Unverified
2026
Replace random or k-means initialization of a k-expert router with a moment-based range finder on a calibration batch of hidden states. Estimate a low-dimensional second-moment subspace, enlarge it using one-free-index third-Hermite contractions, and fit the router's expert centroids and weights only in this resulting subspace. The router can then operate on projected hidden states while retaining an optional small residual adapter.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Insert a proximal layer after a graph, mesh, or spherical convolution that groups all coordinates belonging to the same Laplacian eigenspace and applies one shared shrinkage gate to the whole group. Unlike coefficientwise spectral pruning, the result is unchanged if the eigenvectors inside a repeated eigenspace are rotated, preventing arbitrary basis-dependent feature selection.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Make Laplacian latency attention hardware-friendly by quantizing the exponential decay and row normalization to powers of two. Exponentials and divisions can then be implemented with lookup tables and integer shifts, enabling a low-bit attention kernel for neuromorphic and edge accelerators.
Useful6/10
Difficulty4/10
Novelty7/10
Unverified
2026
Approximate a long hidden-state or key/value trajectory by a small sum of exponential modes, storing only the mode nodes and vector weights instead of every timestep. Recover the modes from a Hankel matrix through an annihilating polynomial, then reconstruct the trajectory or a compact recurrent state during inference.
Useful6/10
Difficulty6/10
Novelty5/10
Unverified
2026
Add a neural feature, adapter, or expert block only through the component of its outputs that is orthogonal to the span of all previously installed blocks. Quotient coefficient directions that produce nearly identical outputs with an SVD or pseudoinverse, so the new block contributes intrinsic representational dimensions instead of duplicating old features. The expected benefit is a smaller effective architecture and better-conditioned block expansion.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Replace an unconstrained recurrent transition with a second-order resonant state whose restoring matrix is full-rank but whose damping is low-rank. The low-rank damping creates a small set of rapidly controlled bright modes and a large dark subspace with long memory, while a small optional damping term prevents numerical drift in completely dark modes.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Construct a sparse recurrent network with positive edge weights and Leaky-ReLU updates so that one selected hidden node, observed over a finite time window, contains enough information to reconstruct the full hidden state. Add an auxiliary decoder from the observed trajectory to the initial state or current state, and use graph rewiring or edge-growth until every hidden node has a directed path to the sensor within the observation horizon.
Useful6/10
Difficulty5/10
Novelty8/10
Unverified
2026
Replace a learned dense bilinear map with a structured family of signed orthogonal matrices. Given feature vectors y,z in R^n, produce r interaction features h_a = y^T H_a z / sqrt(n), where the H_a form a Hadamard/Clifford-like family; the resulting bilinear map has operator norm at most one when r is within the Hurwitz–Radon limit. Learn only channel projections and optional scalar gates around this fixed mixer.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Use a low-rank controller that observes and actuates only the graph's harmonic coordinates rather than all edge features. For a graph with first Betti number beta_1 = dim ker(B), a beta_1-dimensional cycle basis is sufficient to represent the entire harmonic sector, yielding a compact recurrent memory or adapter for circulation-dependent graph dynamics.
Useful6/10
Difficulty6/10
Novelty8/10
Unverified
2026
Implement f(A)b inside a neural network with a short Lanczos recurrence instead of an eigendecomposition or dense matrix-function operation. Use an SPD operator A such as a regularized graph Laplacian or feature covariance matrix, and choose the number of iterations by monitoring successive approximations. For Stieltjes functions, Lanczos is guaranteed to be close to the best vector in the same Krylov subspace.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Replace an unconstrained spatial gate or interpolation kernel by a compactly supported function whose translates under a lattice exactly sum to one. Impose zero products between translates under a second lattice, so active gates do not collide; thresholding a positive superlevel set then provides a nonzero separation margin and predictable sparse computation.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Use an LKJ correlation factor as the correlation component of a variational posterior over a compact adapter, LoRA factor, or Bayesian neural-network parameter block. The model learns marginal scales separately while the correlation matrix remains automatically positive semidefinite and unit-diagonal, avoiding unconstrained covariance matrices, invalid correlations, and fragile covariance decompositions.
