Beyond Scalar Probes: Exploiting Vector-Valued Outputs in ReLU Networks For Signature Extraction

2026-09-28

AI Summary

This study addresses the challenges of incomplete scalar output information and extraction difficulties under low-precision settings in ReLU network cryptanalysis. We propose a vector-valued analytical framework from both geometric and algebraic perspectives. By exploiting the rank-one characterization of Jacobian differences across adjacent linear regions, our method recovers row signatures and transcends traditional single-component limitations to extract complementary column-side information. This formulation effectively extends the analysis to low-precision scenarios such as float16. The proposed approach significantly enhances numerical estimation stability across multiple precision levels and improves the overall effectiveness of network signature extraction.

Abstract

We revisit cryptanalytic extraction of ReLU networks from a geometric and algebraic perspective. Rather than restricting attention to a single output component, we study the full vector-valued behavior across adjacent linear regions. This leads to a rank-one characterization of Jacobian differences that recovers the usual row-signature information while also revealing complementary column-side information. Our experiments show how this additional structure can be used in ex- traction and improves numerical estimation under different numerical- precision regimes (float64, float32 and float16). We extend the analysis beyond the high-precision and output-rounding settings commonly con- sidered in the literature towards the low-precision settings encountered in many practical settings.

Problem

• ReLU network extraction
• cryptanalysis
• vector-valued outputs
• low numerical precision
• signature extraction

Innovation

• Vector-Valued Outputs
• Rank-One Characterization
• Signature Extraction
• Jacobian Differences
• Low-Precision Regimes