When Can Depth Replace Precision? A Resource Theory of Quantized Neural Computation

What the math gives to ML

This paper provides a resource-theoretic way to reason about low-bit residual networks: extra depth can reduce synthesis error only down to the distance from the target map to the closed relaxed reachable set of the declared operation library. The most directly transferable mechanism is increment error feedback, which prevents quantization errors from accumulating linearly across residual steps and instead yields a telescoping carry term. Its explicit decomposition of structural, scheduling, metadata, and execution-arithmetic errors also suggests a practical pre-training feasibility screen that can avoid training architectures incapable of meeting a target accuracy. The strongest initial experiments should compare ordinary quantized residual write-back against lattice-compatible error-feedback residual blocks, and use the paper's bounds to select depth before optimization.