Math: Computation

Machine-learning ideas tagged Computation in the Math taxonomy of the Math2NN corpus.

△ Mechanism confirmed, baseline not beaten 2026

Log-Depth Chunked Linear-Attention Scan

Implement causal linear attention in chunks and combine chunk summaries with an associative scan instead of carrying the recurrent state through all chunks sequentially. This preserves the exact causal computation while reducing inter-chunk dependency depth from the number of chunks to its logarithm, enabling substantially more GPU parallelism for long-context training and prefill.

Useful8/10
Difficulty6/10
Novelty6/10
Paper: Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones arXiv:2607.17419
△ Mechanism confirmed, baseline not beaten 2026

Causal E/I Micro-Event Cell

Replace signed-input aggregation in a spiking recurrent cell with a causal micro-event queue that processes excitatory and inhibitory arrivals in timestamp order, applying threshold and reset after each event. This preserves computations that disappear when all events in a timestep are replaced by one net current, particularly near threshold.

Useful7/10
Difficulty5/10
Novelty7/10
Paper: Order-Sensitive Fast-Synapse Limits in Sparse Excitatory-Inhibitory Threshold-Reset Networks arXiv:2608.16701
△ Mechanism confirmed, baseline not beaten 2026

Persistent Workspace for Online Adaptation

Turn the latent substrate into a persistent computational workspace for sequential inputs: each new observation is written into a designated subspace, processed by the same local rule, decoded, and then selectively retained or reset. This creates a compact recurrent model whose state can accumulate algorithmic information across a stream without expanding the parameter count.

Useful7/10
Difficulty6/10
Novelty7/10
Paper: Emergent Models: Intelligence from Tiny Substrates arXiv:2608.14019
✓✓ Beats tuned baseline 2026

Tiny Local Recurrence with Adaptive Computation

Replace a stack of independently parameterized residual or MLP blocks with a small latent grid or vector repeatedly updated by one shared transition rule. Let the number of updates depend on the current latent state, so easy examples terminate early while hard examples receive more computation, potentially improving parameter efficiency and extrapolation.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: Emergent Models: Intelligence from Tiny Substrates arXiv:2608.14019
△ Mechanism confirmed, baseline not beaten 2026

Boundary-Radial Persistence Loss

Add a topology-aware loss to a segmentation or implicit-shape network by computing radial extended persistence on the predicted boundary rather than on the full predicted mask. Match signed persistence intervals of the prediction to those of the target, penalizing missing, extra, or incorrectly ordered radial components and holes. This should provide a compact shape prior that is sensitive to anatomy-specific radial organization while avoiding volumetric homology computation.

Useful7/10
Difficulty6/10
Novelty6/10
Paper: Computing extended persistent homology of radial distance filtrations of Euclidean shapes arXiv:2608.11963
△ Mechanism confirmed, baseline not beaten 2026

Event-driven shared-neuron graph

Replace a conventional feed-forward block with a sparse temporal graph whose hidden units are shared across many computation paths. Each arriving message updates a shared accumulator, applies a nonlinear response, and schedules delayed messages to downstream neurons; constructive or destructive interaction emerges when multiple paths visit the same unit.

Useful7/10
Difficulty6/10
Novelty8/10
Paper: NeuronSoup: Evolving Asynchronous, Shared-Neuron Temporal Graphs without Backpropagation arXiv:2607.15217
✓ Mechanism works 2026

Latent Bayesian Discovery of Symbolic Optimizers

Search for a compact symbolic optimizer instead of selecting among fixed AdamW-like formulas. Encode optimizer programs as token sequences, learn a continuous variational representation of those sequences, and use a Gaussian-process Bayesian optimizer to propose promising update rules based on short neural-network training rollouts.

Useful7/10
Difficulty6/10
Novelty6/10
Paper: Symbolic Discovery of Iterative Algorithms: A Continuous Latent Space Bayesian Optimization Framework arXiv:2607.01552
Unverified 2026

Order-Sensitivity Margin Regularizer

Train a threshold-reset recurrent network to suppress dependence on unresolved excitatory/inhibitory arrival order. Penalize states that fall in the paper's order-sensitive firing interval, or augment training with excitatory-first and inhibitory-first counterfactuals and enforce consistent outputs.

