ML: Kv cache

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

△ Mechanism confirmed, baseline not beaten 2026

Rate-adaptive KV-cache quantizer

Allocate different entropy budgets to different KV-cache blocks instead of assigning every token and head the same nominal bitwidth. Use the ECASQ Lagrangian so high-variance or attention-sensitive blocks receive more codepoints, while predictable blocks collapse to fewer symbols and become highly compressible. Preserve unbiasedness per scalar or block so reconstructed keys and values have zero mean quantization error conditional on the original tensor.

Useful8/10
Difficulty6/10
Novelty7/10
Paper: Entropy-Constrained Adaptive Stochastic Quantization arXiv:2608.18147
△ Mechanism confirmed, baseline not beaten 2026

Entropy-constrained unbiased block quantization

Replace fixed-grid stochastic quantization of each tensor block with an adaptive ordered codebook selected under both an entropy budget and a maximum number of codepoints. Within every interval between adjacent codepoints, use unbiased stochastic interpolation, so the quantized block remains unbiased while the emitted symbol distribution becomes easier for arithmetic or Huffman coding to compress. The representation should reduce actual compressed bytes at fixed MSE, or reduce MSE at fixed…

Useful8/10
Difficulty6/10
Novelty6/10
Paper: Entropy-Constrained Adaptive Stochastic Quantization arXiv:2608.18147
✗ 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

Rank-One PSD KATA Attention

Replace the usual random or elementwise-positive linear-attention feature map with a rank-one positive-semidefinite feature map derived from query and key vectors. For normalized inputs, the resulting kernel is the squared inner product, which is nonnegative and gives a geometrically structured interference pattern that is better suited to associative recall than an arbitrary low-rank feature map.

Useful8/10
Difficulty6/10
Novelty7/10
Paper: Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones arXiv:2607.17419
△ Mechanism confirmed, baseline not beaten 2026

Joint Tucker-rank and residual-bit KV allocator

Compress each layer's KV tensor with a partial Tucker approximation over token and feature axes, then encode the truncation residual with a rotated uniform quantizer. Select token rank, feature rank, and residual bit-width jointly under a global byte budget, allowing values with flat spectra to receive residual bits while keys may receive more low-rank capacity.

Useful8/10
Difficulty6/10
Novelty6/10
Paper: A JoLT for the KV cache: Near-lossless KV cache compression via joint Lagrangian allocation of Tucker ranks and a rotated residual for llms arXiv:2607.12550
△ Mechanism confirmed, baseline not beaten 2026

Equal-Variation KV Cache

Compress a causal sequence by retaining history positions at equal increments of cumulative representation variation instead of at uniform time intervals. Use the resulting N representatives in a decoder that reconstructs piecewise-constant keys and values; the paper's minimax result predicts a worst-case reconstruction error of total variation divided by 2N, independent of where rapid changes occur.

Useful8/10
Difficulty5/10
Novelty6/10
Paper: Optimal history encoding for elastic-plastic hereditary laws: Sharp input and constitutive approximation arXiv:2607.09974
△ Mechanism confirmed, baseline not beaten 2026

DP-Means Distinct-Item Memory

Replace token-by-token KV storage after an SSM or recurrent encoder with an online allocate-on-novelty cache. A new slot is created only when the incoming key is sufficiently dissimilar from every stored key; otherwise the incoming value is merged into its nearest slot, so repeated or redundant content does not grow the cache.

Useful8/10
Difficulty4/10
Novelty6/10
Paper: Remembering Distinct Items, Not Tokens: A Learnable Dirichlet-Process Cache Between State-Space Models and Attention arXiv:2607.09889
✗ Mechanism failed 2026

Ranking-Aware Projection Dimension Rule

Replace the usual JL dimension choice with a task-specific dimension budget based on the paper's asymptotic ranking law. For retrieval, nearest-neighbor search, or compressed attention keys, choose m from a target Kendall correlation and automatically expand the projection when measured ranking quality falls below the target.

Useful7/10
Difficulty3/10
Novelty7/10
Paper: Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models arXiv:2609.02155
△ Mechanism confirmed, baseline not beaten 2026

Residual-Pivoted Kernel Attention

Replace full PSD self-attention with a pivoted Cholesky/Nyström approximation whose landmarks are sampled from the unexplained diagonal mass. Tokens with large residual self-similarity are more likely to become landmarks, so the rank budget is spent on difficult regions rather than uniformly selected tokens.

Useful7/10
Difficulty5/10
Novelty5/10
Paper: A new analysis of the randomly pivoted Cholesky algorithm arXiv:2608.20633
✗ Mechanism failed 2026

Permutation-Mixed Orthogonal Quantization

Precondition activation or cache blocks with a fixed product U = A Sigma B of orthogonal transforms and a random signed permutation before quantization or coordinate sampling. The random permutation makes the product incoherent, so energy is less concentrated in a few coordinates and lossy compression should introduce less worst-case distortion.

Useful7/10
Difficulty5/10
Novelty5/10
Paper: Randomly Permuted Orthogonal Products and Fast Dimension Reduction arXiv:2608.18557
△ Mechanism confirmed, baseline not beaten 2026

Orthogonally mixed 3-bit KV cache

Replace ordinary per-channel or per-token KV quantization with a structured orthogonal transform followed by blockwise 3-bit quantization. Use a normalized Walsh-Hadamard transform and small SO(4) rotations to spread outliers across coordinates, quantize the transformed vectors, and exploit orthogonality to rotate queries and attention outputs so unquantized attention remains mathematically equivalent.

