ML: Inference speedup

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

Unverified 2026

Resolvent response basis for conditioned modules

Compress a module whose output changes with a scalar condition such as diffusion time, temperature, or compute budget by representing its response in a low-rank basis generated by resolvent-like functions. Distinct spectral modes produce rational factors \((1-\tau\lambda_k)^{-1}\), allowing a small number of learned components to approximate a large hypernetwork or condition-dependent parameter table.

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Spectral duality structures and the Fisher--Rao geometry of reset distributions arXiv:2608.15805
Unverified 2026

Degenerate-Backbone Sparse Attention

Constrain a sparse attention graph to split into a k-degenerate backbone and a residual graph with maximum degree at most k-1. Orient the backbone according to a degeneracy order so that each token receives or emits at most k structured interactions in the relevant direction, while the residual edges form a bounded-degree correction layer. This replaces arbitrary sparse attention with a topology that is easier to schedule and whose worst-case edge and local-degree costs are explicit.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Arboricity Nearly Bounds Degeneracy arXiv:2608.15701
Unverified 2026

Uniform PEP selective decoding

Replace raw neural scores with randomized pairwise-error probabilities relative to a reference candidate distribution. Use a fixed PEP threshold to accept, abstain, or form a variable-size candidate list; exact uniformity under the reference law makes the threshold interpretable independently of the model's score scale and robust to ties.

Useful5/10
Difficulty4/10
Novelty5/10
Paper: One-Shot Information Theory via the Pairwise Error Probability: Lossy, Joint Source-Channel, Erasure, and Multiuser Coding arXiv:2608.15169
Unverified 2026

Fingerprint-Aware Neural Graph Certificates

Represent a neural computation or verification pipeline as a directed acyclic graph whose nodes carry cached certificates for tensor shapes, numerical ranges, Lipschitz estimates, quantization error, or equivalence to a reference module. After locally replacing or optimizing one node, compare its old and new interface fingerprints and revoke certificates only along the dependency cone when the interface changed. This enables safe incremental verification during architecture search, compiler…

Useful5/10
Difficulty4/10
Novelty8/10
Paper: Andy: A Mathematical Agent for Rigorous Proof and Autonomous Research arXiv:2608.15052
Unverified 2026

VC-pattern attention compression

Convert attention scores into binary incidence set systems at one or several score thresholds, then group queries that induce the same sampled-key pattern. Compute the expensive key-value aggregation once per pattern and reuse it for all queries in the group. The method is exact for the thresholded routing component and approximates dense attention when queries have a small number of stable high-weight neighborhoods.

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Isomorphism of tournaments with bounded VC dimension arXiv:2608.14486
Unverified 2026

Analytic Gaussian Measurement Bottleneck

For a neural model whose outputs lie on a d-dimensional analytic family in a very high-dimensional space, replace the full output vector by 2d+1 or a modestly oversampled number of fixed Gaussian scalar measurements. The paper's theorem predicts almost-sure injectivity in the noiseless setting, so an inverse network or decoder can recover the same latent instance without processing the full observation. Because the theorem does not provide a noise-stability constant, use M=4d+8 or M=8d in the…

Useful5/10
Difficulty4/10
Novelty5/10
Paper: Analytic inverse problems with finitely many random measurements arXiv:2608.14324
Unverified 2026

Two-Transitive Shuffle Mixer

Construct a sparse token-mixing architecture by interleaving learned per-token transformations with fixed perfect-shuffle and cyclic-pile permutations. For n not a power of k, the generated permutation group is 2-transitive, so sufficiently rich sequences of generator words can expose every ordered token pair without constructing a dense N by N attention matrix.

Useful5/10
Difficulty4/10
Novelty6/10
Paper: Cyclic Shuffle Groups: Universal Two-Transitivity and Complete Classification arXiv:2608.12526
Unverified 2026

Characteristic-plane spectral damping

Use the determinant of the constrained Fourier system as a frequency-aware conditioning certificate. Frequencies close to the characteristic planes receive stronger Tikhonov damping or lower supervision weight, preventing a neural inverse solver from amplifying measurement noise in modes where analytic inversion is unstable.