Useful6/10
Difficulty4/10
Novelty8/10
Paper: Order-Sensitive Fast-Synapse Limits in Sparse Excitatory-Inhibitory Threshold-Reset Networks arXiv:2608.16701
Unverified 2026

Levin-Bit Prompt Scoring

Rank candidate prompts, demonstrations, critiques, or system instructions by how many bits of reproduction cost they save for a specified artifact distribution. Replace raw prompt-token heuristics with a paired score that rewards both higher success probability and lower generation computation, then train or retrieve prompts maximizing this score under a token budget.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: The Value of a Prompt: An LLM-Relative Kolmogorov-Complexity Approach arXiv:2608.16438
Unverified 2026

Dual-certified channel screening

Replace heuristic magnitude pruning in a layerwise convex reconstruction problem with safe screening based on a perspective relaxation of the cardinality constraint. A channel is removed only when a lower bound for every solution containing that channel exceeds the loss of a feasible incumbent; conversely, a channel is forced to remain when every solution excluding it is provably worse.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Safe screening rules for portfolio optimization with linear and cardinality constraints arXiv:2608.01871
Unverified 2026

Geometric parallel optimizer portfolio

Run several independent copies of an optimizer with geometrically increasing training budgets so that at least one copy is close to the unknown budget required by the problem. Allocate workers using staggered schedules rather than launching a full hyperparameter sweep, and periodically select or promote the best checkpoint using a held-out minibatch stream. This targets training regimes where the required number of updates is unknown because smoothness, gradient variance, or noise level is…

Useful6/10
Difficulty5/10
Novelty5/10
Paper: Adaptivity via a Parallel Architecture for Stochastic Gradient Methods arXiv:2607.28902
Unverified 2026

Stochastic Operator Stability Monitor

Instrument selected neural-network operators with cheap stochastic perturbations and estimate how much their outputs change under finite-precision perturbations. Use the resulting per-operator score to identify unstable kernels and selectively switch them to FP32, compensated accumulation, or a stable reformulation instead of running the entire model at high precision.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Automated Numerical Stability Analysis of Deep Learning Operators arXiv:2607.25494
✓✓ Beats tuned baseline 2026

Tropical support-restricted PINN

Represent the PINN solution in a restricted polynomial or Taylor basis whose exponent set is supplied by tropical support analysis, instead of asking an MLP to discover the local series structure from scratch. The restriction removes coefficients that cannot occur in the formal solution, reducing trainable degrees of freedom and preventing spurious low-order or singular terms.

Useful6/10
Difficulty5/10
Novelty8/10
Paper: Tropical Geometry as a Restricted Architecture for Physics-Informed Neural Networks: Applications in Nonlinear Fluid-Structure Examples arXiv:2607.00237
Unverified 2026

SMT-Certified Loss-Preserving Network Rewrites

Represent an original neural-network block and a proposed rewritten block as constrained optimization formulations over inputs and trainable parameters, then certify that the rewrite preserves feasibility and the ordering of losses over a bounded domain. This gives a compiler or pruning pipeline a formal reject/accept gate instead of relying only on numerical regression tests.

Useful5/10
Difficulty7/10
Novelty8/10
Paper: SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification arXiv:2609.00728
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

Least-Fixed-Set Propagation for Recurrent Networks

Represent the hidden state of a recurrent or implicit neural block by a convex reachable set and encode its recursive constraints as containment inequalities rather than unrolling a fixed number of steps. Eliminate the set variables to obtain the smallest representable invariant set, which can be used as a tighter robustness certificate, a training regularizer, or a principled initialization for equilibrium solvers.

Useful5/10
Difficulty7/10
Novelty6/10
Paper: Solving polynomial inequalities over spaces of convex sets and applications arXiv:2608.07794
Unverified 2026

Division-free adaptive learning-rate ladder

Convert unknown optimizer scales into a small parallel ladder of learning rates and training horizons whose values differ only by powers of two. Each worker runs stochastic gradient descent for a geometrically increasing budget, allowing one worker to land near both the correct step-size scale and the useful horizon without explicitly estimating smoothness or gradient variance.

Useful5/10
Difficulty3/10
Novelty4/10
Paper: Adaptivity via a Parallel Architecture for Stochastic Gradient Methods arXiv:2607.28902
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

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