Useful6/10
Difficulty6/10
Novelty6/10
Unverified
2026
Replace repeated full-dimensional matrix-exponential or ODE solves in a conditioned continuous-time state-space layer with contour quadrature evaluated in a projection basis. The same reduced basis and contour nodes can serve many conditioning vectors, while shifted reduced resolvents provide a stable and differentiable approximation over a prescribed time window.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Use enumerated weighing matrices as sparse orthogonal channel-mixing operators inside MLPs or residual blocks. Their ternary entries reduce multiplication to signed additions, while exact orthogonality prevents amplification or attenuation of feature norms; a trainable fixed-support version can recover expressivity without giving up computational sparsity.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Replace ordinary reverse-mode differentiation through a long sequence of stiff relaxation updates with a projected adjoint that separates slow conserved features from rapidly relaxing residual features. The neural layer can use large outer time steps even when its internal relaxation time is very small, while reconstructing only the microscopic gradient component required by the preceding layer.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Represent a neural-network weight tensor by rank-one terms whose mode factors are selected from shared orthonormal bases, and impose the same basis alignment across tensor flattenings. During or after training, retain the largest coefficients to obtain a structured truncation analogous to truncated SVD. This should produce better-conditioned tensorized layers than unconstrained CP factors while preserving a directly controllable accuracy/compute tradeoff.
Useful6/10
Difficulty5/10
Novelty5/10
Unverified
2026
Use a strictly upper-triangular block operator to represent interactions between ordered layers, experts, or token groups, and compute its inverse exactly with a finite Neumann series. Because nilpotency truncates the series after a known number of blocks, the module avoids an iterative solver while retaining controlled long-range interactions.
Useful6/10
Difficulty5/10
Novelty8/10
Unverified
2026
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
Unverified
2026
Replace a learned sequence-mixing matrix with a structured lower-triangular Sprugnoli operator whose square is exactly the identity. Applying the same operator in reverse reconstructs activations exactly, so it can be used as a reversible Transformer mixer or reversible channel permutation while retaining nontrivial long-range mixing.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Replace a generic recurrent update by a positive-state continuous-time cell whose interactions are restricted to a quadratic zero-one reaction-network motif with three state variables and six reactions. Select a motif known to possess three positive equilibria, then use the two stable equilibria as binary memory states and the intervening unstable equilibrium as the separatrix. This creates an explicitly multistable RNN module with a bounded attractor count and a measurable stability…
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Construct a symmetric token affinity matrix and approximate only its spectrally outlying token-mixing modes using a small set of sampled landmark columns. The resulting low-rank operator replaces an \(O(n^2)\) dense mixer by two skinny matrix multiplications, while the paper's residual guarantee predicts that large-magnitude global interaction modes are preserved.
Useful6/10
Difficulty5/10
Novelty5/10
Unverified
2026
Replace a learned nonnegative banded transition matrix by an ordered product of learnable stochastic bidiagonal factors. Each factor performs one local left or right transport step, so a product of p lower and q upper factors creates an effective bandwidth of p+q while retaining nonnegative entries, row sums equal to one, and a highly structured propagation kernel.
Useful6/10
Difficulty3/10
Novelty7/10
Unverified
2026
Replace unconstrained low-rank compression of a neural state with an augmented basis that always contains vectors representing known conserved quantities or diagnostically important linear statistics. After each learned transition, project the state back onto the affine constraint set with an exact minimum-norm correction, preventing rank truncation and model error from accumulating in those statistics.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Construct one reference Lanczos basis for a symmetric propagation operator H, then derive several seed-specific spectral responses for Q_a(H)x_0 through finite-band polynomial connectors. With degree-r seeds, each transformed basis vector uses at most 2r+1 neighboring reference basis vectors, avoiding a separate Lanczos factorization for every seed.
Useful6/10
Difficulty6/10
Novelty7/10