ML: Inference speedup

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

Unverified 2026

Polynomial Spectral Mode Controller

Replace an eigendecomposition-based spectral controller in a small recurrent or state-space transition layer with explicit polynomial projectors. Each hidden state is split into invariant modes, and each mode receives a separately constrained recurrent multiplier, enabling direct suppression of unstable modes or selective retention of long-memory modes using only matrix-polynomial evaluations.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: A Direct Polynomial Approach to Spectral Decomposition arXiv:2607.20218
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
Unverified 2026

Non-crossing d-arc sparse attention

Represent sequence positions as vertices on a circle and use a maximal family of mutually non-crossing d-arcs to define the allowed attention interactions. Rotate the family by d positions, or use several phase-shifted families across successive layers, so each layer has only O(N) edges but repeated layers propagate information over long distances. The geometric compatibility rule replaces arbitrary local-window or hand-designed sparse masks with a structured family whose maximality gives broad…

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Higher cluster tilting objects in locally finite triangulated categories arXiv:2607.19916
Unverified 2026

Rational-Pole Neural Field Pooling

Replace dense spatial pooling or integral evaluation over a planar domain by a sparse cubature layer whose nodes are poles of a rational approximation fitted only on the domain boundary. For analytic or nearly analytic neural-field channels, the same learned field can then be integrated using substantially fewer evaluations than a uniform grid, while the boundary approximation residual supplies a cheap reliability signal.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Cubature from rational approximation arXiv:2607.17851
Unverified 2026

Dense-support discrete random features

Build a single-hidden-layer network whose hidden weights and biases are sampled from a non-continuous distribution supported on a dense subset of parameter space, then train only the output coefficients. The result motivates discrete or mixed-precision hidden parameters without requiring a continuous Gaussian initialization; finite-width experiments can test whether this retains accuracy while reducing hidden-layer storage and arithmetic cost.

Useful5/10
Difficulty4/10
Novelty5/10
Paper: On high probability of universal approximation in random basis expansions with non-continuous weight sampling arXiv:2607.16551
Unverified 2026

Incremental Gray-code counter state

Use the one-edit Hamiltonian walk as an explicit state machine for counters in autoregressive models or world models. Instead of regenerating and re-embedding an entire numeric string after every increment, update only the digit that changes, or append the single leading digit at a block transition.

Useful5/10
Difficulty6/10
Novelty9/10
Paper: Variable-length Gray codes for the Natural Numbers arXiv:2607.16088
Unverified 2026

Signed Block-Aggregation Attention

Replace a dense or irregular binary interaction matrix in a value-aggregation layer with a signed sum of blocky masks. Each blocky mask groups a set of query rows with a disjoint set of key columns, allowing all queries in a group to reuse one summed value vector. This is most suitable for linear attention, graph message passing, or any layer where the interaction matrix is applied directly to values rather than passed through a row-wise softmax.

Useful5/10
Difficulty7/10
Novelty7/10
Paper: A characterization of idempotent Schur multipliers arXiv:2607.14316
Unverified 2026

Entropy-Recycling Categorical Sampler

Replace independent categorical sampling calls with a shared exact sampler carrying a reusable uniform integer state. After sampling category X from a distribution with CDF F, retain the unused portion of the underlying random interval as a new state (Z', M'), so later samples consume residual randomness instead of requesting fresh random bits. The expected random-bit cost should approach the sequence entropy rather than paying a fixed word or byte cost per sample.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Online Random Sampling with Real Probabilities arXiv:2607.13828
Unverified 2026

Main-Krylov Structural Encoder

Add a structural positional channel formed from the Krylov sequence generated by the graph adjacency matrix and the all-ones vector. For graphs with k main eigenvalues, this sequence has rank k, so a GNN can retain all information obtainable from global walk counts using only k node features rather than storing many adjacency powers.

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Trees with exactly three main eigenvalues arXiv:2607.13577
Unverified 2026

Residual-aware adaptive training step

Use a CFL-like step-size controller for neural simulators or neural ODE rollouts, shrinking the integration step when the predicted state changes rapidly and relaxing it when dynamics are smooth. The controller uses the smallest spatial resolution and maximum predicted velocity, rather than a fixed global step chosen for the worst case.

Useful5/10
Difficulty3/10
Novelty4/10
Paper: A Structure-Preserving Method of Fundamental Solutions for the Multi-Phase Mullins-Sekerka Flow arXiv:2607.12759
Unverified 2026

Branching-Fanout Sparse MoE

Replace a fixed top-k expert count with a stochastic, token-specific fanout generated by a supercritical binary branching process stopped at a geometric time. The resulting number of active experts has finite mean but a power-law tail with log-periodic modulation, allowing most tokens to use little compute while reserving larger computation for difficult or ambiguous tokens.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Power-law and log-periodic degree tails for a family of probability generating function equations arising in evolving networks arXiv:2607.12564
Unverified 2026

Criticality-Gated Resolution Switching

Use effective coupling and field values from a local coarse-grained motif to decide whether a neural network should operate at fine or coarse resolution. Near the continuous critical boundary, retain fine-scale features because correlations become long-ranged; away from criticality, aggregate aggressively. Near discontinuous or reentrant boundaries, hysteresis prevents rapid switching between resolutions.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Thermal phase transitions in a mixed-spin Ising model on the Lieb lattice: Exact results beyond zero magnetic field arXiv:2607.11661
Unverified 2026

Golden-Ratio Constrained Weight Storage

Store quantized magnitudes as finite golden-ratio digit strings satisfying the no-adjacent-ones constraint, rather than as unconstrained binary words. A local rewrite pass converts equivalent but invalid patterns such as 011 into 100, making illegal adjacent-one patterns detectable after memory faults while preserving the represented scalar. This is a storage-integrity and decoding scheme, not a claim that canonicalization alone can correct arbitrary bit flips.

