Golden-Ratio Constrained Weight Storage

Integrate this at the quantizer-to-storage boundary for binary or low-bit weights, activation snapshots, or KV-cache blocks. First choose a scale \(s>0\) and represent each nonnegative quantized magnitude \(q\in[0,Q]\) by a finite golden-ratio expansion \(q\approx s\sum_{i=-R}^{L}d_i\varphi^i\), storing one sign bit separately for signed weights. Precompute a scalar lookup table mapping each ordinary integer or uniform quantization bin to the nearest admissible codeword in \(C_\varphi^{L,R}\); the table is feasible for small widths and can later be replaced by a finite-state encoder. On encoding, run a canonicalizer that repeatedly scans for 011 and replaces it with 100, carrying into neighboring positions when necessary. Store the resulting digit string plus scale and sign. On readback, first test every adjacent pair; an occurrence of 11 marks the word as structurally corrupted. Optionally run the inverse normalization pass 011-to-100 until no rule applies, but do not claim that this corrects arbitrary errors: a valid 1-to-0 flip can remain canonical and is semantically ambiguous, exactly as the paper's injectivity argument predicts. For stronger correction, append a small parity or CRC field and use it to request retransmission or select a redundant codeword. Benchmark a 4-layer MLP and a small CNN on MNIST or CIFAR-10 against int8 and packed binary storage at equal quantization error. Inject random single-bit and contiguous burst faults into stored weights after every checkpoint or into activation buffers during inference. Measure packed bits per parameter, fraction of faults detected by the adjacency test, post-fault accuracy, decoder latency, and the number of rewrite operations. The key falsifiable signal is improved accuracy under memory faults at comparable storage cost, with a warning that worst-case normalization latency grows linearly with codeword width.