Solves: Accuracy

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

2078 ideas found

✓✓ Beats tuned baseline 2026

Jacobian-aligned infill for black-box neural tuning

Add a geometry-guided infill operator to a population optimizer used for black-box neural-network tuning. Fit a local Jacobian from recent parameter perturbations and validation-residual vectors, generate a damped Gauss-Newton candidate for exploitation, and sample exploratory candidates in the same Jacobian-derived metric. The host optimizer retains selection, population survival, covariance adaptation, and its total evaluation budget; only a configurable fraction of new candidates is replaced…

Useful6/10
Difficulty5/10
Novelty7/10
Paper: JANUS: Online Jacobian-Aligned Infill for Black-Box Optimization arXiv:2608.22862
Mechanism confirmed, baseline not beaten 2026

Missingness-as-a-Label Signal

Use the observed label-availability indicator as an auxiliary supervision signal when labels are preferentially missing for uncertain or difficult examples. Train the classifier with a joint likelihood containing both the class-label likelihood for labeled examples and a missingness likelihood whose probability depends on the classifier's posterior uncertainty.

Useful6/10
Difficulty4/10
Novelty5/10
Paper: Favourable Missingness in Semi-Supervised Classification for Exponential Mixture Models arXiv:2608.22843
Mechanism failed 2026

Boundary-Safe Log-Barrier Mirror Optimizer

Replace AdamW or SGD updates on simplex-valued routing probabilities with a logarithmic-barrier mirror step. The update remains strictly positive, avoids projection-induced zero coordinates, and can approach a boundary solution asymptotically while retaining the paper's theoretically motivated O(log k/k) convex convergence behavior.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Mirror descent algorithms with logarithmic barriers arXiv:2608.22834
Mechanism confirmed, baseline not beaten 2026

Convex-gradient robust augmenter

Replace unconstrained adversarial example generation with an invertible transport map that is the gradient of a convex potential. For each class, the map pushes a kernel-smoothed empirical distribution toward a least-favorable distribution inside a prescribed KL/Sinkhorn ambiguity radius, producing hard but globally coherent training examples rather than pointwise perturbations.

Useful6/10
Difficulty6/10
Novelty5/10
Paper: Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing arXiv:2608.22746
✓✓ Beats tuned baseline 2026

Cyclic Lie-Bracket Residual Block

Replace one deterministic residual update with a short cyclic composition of learned vector fields evaluated for randomized, short run times. Because finite compositions of noncommuting flows generate directional-derivative and Lie-bracket terms, changing the cycle order gives the network an explicit, low-cost way to learn drift directions that are unavailable from the individual vector fields alone.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Diffusion limits of cyclic finite-velocity random motions along vector fields arXiv:2608.22514
Failed on benchmark 2026

Conditioned PSD sensing bottleneck

Represent an intermediate feature as a low-rank PSD matrix and compress it using nonnegative measurements \(\langle A_i,X\rangle\), while penalizing the empirical ratio between maximum and minimum measurement distortion over low-rank feature pairs. This directly discourages collapsed directions and excessively amplified directions in a covariance or Gram-feature bottleneck.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Optimal Condition Numbers in Low-Rank Positive Semidefinite Matrix Sensing arXiv:2608.22418
Mechanism confirmed, baseline not beaten 2026

Gramian-balanced neural SSM compression

Compress the hidden state of a stable neural state-space layer using low-rank controllability and observability Gramians. States that are difficult to excite from the input or weakly visible at the output are removed, producing a smaller recurrent state with a principled input-output preservation criterion.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations arXiv:2608.22406
Failed on benchmark 2026

Laplace-Heterogeneous MoE Routing

Replace the usual hand-designed expert-load penalty with a heterogeneous survival penalty derived from a susceptibility distribution. Each expert receives an availability factor q_e=G(A_e), where A_e is its cumulative recent routing pressure and G_e is a learned or fixed mixture of exponentials; highly used experts are suppressed smoothly, while heterogeneous experts can have different resistance to pressure. The mixture produces adaptive curvature and long-tailed penalties that may reduce…

Useful6/10
Difficulty4/10
Novelty6/10
Paper: From Individual-Based Stochastic Epidemics to Heterogeneous SIR Equations arXiv:2608.22122
Failed on benchmark 2026

Fourier Replay-Mode Stabilizer

Regularize a circular recurrent kernel by directly controlling the growth rate and phase velocity of its Fourier modes. This converts replay-speed selection into a low-dimensional spectral control problem and can suppress unstable or excessively slow modes without adding recurrent parameters.