Useful5/10
Difficulty5/10
Novelty8/10
Paper: Intrinsic Redundancy and Local Robustness in Finite $β$-Expansion Systems arXiv:2607.08795
Unverified 2026

Masked Universal Host Layer

Represent many related sparse graph or attention patterns inside one fixed host connectivity pattern and activate each target instance with binary directional masks. The learned edge transformation and sparse-kernel layout are shared across instances, while the mask selects the target graph, enabling one compiled operator to process heterogeneous structures.

Useful5/10
Difficulty5/10
Novelty5/10
Paper: A universal emulator for planar Ising lattices arXiv:2607.05308
Unverified 2026

Tensor-Core Limb Expansion for Stable Accumulation

Represent selected activations, weights, or optimizer accumulators as four floating-point limbs and evaluate products through tensor-core matrix multiplications encoding limb convolution. Retain the convolution components during reductions and renormalize only at block boundaries, avoiding branch-heavy multi-double arithmetic inside every multiply-add.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: Multiple Double Arithmetic on NVIDIA Tensor Cores arXiv:2607.06881
Unverified 2026

Lower-bound-guided binary latent bottlenecks

Use the paper's one-bit compressed-sensing lower bound to choose the number of binary latent measurements and to set a nonzero achievable-error floor during training. A sign bottleneck should not be given an unrealistically small bit budget: for approximately sparse latents, the target reconstruction error scales no faster than a power of effective sparsity divided by the number of sign measurements.

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Near-Optimal Lower Bounds on One-Bit Compressed Sensing of Approximately Sparse Signals arXiv:2607.06750
Unverified 2026

Random-label irregular sparse attention

Construct a sparse attention mask from a fixed regular candidate graph and one scalar random label per token, retaining edge $(u,v)$ when $x_u+x_v\geq\tau$. Unlike independent random pruning, this produces correlated neighborhoods and a controllable distribution of token degrees, potentially giving some tokens broad receptive fields while retaining a fixed sparse budget.

Useful5/10
Difficulty3/10
Novelty7/10
Paper: Irregular subgraph in a regular graph arXiv:2607.06465
Unverified 2026

Subcritical Preferential Sparse Attention

Construct a sparse attention or message-passing mask by sampling edges with preferential weights (d_u+alpha)(d_v+alpha), while keeping the edge count below the predicted connectivity threshold. This creates hub-like local communication patterns but prevents one giant component from forcing dense information mixing, reducing attention cost and potentially mitigating oversmoothing.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: Sharp Asymptotics for the Largest Component in the Subcritical Regime of Preferential Attachment Without Vertex Growth arXiv:2607.00731
Unverified 2026

Leading-Term Strand Router

Build a sparse neural mixing layer from colored directed strands rather than a dense all-to-all matrix. Feature channels are assigned ordered colors, local trivalent junctions conserve every color, and an edge width is the weighted sum of the colors carried by that edge; a differentiable penalty favors monotone, crossing-free routings that define a canonical leading term. This creates a structured routing prior that can be compared directly against dense attention and unconstrained sparse…

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Leading term strandings for webs arXiv:2608.27425
Unverified 2026

Compositional Contraction Budget for Residual Blocks

Estimate how strongly each neural block contracts distinguishability and use the paper's weighted composition inequality to allocate depth, residual strength, or precision where information is actually preserved. Blocks that strongly contract information beyond the reference path receive a smaller residual gate, higher numerical precision, or are replaced by a cheaper identity-like operation.

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Conditional contraction coefficients and their applications to quantum networks arXiv:2608.27171
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
Unverified 2026

m-Binomial Global Mixer

Insert a fixed or lightly gated lower-triangular binomial-transform layer into a sequence model to create global interactions across positions without forming attention logits. For a sequence of length N, mix each output position with all earlier positions using coefficients determined by an integer m; initialize the layer fixed and optionally learn a diagonal channel gate or a small mixture over m values.

Useful4/10
Difficulty5/10
Novelty8/10
Paper: $m$-Bell and $m$-Stirling numbers: Iterated binomial transforms, hyper-Bessel functions, and moments of the Conway--Maxwell--Poisson distribution arXiv:2608.12011
Unverified 2026

Adaptive Hankel constraint curriculum

Exploit the paper's nested obstruction hierarchy by applying cheap low-order Hankel tests to every example and evaluating larger matrices only for outputs near the current feasibility boundary. This turns higher-order structural validation into an adaptive curriculum rather than an always-on expensive eigendecomposition.

Useful4/10
Difficulty5/10
Novelty8/10
Paper: Higher-Order Hankel Obstructions to Free Infinite Divisibility for Beta Distributions arXiv:2607.17630