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.

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