Useful6/10
Difficulty6/10
Novelty8/10
Paper: Forward and reverse delay-driven hippocampal replay without symmetric plasticity arXiv:2608.21814
Failed on benchmark 2025

Log-Scale Self-Similar Activation

Replace a conventional scalar activation by a geometrically indexed family of affine pieces whose slope changes with the logarithmic magnitude of the input. The same two endpoint parameters are reused across all scales, giving a compact, explicitly scale-aware activation that can represent different responses for exponentially separated activation magnitudes.

Useful6/10
Difficulty4/10
Novelty7/10
Paper: From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of maps arXiv:2512.02291
Unverified 2026

Certified Radical Coordinate Layer

Replace Fourier or sinusoidal one-dimensional coordinate features with a trainable radical layer f(x)=sum_i c_i sqrt(P_i(x)), where every P_i is a strictly positive quadratic. A nonzero scalar output formed by such a layer has at most 2n distinct real zeros, providing an explicit bound on sign changes and suppressing uncontrolled ringing. Use the radical features as an input embedding for a conventional MLP or neural implicit field.

Useful5/10
Difficulty4/10
Novelty8/10
Paper: Estimating the number of real zeros of linear combinations of radicals of polynomials arXiv:2609.02871
Unverified 2026

Robin-Boundary Diffusion Sampler

Train a score-based diffusion model on a domain with partially reactive constraints, replacing hard rejection or large boundary penalties by a Robin boundary condition. Samples approaching the constraint boundary acquire a hazard proportional to accumulated boundary local time, giving a continuous interpolation between reflection and absorption.

Useful5/10
Difficulty6/10
Novelty8/10
Paper: Survival in a partially reactive wedge arXiv:2609.02665
Unverified 2026

Mixed-Subgroup Conservation Router

Replace an unconstrained Cartesian-product router over heterogeneous branches with a router whose joint expert or state assignments obey a finite-group conservation rule. Branch i emits a distribution over labels in its own subgroup H_i of a common finite abelian group G; only tuples whose group sum is zero are retained. This gives an exact, differentiable structural prior for modular arithmetic, multi-relational graphs, multi-view fusion, or any setting where latent labels compose by a…

Useful5/10
Difficulty5/10
Novelty7/10
Paper: An Affine Semigroup from Orbifold Boundary Conditions: cut, phylogenetic and hierarchical models in the unit-weight sector, and weighted configurations beyond them arXiv:2609.02630
Unverified 2026

Spherical-Design Prototype Initialization

Initialize directional prototypes, cosine-classifier weights, or angular attention directions with a spherical t-design rather than iid random vectors. Exact matching of spherical moments through degree t should provide uniform angular coverage and reduce initialization anisotropy, especially when the number of prototypes is small.

Useful5/10
Difficulty4/10
Novelty5/10
Paper: Dual Geometry of Spherical Designs: Polarity, Self-Polar Rigidity, and Quadrature Structure arXiv:2609.02439
Unverified 2026

Sharp Sub-Gamma Laplace Regularization

Replace ad hoc Gaussian or Laplace noise injection with a Laplace majorant calibrated to the observed finite-range sub-Gamma parameters of a neural perturbation. For convex perturbation losses, the calibration guarantees that the expected loss under the scaled Laplace noise upper-bounds the expected loss under every centered random perturbation satisfying the same Bernstein-type MGF constraint.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: Convex Order Comparisons for Sub-Gamma Random Variables arXiv:2609.02398
Unverified 2026

Spherical covering initialization

Replace independently random unit-normalized prototypes in a spherical classifier, vector-quantizer, or prototype contrastive head with prototypes selected to cover the sphere evenly. The method directly targets the paper's finding that weak-signal spherical K-means preserves initialization-induced Voronoi structure, reducing redundant prototypes and making early assignments less dependent on random seed.