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Single-axis high-energy X-ray diffraction tomography for elastic residual strain: uniqueness and stability of solutions in the presence of equilibrium constraints arXiv:2608.12364
Unverified 2026

Monotone Hardy Mixer

Replace a learned causal mixing profile by a monotone profile followed by a prefix-average Hardy mixer. The monotonicity constraint makes the mixer provably non-degenerate in the BMO sense: localized variation in the profile cannot be reduced below a calibrated factor by prefix averaging. This is a cheap alternative to dense causal attention for tasks where importance or state profiles are expected to decay along sequence position.

Useful5/10
Difficulty4/10
Novelty8/10
Paper: The sharp reverse Hardy inequality in BMO for nonincreasing functions arXiv:2608.08093
Unverified 2026

Rank-Collapse Quadratic Token Router

Replace independent token scores with a query-conditioned positive-semidefinite low-rank quadratic score over a fixed-size selected subset. Repeatedly convert the quadratic objective into a linear exposure vector and apply a cheap top-k oracle, allowing the selector to model joint token interactions without constructing an n-by-n attention matrix. The margin between the current low-dimensional shadow and alternatives provides a practical confidence or early-stopping signal.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: The Rank-Collapse Principle for Quadratic Optimization arXiv:2608.07828
Unverified 2026

Global-Shift Randomized Batching

Sample one batching aggressiveness parameter once per serving epoch and use it for all busy periods, instead of independently randomizing every batch. This globally coupled randomness preserves nested batching behavior while preventing a fixed traffic pattern from repeatedly aligning with a deterministic timeout.

Useful5/10
Difficulty3/10
Novelty7/10
Paper: Online Multi-Level Aggregation with Per-Batch Maximum Delay arXiv:2608.06796
Unverified 2026

Sharp independent-load tail regularizer

Apply the paper's extremal tail bound to independently sampled nonnegative neural-network contributions, such as stochastic-depth branch activations, independently gated expert loads, or separately allocated memory chunks. Penalize the analytic worst-case probability that their sum exceeds a budget, using the fact that the worst admissible distribution is a sparse Bernoulli spike at the threshold.

Useful5/10
Difficulty4/10
Novelty8/10
Paper: Sharp Tail Bounds Beyond Twice the Mean arXiv:2608.06317
Unverified 2026

WKB-Stokes Sparse Mixer

Replace a dense channel-mixing matrix in a sequence layer with alternating diagonal propagation and sparse unipotent Stokes jumps. The diagonal part carries independently controlled exponential phases, while the unipotent factors implement cheap residual-like mode conversion without changing determinant or requiring a dense matrix multiply. Constrain the phase magnitudes and jump coefficients during training to obtain a reversible, norm-monitorable mixer.

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Holonomy Asymptotics along Quartic Differential Rays arXiv:2608.04729
Unverified 2026

Repair-cost detector for incompatible similarity predictions

Use the paper's lower bound on nearest-correlation repair cost to detect when a neural network's pairwise similarity predictions contain too much globally incompatible off-diagonal energy. Instead of projecting every predicted matrix onto the correlation cone, train the network to reduce the repair-risk statistic or trigger expensive repair only when a cheap diagnostic predicts substantial distortion.

Useful5/10
Difficulty4/10
Novelty6/10
Paper: Correlation Matrices in High Dimensions: The Elliptope as a Sample-Correlation Ensemble arXiv:2608.04162
Unverified 2026

Finite-State Extinction Monitor and Threshold Scheduler

Treat a quantized recurrent network as a finite deterministic state-transition system and distinguish absorption from latent periodic behavior during inference or training. Use the observed extinction threshold to adapt the activation threshold or recurrent gain, stopping once all tested trajectories reach the zero state and increasing the threshold when trajectories enter nontrivial cycles.

