Solves: Inference speedup

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

△ Mechanism confirmed, baseline not beaten 2026

Dataset-adaptive unitary spectral codec

Replace a fixed DCT or Fourier transform in transform coding with a trainable isometric tensor-network transform whose local gates are learned once on a dataset. Retain the k coefficients with largest magnitude and reconstruct with the exact adjoint transform; the transform remains norm-preserving and fast while adapting its coefficient ordering to the data distribution.

Useful8/10
Difficulty5/10
Novelty7/10
Paper: Fast Trainable Multilinear Bases for Image Compression arXiv:2608.00053
✗ Mechanism failed 2026

Channel-aware attention-head pruning

Prune redundant attention heads using separate similarity scores for sink behavior and content routing. Two heads are considered safely redundant only when their normalized content compositions are close in Aitchison distance and their sink-mass trajectories are also close, avoiding pruning decisions dominated by a shared sink token.

Useful7/10
Difficulty4/10
Novelty7/10
Paper: Which Question Is Your Attention Metric Answering? Attention Rows as Compositional Data arXiv:2608.14712
✗ Mechanism failed 2026

Regret-aware evidential cost compression

Attach an evidential cost head to a neural graph model, representing each edge cost by a weighted set of interval boxes, and compress this representation before the downstream shortest-path or routing solver. Instead of minimizing Jaccard or Jousselme distance between the original and compressed mass functions, choose merges that minimize the induced cost error on the currently selected route, while enforcing a conservative monotonicity condition so that the resulting path regret is bounded.

Useful7/10
Difficulty5/10
Novelty8/10
Paper: Decision-Aware Approximation of Belief Functions for Evidential Combinatorial Optimization arXiv:2608.10650
✗ Mechanism failed 2026

Signed-Distance Ambient FNO

Embed every variable-domain sample into one fixed ambient hyperrectangle and append its signed-distance function as an additional channel to the operator input. Deterministically extend fields outside the physical domain, resample them onto a shared latent grid, apply standard Fourier layers, then interpolate and mask the output on the requested target discretization. The network learns the operator rather than a separate geometry encoder, so the same weights can be used across shapes and mesh…

Useful7/10
Difficulty4/10
Novelty6/10
Paper: ADEx-FNO: A Unified Ambient-Domain Framework for Fourier Neural Operators on Varying Geometries arXiv:2608.08608
△ 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

Lipschitz-Certified Cache Refresh

Attach a certificate to a cached transformer KV state or recurrent latent state and refresh it only while its predicted certificate remains inside a latency-contracted admissible region. The controller uses a bound on certificate drift to guarantee that the state will remain admissible throughout the next sampling, communication, and execution delay, reducing unnecessary recomputation while exposing a measurable refresh boundary.

Useful7/10
Difficulty5/10
Novelty8/10
Paper: CIPS: Maximal Certified Persistence in Cyber-Physical Systems arXiv:2608.06626
Unverified 2026

Orientation-consistent adaptive tetrahedral neural field

Represent a 3D neural field using high-order polynomial coefficients attached to an adaptively refined tetrahedral mesh, with a small MLP predicting residual corrections from local coordinates. Refine only tetrahedra whose prediction, rendering, or PDE residual is large, and use globally ordered vertices so neighboring tetrahedra share identical face and edge coefficients without hanging-node constraint solves.

Useful6/10
Difficulty6/10
Novelty7/10
Paper: An $h$-adaptive Tetrahedral Spectral Element Method with Applications to Kohn-Sham Density Functional Theory arXiv:2608.14006
Unverified 2026

Zeno-Free Minkowski Routing

Represent adaptive computation or MoE routing as a continuous latent trajectory that crosses convex mode walls, with a Minkowski norm defining computational speed. At a wall, choose the outgoing latent velocity by the same constrained variational rule as billiard reflection, and use the local path-length certificate to detect or prevent pathological accumulation of infinitely many routing events in finite depth.

Useful6/10
Difficulty7/10
Novelty8/10
Paper: Local finiteness of the number of reflections in semi-dispersing Minkowski billiards arXiv:2608.12618
Unverified 2026

Two-chart refinement cell

Build a recurrent ReLU module that evaluates a binary refinement cascade using a fixed-dimensional state and shared cell weights. Replace hard binary digit selection with two overlapping circle coordinates; switch between their affine state updates only at points where the two candidate updates agree, so the switch is an exact continuous piecewise-linear ReLU operation rather than a multiplicative gate.

Useful6/10
Difficulty6/10
Novelty7/10
Paper: Neural network realization of binary refinement iterates via a two-chart atlas selector arXiv:2608.02624
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

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