Useful7/10
Difficulty6/10
Novelty6/10
Paper: RotaryQuant: Fitting 120B MoE Models on Consumer Hardware via Fused Compressed-Space Attention arXiv:2608.08081
△ Mechanism confirmed, baseline not beaten 2026

Spectral Message Basis

Replace full agent-to-agent state transmission with coefficients in a learned dominant Koopman mode basis. Agents communicate only the leading spectral coordinates that explain slowly decaying collective behavior, while retaining a certificate based on the spectral gap and subdominant eigenvalue to decide whether the compressed representation is safe.

Useful7/10
Difficulty6/10
Novelty6/10
Paper: Certifying Collective Reasoning in Multi-Agent Systems via Koopman Spectral Analysis arXiv:2608.05956
✗ Failed on benchmark 2026

Rank-Revealing Representative Tokens

Compress a transformer KV cache by selecting actual past tokens whose key or hidden-state columns form a stable basis for all cached tokens. Instead of retaining tokens with the largest attention scores or leverage scores independently, compute rank-revealing pivoting of the leading right-singular-vector matrix and retain its pivot columns, then evaluate attention using the representatives plus an optional low-cost residual correction.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: Computing Strong Rank-Revealing Factorizations for Matrices with Orthonormal Rows arXiv:2607.13532
✗ Failed on benchmark 2026

Rotated Tucker residual for outlier-resistant KV quantization

Use a low-rank Tucker reconstruction as a structured backbone and quantize only its residual after an orthogonal rotation. The rotation preserves residual energy but redistributes it across coordinates, reducing dynamic-range imbalance and making 2- or 4-bit uniform quantization less damaging than direct quantization of the original KV tensor.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: A JoLT for the KV cache: Near-lossless KV cache compression via joint Lagrangian allocation of Tucker ranks and a rotated residual for llms arXiv:2607.12550
△ Mechanism confirmed, baseline not beaten 2026

Residual-energy cross attention

Replace dense query-key attention with an adaptive cross approximation constructed from selected query and key pivot tokens. At each rank, choose the pivot pair that removes large estimated residual energy, update the residual by a rank-1 cross correction, and stop when the residual estimate reaches a target tolerance. The resulting factorization computes approximate attention using a small number of landmark interactions while adapting to the actual token distribution.

Useful7/10
Difficulty6/10
Novelty5/10
Paper: Continuous Cross Approximation of Matrices Arising Out of Kernel Functions arXiv:2607.12540
Unverified 2026

Local-Tail Adaptive Attention

Replace a global attention truncation rule with a per-query local-tail budget. For each query token, retain nearby or high-priority keys until the estimated discarded interaction strength is below a target epsilon; this uses the paper's central distinction between local tail mass and the extensive norm of the discarded operator. The resulting attention pattern can allocate long-range computation only to tokens whose local tail is large.

Useful6/10
Difficulty5/10
Novelty5/10
Paper: Local observable errors from truncating interaction tails in gapped quantum lattice systems arXiv:2608.15576
Unverified 2026

Residual-pivoted landmark attention

Replace uniform or random landmark selection in low-rank attention with approximate greedy pivoted QR selection on the attention matrix. At each step, select the key whose residual attention column has the largest norm, orthogonalize it against previously selected columns, and stop when the residual energy falls below a target tolerance. Use the selected columns as an adaptive attention basis and reconstruct the full attention output through a small coefficient matrix.

Useful6/10
Difficulty6/10
Novelty5/10
Paper: Convergence rates for pivoted QR and LU arXiv:2607.26863
Unverified 2026

Effective-Rank Spectral Bottleneck

Use the paper's effective-rank and eigengap-dependent covariance estimation rates to construct a confidence-aware low-rank bottleneck for transformer activations or key/value tensors. The bottleneck is enabled only when the top-p empirical eigenspace can be estimated more accurately than the desired compression error; otherwise the layer remains full-rank.

Useful6/10
Difficulty5/10
Novelty5/10
Paper: Estimating eigenvectors and eigenspaces of covariance matrices: Optimal Bounds and Conditions for Consistency arXiv:2607.23964
Audited (legacy) 2026

Entropy-Budgeted Contiguous KV Pooling

Use the attention probability distribution over an ordered context to choose contiguous token groups whose pooled attention masses have entropy as close as possible to a prescribed upper budget R. Replace the corresponding key/value vectors by one weighted representative per group, preserving token order and reducing the KV-cache length from n to m. Unlike unconstrained token merging, the entropy constraint gives a direct control knob over how concentrated or diffuse the retained attention…

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Constrained Maximum Entropy Contiguous Aggregations arXiv:2608.25533
Unverified 2026

Affine lattice latent quantizer

Replace coordinatewise rounding of activation or embedding vectors with nearest-point quantization in a learned full-rank lattice. Learn an affine transform that makes the empirical activation region more isotropic, while regularizing the lattice covering density so it does not become inefficient as dimension grows.

Useful5/10
Difficulty5/10
Novelty5/10
Paper: Nearly Sharp Bounds for Lattice Coverings by Convex Bodies arXiv:2607.28429
Unverified 2026

Flip-Order Local Reconfiguration

Use local split-fusion rewrites as a structured alternative to globally recomputing token clusters. A model proposes a small number of neighboring tree edits per input, accepts only valid edits that reduce a learned energy, and retains the previous hierarchy across layers or decoding steps.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Generalised flip order on the faces of nestohedra arXiv:2607.20132