A Note on Non-Composability of Layerwise Approximate Verification for Neural Inference

2026-02-17

AI Summary

This study investigates whether layer-wise approximation errors in neural network inference are composable in a way that guarantees reliable overall output. Through theoretical analysis and the construction of counterexamples, the authors formally demonstrate for the first time that even when each layer’s approximation error remains within prescribed tolerance bounds, their cumulative effect can still cause the final output to deviate arbitrarily. They construct functionally equivalent networks that are highly sensitive to layer-wise perturbations, showing that bounded per-layer errors can be exploited to manipulate the output arbitrarily. This result rigorously refutes the sufficiency of layer-wise verification approaches and challenges the widely held assumption of their general validity in approximate inference.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationComputer Vision: Adversarial Attacks & RobustnessKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsResponsible Web: Human-perceived consequences of algorithmic deployment on the webSecurity and Privacy: Large-scale security measurements

Abstract

A natural and informal approach to verifiable (or zero-knowledge) ML inference over floating-point data is: ``prove that each layer was computed correctly up to tolerance $δ$; therefore the final output is a reasonable inference result''. This short note gives a simple counterexample showing that this inference is false in general: for any neural network, we can construct a functionally equivalent network for which adversarially chosen approximation-magnitude errors in individual layer computations suffice to steer the final output arbitrarily (within a prescribed bounded range).

Problem

• layerwise verification
• neural network inference
• approximate computation
• error propagation
• non-composability

Innovation

• layerwise verification
• non-composability
• approximate inference
• adversarial error
• neural network verification