Interference-Resistant Weight Matrix Updates in a Shared Holographic Volume via Differentiable Beam Propagation

We introduce a mechanism for interference resistant weight matrix updates in a shared storage medium, inspired by volume holography's angle multiplexed storage of multiple patterns in one crystal. Multiple weight matrices are stored as angle multiplexed volume holograms in a three dimensional voxel volume, simulated via a differentiable Beam Propagation Method (BPM). Each matrix is updated by optimising the voxel tensor to land new target values while preserving the readouts of all others.

Ablation shows BPM's structured spatial coupling is required: dense random projections of identical dimensionality preserve channel separation but fail to support selective within channel updates. Volume geometry experiments reveal that lateral spatial resolution at the readout face governs encoding precision rather than total voxel count: wide volumes (Nx = Ny >> Nz) achieve up to 16x lower worst case MAE than cubic volumes at matched voxel count. Within wide geometries, worst case MAE decreases with pixels per weight (R^2 = 0.57, wide subset); at 4 ppw the substrate achieves >= 95% 4 bit bucket accuracy for matrices up to 128 x 128.

Across five seeds, four 32 x 32 matrices maintain worst case MAE of 0.0043 +/- 0.0013 over 200 update rounds with no systematic drift. At larger scale, four 128 x 128 matrices with 4 bit quantised targets achieve 95.5% +/- 0.2% accuracy across three seeds. A single 512 x 512 demonstration reached 95.6% at 4 ppw, indicating the substrate scales to transformer layer dimensions in principle. Increasing co stored matrices improves mean per matrix precision (d ~ 1.9 across three seeds), attributed to preservation constraints regularising the solver (analysed in companion work). Weight updates are random replacements rather than gradient derived, and downstream task learning is not demonstrated; this work characterises the encoding substrate in isolation.