Useful5/10
Difficulty4/10
Novelty8/10
Paper: Extinction thresholds in a graph-based model of HIV infection dynamics arXiv:2608.00340
Unverified 2026

Noise-aware randomized Milstein sampler

Replace an Euler-Maruyama reverse-diffusion sampler with a scalar or coordinatewise randomized Milstein step that uses an autodifferentiated score or drift derivative and explicitly tolerates noisy coefficient and Brownian evaluations. Use the paper's additive error law to stop refining the time grid when discretization error falls below the neural-oracle noise floor.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Error of randomized Milstein scheme for scalar SDEs with noisy information about coefficients and Wiener process arXiv:2607.29578
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

Binomial-thinning (s,S) capacity controller

Replace continuously fluctuating conditional-computation decisions with a fixed-charge (s,S) controller for the number of active experts or channel groups. If the currently provisioned capacity falls below s, activate capacity up to S; otherwise retain the current capacity, preventing repeated small routing or kernel-launch decisions. Binomial thinning models the random subset of provisioned experts or channels that are actually available after token load, dropout, failures, or admission limits.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: The optimality of an (s, S) hiring policy on a workforce planning problem with fixed recruitment costs and binomial turnover arXiv:2607.28171
Unverified 2026

Shifted-Hermite Gaussian-tail primitive

Replace repeated evaluations of a Gaussian tail or Mills ratio in a neural loss or sampler with a short shifted-Hermite expansion. Choose a positive reference threshold x and represent the actual threshold as x+t; the same expansion then handles a whole batch of different shifts t using recursively generated Hermite coefficients.

Useful5/10
Difficulty3/10
Novelty6/10
Paper: Appell Polynomials in Shifted Asymptotic Expansions: the Mills ratio, Hermite polynomials, and Stieltjes bounds arXiv:2607.26636
Unverified 2026

Pyramid-Coupled Multiscale Representations

Construct a nested sequence of representations in which each coarser representation is obtained from the previous one by a 1-Lipschitz projection. Train prediction heads at multiple scales so coarse predictions remain stable and approximately recoverable from the finer representation, enabling early exit, token pooling, and controlled multiresolution inference.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: Pyramids and Extended Metric Measure Spaces arXiv:2607.26626
Unverified 2026

Selector-Driven Hierarchical Permutation Mixer

Replace part of dense token mixing with a small bank of structured permutations acting on a hierarchical token tree. Diagonal inheritance shares the same local permutation across all descendant copies, while selector words activate one connector type at a chosen level and remain inactive on the next type, providing controllable multiscale receptive fields without constructing a dense attention matrix.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: Near full groups of bounded type, \rom{2} arXiv:2607.26572
Unverified 2026

Antichain Multiscale Attention Windows

Replace an unrestricted collection of nested dyadic attention windows on a 2D token grid by a sparse antichain: no selected window may contain another selected window. Use the paper's exponential occupancy guarantee to control how many attention blocks reuse the same token, and add a differentiable log-moment penalty during training when exact antichain selection is relaxed. The expected benefit is bounded peak KV reuse and more predictable sparse-attention cost without discarding multiscale…

Useful5/10
Difficulty5/10
Novelty7/10
Paper: An antichain approach to a conjecture of Zygmund arXiv:2607.25957
Unverified 2026

Residual-Contraction log1p Kernel

Implement \(\log(1+u)\) through the bounded residual \(\rho(u)\), refining the argument by repeated square roots and propagating the residual backward with a rational recurrence. Use this table-free approximation in softplus and log-sum-exp kernels, where millions of logarithms are evaluated and predictable arithmetic can outperform general-purpose library calls on vectorized hardware.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: A Fixed-Point Construction of the Elementary Transcendental Functions arXiv:2607.23196
Unverified 2026

Constant-gap brickwork unitary initialization

Initialize a unitary feature-mixing layer with a shallow brickwork circuit of independent random SU(4) gates instead of sampling or factorizing a dense Haar-random unitary. Stack enough layers to obtain a target contraction of non-Haar components, using the paper's constant spectral-gap principle to make the required depth essentially independent of the number of qubits. The resulting layer is local, parameter-efficient, exactly norm-preserving, and should provide Haar-like scrambling at…

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Random unitary circuits with constant spectral gap arXiv:2607.20919