ML: Cnn

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

△ Mechanism confirmed, baseline not beaten 2026

Partial-ReNoise Neural Architecture Mutation

Replace independent architecture generation with a diffusion mutation kernel that starts from a known valid neural architecture, re-noises it for only a fraction of the diffusion horizon, and denoises it conditionally toward a new architecture. The resulting candidates should remain closer to the parent and retain validity at low mutation strength, while larger re-noising fractions should produce greater novelty and access to distinct architectural basins.

Useful8/10
Difficulty6/10
Novelty6/10
Paper: From Generation to Discovery: Diffusion Mutation Kernels for Circuit and Physical Design arXiv:2608.27649
✗ Mechanism failed 2026

Conformal Early-Rejection for Diffusion Architecture Search

Attach a calibrated risk monitor to intermediate diffusion states and terminate mutations that are likely to violate hard architecture or performance constraints before full decoding and training. This transfers the paper's separation between proposal generation and authoritative external evaluation into an early-stopping controller for expensive neural architecture trials.

Useful7/10
Difficulty5/10
Novelty7/10
Paper: From Generation to Discovery: Diffusion Mutation Kernels for Circuit and Physical Design arXiv:2608.27649
△ Mechanism confirmed, baseline not beaten 2026

Covariance-Lifted Residual Step Controller

Use the lifted second-moment operator to adapt the residual step size of a deep residual network or neural ODE under multiplicative layer noise. Instead of choosing a fixed residual coefficient, shrink or enlarge it online to keep the predicted covariance-growth factor below a target margin, producing a stochastic stability controller for depth and inference time.

Useful7/10
Difficulty5/10
Novelty8/10
Paper: Linear Stochastic Systems with i.i.d. uncertainties: Exact Covariance Characterization, Stability Analysis and State-feedback Design arXiv:2608.07028
✗ Failed on benchmark 2026

Percolation-Certified Neural Cellular Automaton

Construct a finite-range, translation-equivariant recurrent convolutional module with an absorbing inactive state, then train its local dynamics so that seeded activity crosses coarse-grained space-time blocks with probability above an oriented-percolation threshold. This should produce reliable long-range propagation without dense global attention while remaining robust to non-monotone local updates and perturbations. Block statistics also provide a diagnostic for vanishing propagation or…

Useful7/10
Difficulty5/10
Novelty8/10
Paper: Linear spreading speed in non-monotone population models arXiv:2607.08914
Unverified 2026

Nonreciprocal mutant feature fields

Replace a single residual feature field with two nonnegative streams: a primary representation A and a mutant or corrective representation B. A produces B through a one-way source term, while B suppresses A, creating an explicitly tunable competition mechanism that can prevent feature collapse and encourage complementary representations.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Death by mutants: unusual multicritical dynamics in a two-species model for absorbing state transitions arXiv:2609.03123
Unverified 2026

Noise-Induced Compact-Support Neural Field

Replace ordinary dropout or soft sparsity penalties on a nonnegative spatial or token activation field with sublinear multiplicative stochastic dynamics. The field receives local diffusion or graph smoothing, while noise amplitude u^gamma vanishes at zero but is relatively strong near zero; this creates an absorbing zero state and may produce exact contiguous inactive regions. The module is suitable for feature maps, graph-node fields, token routing scores, or continuous neural operators.

Useful6/10
Difficulty6/10
Novelty8/10
Paper: Instantaneous shrinking of supports for stochastic PDEs arXiv:2609.01984
Unverified 2026

Annihilating Density-Transport Feature Mixer

Replace an ordinary local convolution or token-mixing block by two nonnegative feature populations A and B that diffuse and drift along the spatial or token axis, with transport rates increasing quadratically with local population and with an optional directional bias. Add a local A plus B to empty reaction so mutually conflicting feature mass is removed rather than merely averaged. The module should produce adaptive competition, and its isolated relaxation should exhibit a measurable t raised…

Useful6/10
Difficulty5/10
Novelty8/10
Paper: Effective Hardcore Exclusion Without Exclusion: Two-Species Pair Annihilation Revisited arXiv:2608.30630
Unverified 2026

Incompressible transport noise for feature maps

Replace independent additive noise on spatial feature maps with stochastic advection by divergence-free vector fields. The perturbation preserves spatial volume and feature mass, while the associated Stratonovich-to-Itô correction provides a tunable diffusion that preferentially damps high-frequency spatial fluctuations.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation arXiv:2608.13332
Unverified 2026

Dyadic Stable-Diffusion Residual Block

Insert an anisotropic fractional diffusion operator into residual blocks so that feature energy in dyadic frequency band j is damped at a rate proportional to 2^{alpha j}. Combine this fixed nonlocal dissipative branch with a learned convolutional residual branch. The resulting block is a frequency-selective alternative to ordinary residual updates, with stronger damping of unstable high-frequency feature modes.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: On the Schauder Estimates for Non-local Equations with Drift: The Supercritical Case arXiv:2608.09051
Unverified 2026

Fourier Turing Recurrent Layer

Replace one spatial convolution block by a recurrent Fourier-domain layer that couples every mode k to its opposite mode -k and gives the strongest amplification to a nonzero selected wave number k*. The layer crosses a controlled Turing-like instability at k* and uses cubic saturation to produce bounded structured features instead of unbounded activation growth.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Quantum Turing Patterns arXiv:2607.26331
Unverified 2026

Morphogen-Controlled Topology-Preserving Sparse Growth

Replace fixed sparse masks with a stochastic birth-death process for neural connections or spatial units. A diffusing morphogen-like utility field controls where connections are added or removed, while a local simple-point test rejects removals or additions that would disconnect a layer or alter a prescribed computational topology. This creates an adaptive sparse architecture with a tunable compact-to-branched transition rather than unconstrained magnitude pruning.

Useful6/10
Difficulty6/10
Novelty6/10
Paper: Control of morphology and topology in a lattice model of branching morphogenesis arXiv:2607.24619
Unverified 2026

Divergence-Free Transport Noise Layer

Inject Stratonovich transport noise into intermediate spatial feature maps instead of adding independent elementwise Gaussian noise. Choose divergence-free vector fields whose covariance is approximately isotropic, so the corresponding Itô correction acts like a tunable Laplacian and preferentially suppresses unstable high-frequency feature components.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Absence of blow-up in the 3D Navier-Stokes equations with transport noise arXiv:2607.15140
✗ Mechanism failed 2026

Conserved Poisson Feature Noise

Replace iid dropout or iid activation noise on spatial tokens with fluctuations generated by a conserved diffusing density. Each token receives a positive mass variable whose total mass is preserved, while Poissonian stochastic flux produces correlated perturbations that explore coherent local patterns rather than independently corrupting every feature. The density is autonomous and detached from autograd, so the regularizer adds little computational overhead.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: Non-equilibrium phase transition in the Brownian Ising Model: field theory, renormalization group, and exact results arXiv:2607.02667