Useful5/10
Difficulty4/10
Novelty5/10
Paper: A Geometric Analysis of Initialization Bias in Spherical $K$-means in the Weak Signal Regime arXiv:2609.02205
Unverified 2026

Overlap-Field Coverage Regularizer

Represent augmentation centers or training examples in a low-dimensional torus and accumulate the geometric overlap of their augmentation neighborhoods. Add a finite-horizon penalty that detects latent locations with insufficient accumulated coverage, while constraining center uniformity so that coverage optimization does not collapse all samples to one location.

Useful5/10
Difficulty5/10
Novelty7/10
Paper: The higher-dimensional Shepp problem: an exact criterion for random ball coverings of tori arXiv:2609.02156
Unverified 2026

Dominance-aware mode extraction for binary neural samplers

Replace nearest-center or k-modes assignment on a pool of binary neural-network samples with responsibility thresholding followed by a coordinate-wise dominance screen. Only retain a candidate mode when its assigned samples are sufficiently explained by that mode and, at every bit position, the responsibility-weighted majority agrees with the proposed center; otherwise mark the mode unreliable or discard it.

Useful5/10
Difficulty4/10
Novelty7/10
Paper: Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering arXiv:2609.01744
Unverified 2026

Lp Spectral-Gap Invariance Regularizer

Apply a regularizer that penalizes feature disagreement under a finite set of known transformations. The paper's spectral-gap inequality gives a quantitative reason that this local consistency penalty controls distance from the subspace invariant under the transformation group, while the task loss prevents undesirable collapse.

Useful5/10
Difficulty5/10
Novelty5/10
Paper: Kazhdan's Property $(T)$ for Subspaces and Quotients of $L_p$-Spaces arXiv:2609.01447
Unverified 2026

Mixed Coordinate-Spectral Barron Penalty

Add a mixed Fourier-L1 penalty to a particle or molecular neural network so that frequencies involving selected coordinate blocks are penalized by products of per-coordinate weights, rather than only by one isotropic norm. This should favor representations that capture pairwise or blockwise structure efficiently in high-dimensional configuration spaces, especially for wavefunctions, molecular energies, and other permutation-structured functions.

Useful5/10
Difficulty6/10
Novelty7/10
Paper: Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions arXiv:2609.00872
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

ABP Tangential-Curvature Regularizer

Regularize a scalar network output so that its superlevel sets are approximately quasiconcave in input or latent space. Instead of penalizing the full Hessian, penalize positive curvature only in directions orthogonal to the output gradient, matching the paper's projected-Hessian and weighted 1-Laplacian structure.

Useful5/10
Difficulty6/10
Novelty6/10
Paper: On the Aleksandrov--Bakelman--Pucci estimates for the weighted $1$-Laplacian arXiv:2609.00719
Unverified 2026

Cycle-stable graph MoE routing

Use the graph-coloring stability concept to route graph nodes to experts. Nodes rank experts by router logits, adjacent nodes are constrained to use different experts, and a blocking cycle is a directed cycle in which every node prefers the expert currently assigned to the next node. Eliminate profitable feasible cycles or penalize their existence so routing reaches a locally stable assignment instead of oscillating between equally plausible expert allocations.

Useful5/10
Difficulty6/10
Novelty9/10
Paper: Graph Coloring with Color Preferences arXiv:2609.00569
Unverified 2026

Matrix-perspective feature divergence

Represent each example or minibatch by two positive semidefinite feature maps, such as teacher and student covariance operators, and penalize their noncommutative operator-valued f-divergence rather than only a scalar KL or Frobenius distance. The matrix-valued penalty preserves directional disagreement in feature space and is compatible with positive postprocessing, making it a candidate replacement for covariance matching in distillation and representation regularization.

Useful5/10
Difficulty5/10
Novelty6/10
Paper: Operator-valued maximal $f$-divergences for completely positive maps arXiv:2609.00554