in agent memory are irreducibly n-ary and reifying them into binary edges destroys exactly the structure later stages need. On that substrate we specify three mechanisms. Consolidation is gated on whether a merged region still decomposes into the inferences it was meant to support, a structural and label-free test that needs no paired QA data and no per-environment training. Conflict is preserved through four lifecycle primitives, demotion, supersession, revocation and invalidation, of which three share a single inverse transition and revocation deliberately has none. Retrieval returns a coverage-guaranteed evidence subgraph with the guarantee conditional on the type of edge retrieved rather than marginal over a query distribution, and it answers with three outcomes rather than one score: supported, insufficient, refuted.The paper’s most portable result is a criterion for when two memory mechanisms can affect each other at all: only where one writes a property of the store that the other reads, at a granularity they share. The criterion is checkable from the specifications before anything is built, it discriminates rather than merely predicting failure, and it carries a stated falsifier.
Category: Artificial Intelligence