Research ideas

Every idea extracted from recent arXiv mathematics papers — verified and unverified. Click an idea to open its full card; badges show the empirical verdict.

2 ideas found

Status: Beats tuned baseline Solves: Sample efficiency ML: Transformer Clear all

✓✓ Beats tuned baseline 2026

Continued-Fraction Lacunary Features

Replace random Fourier features or a dense sinusoidal positional encoding with a compact bank whose frequencies are the continued-fraction denominators of an irrational number. Inverse-frequency amplitudes provide multiscale structure with a controlled sub-Lipschitz regularity profile, while lacunarity reduces the number of frequencies needed to represent oscillatory structure.

Useful6/10

Difficulty3/10

Novelty5/10

Architecture Generalization Sample efficiency Scalability

Paper: Regularity, quantitative deviation, and non-rigidity of a lacunary skew product arXiv:2608.25821

✓✓ Beats tuned baseline 2026

Private spectral whitening front-end

Estimate the temporal spectrum of each sequence channel using a locally private procedure, then apply a regularized inverse-square-root spectral filter before the sequence enters attention or an SSM. The filter removes predictable low-frequency or narrow-band redundancy while avoiding unstable amplification at frequencies where the private estimate is small.

Useful6/10

Difficulty5/10

Novelty7/10

Architecture Stability Sample efficiency Accuracy

Paper: On the privacy cost for dependent Gaussian data: spectral density estimation under local differential privacy arXiv:2608.24847