ML: Quantization

Machine-learning ideas tagged Quantization in the ML taxonomy of the Math2NN corpus.

✗ Failed on benchmark 2026

Equal-Volume KV Vector Quantization

Replace consecutive or randomly assigned transformed KV coefficients with groups whose variance-volume is approximately equal. Train one equal-size vector-quantizer codebook per group, so a fixed-width cache does not waste its low-rate budget by forcing high-variance and low-variance coordinates into badly mismatched groups. This is a drop-in quantization-layout change that can be applied to keys, values, or both.

Useful8/10
Difficulty5/10
Novelty7/10
Paper: Spend Bits Where Queries Look: KV Cache Vector Quantization with Attention-Preserving Transforms arXiv:2608.04074
✗ Failed on benchmark 2026

MI-Guided Latent Protection

Use the estimated task relevance of each latent coordinate to allocate corruption, precision, or redundancy non-uniformly rather than applying uniform dropout or quantization noise. Coordinates with larger mutual-information sensitivity receive lower noise or more bits, while low-relevance coordinates are compressed or corrupted more aggressively.

Useful7/10
Difficulty4/10
Novelty6/10
Paper: Adaptive Unequal Error Protection for Semantic Split Learning over Wireless Channels arXiv:2608.16227
△ Mechanism confirmed, baseline not beaten 2026

Influence-Adaptive Strategic Quantization

Insert a topology-controlled strategic communication layer into graph neural networks: each node maps a bounded latent scalar to either a clipped amplified signal or an interval-quantized message, with the amplification determined by how much influence the receiver exerts on the sender. Weakly influential communication channels should become aggressively quantized, while highly influential channels retain more resolution. This creates a principled variable-rate message-passing architecture…

Useful7/10
Difficulty5/10
Novelty7/10
Paper: Network-Induced Strategic Communication in Opinion Dynamics arXiv:2607.16036
Unverified 2026

Fourth-Mass Regularization for Signed Projections

Add a differentiable fourth-order-mass penalty to coefficient vectors used by randomized signed projections, sign-noise layers, or stochastic quantizers. The penalty controls the effective number of active coefficients and therefore the distribution of the injected random fluctuation: diffuse coefficients generate nearly Gaussian perturbations, whereas concentrated coefficients generate larger non-Gaussian deviations.

Useful6/10
Difficulty3/10
Novelty7/10
Paper: Fourth-Moment Geometry of Rademacher Sums arXiv:2608.17802
Unverified 2026

Polarized Gaussian bottleneck

Replace isotropic variance control in a bottleneck or router with a spectral polarization penalty that drives each latent direction toward either variance 0 or variance 1. The intended result is an automatically selected active subspace: inactive coordinates can be pruned or quantized aggressively, while active coordinates retain information instead of being uniformly attenuated.

Useful6/10
Difficulty4/10
Novelty7/10
Paper: Sharp stability for the (B)-theorem arXiv:2608.08472
Unverified 2026

Nonadaptive multiscale one-bit gradient sketch

Replace communicated floating-point gradients in synchronous federated or data-parallel training with one-bit threshold queries whose thresholds are sampled publicly before gradients are observed. Use several fixed geometric amplitude scales so the same protocol handles unknown gradient means and heavy-tailed client updates without an interactive localization round. Decode each coordinate from the scale whose neighboring estimates are statistically consistent, then apply the decoded aggregate…

Useful6/10
Difficulty6/10
Novelty6/10
Paper: Interaction Is Not Necessary for Order-Optimal 1-Bit Mean Estimation arXiv:2608.02538
Unverified 2026

Decoder-Side Refinement for Heavy-Tailed Gradients

Replace ordinary sign-gradient or fixed-range gradient quantization in distributed training with a non-adaptive one-bit refinement block. Workers generate all localization and multiscale residue bits using public randomness before the server knows the current aggregate gradient; after decoding a coarse center, the server chooses which stored phase and scale interpretation to use. This should reduce clipping and variance for heavy-tailed gradients without requiring a second communication round.

Useful6/10
Difficulty6/10
Novelty7/10
Paper: Universal Refinement without Interaction: Order-Optimal 1-Bit Mean Estimation arXiv:2607.24358
✓✓ Beats tuned baseline 2026

Capacity-Shaped Binomial Bottleneck

Replace a continuous scalar latent or probability with a stochastic count Y generated by Y|X=x ~ Binomial(n,x), and feed Y/n to the downstream network. Regularize the aggregate count distribution toward the beta-binomial distribution induced by the arcsine input X~Beta(1/2,1/2), while maximizing the mutual information carried by the count. This creates a compact discrete representation with an analytically specified, nonuniform prior that places more mass near the extreme counts without…

Useful6/10
Difficulty4/10
Novelty7/10
Paper: The Binomial Channel: On Capacity, Optimal Inputs, and Beta-Binomial Approximation arXiv:2607.02683
✗ Failed on benchmark 2026

Double-Geometric Layerwise ES

Replace Gaussian perturbations in a low-dimensional neural-network optimizer with independent double-geometric integer mutations and adapt each mutation scale using its exponential-family natural gradient. Apply the method to layerwise quantization scales, adapter coefficients, pruning thresholds, or other integer/discrete hyperparameters rather than to every individual weight.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Integer Natural Evolution Strategies arXiv:2608.23714
Unverified 2026

Fisher-Geometry Expert Menu

Construct a finite menu of experts or LoRA adapters by quantizing the oracle action manifold under a task-aware Fisher-information distortion rather than Euclidean parameter distance. The router can choose an installed expert after observing the input, but only k experts are stored or evaluated. The paper's frontier rate gives a falsifiable accuracy-versus-menu-size prediction.

Useful5/10
Difficulty6/10
Novelty4/10
Paper: Pre-Disclosure Experiment Menus: Oracle-Relative Risk and Joint Sample--Menu Asymptotics arXiv:2608.22905