△ Mechanism confirmed, baseline not beaten
2026
Replace an unconstrained recurrent transition with a two-dimensional damped rotation whose parameters are induced by a learnable circular reorientation distribution. The first Fourier mode controls both memory persistence and phase rotation, giving the network an interpretable oscillatory memory while guaranteeing contraction when the effective decay rate is positive.
Useful7/10
Difficulty5/10
Novelty7/10
✗ Failed on benchmark
2026
Replace a dense Haar or Gaussian random projection with a streamed product of random two-coordinate rotations followed by coordinate subsampling. The transform is exactly orthogonal before subsampling, requires only a list of rotation triples, and the paper's pseudo-mixing result predicts that degree-two statistics relevant to norm preservation and Johnson–Lindenstrauss embeddings become Haar-like after only O(n polylog(n)) rotations.
Useful7/10
Difficulty4/10
Novelty5/10
△ Mechanism confirmed, baseline not beaten
2026
Replace an unconstrained recurrent matrix by a structured asymmetric circulant coupling whose Fourier modes have analytically known complex eigenvalues. A selected nonzero mode becomes a rotating attractor, providing a phase-coded recurrent state that can preserve information through oscillatory dynamics without requiring the optimizer to discover a stable spectral structure from scratch. A weak input projection and optional mode-selection loss can use the attractor as a nonlinear memory…
Useful7/10
Difficulty5/10
Novelty7/10
Unverified
2026
Replace a dense token-mixing, MLP, or low-rank-adapter projection with a Bernoulli-signed sparse matrix normalized by the paper's predicted operator scale. Estimate the active representation dimension and use the effective scale to detect regimes in which extreme sparsity is likely to cause unstable amplification or dead rows.
Useful6/10
Difficulty4/10
Novelty5/10
Unverified
2026
Use paired recurrent channels with exactly reciprocal gains while applying a common phase rotation. One channel carries a controlled expanding mode and the other a matching contracting mode, creating a tunable hyperbolic memory spectrum without the optimization fragility of an unconstrained recurrent matrix.
Useful6/10
Difficulty5/10
Novelty5/10
Unverified
2026
Initialize a stable diagonal state-space layer with decay rates \(\omega_i=|\xi_i|\), where \(\xi_i\sim\mathcal N(\mu,\sigma^2)\), instead of using a narrowly clustered rate distribution. The nonzero density of rates near zero creates a population of slow modes whose aggregate impulse response has an algebraic tail, enabling long-horizon memory while every finite-dimensional mode remains exponentially stable.
Useful6/10
Difficulty4/10
Novelty6/10
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
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 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 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
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
Unverified
2026
Replace a dense Gaussian or learned projection from dimension N to m with a normalized partial circulant projection generated by a single Gaussian vector. For K-sparse hidden states, the restricted-isometry guarantee predicts approximate norm preservation while reducing stored projection parameters from O(mN) to O(N). The projection can be evaluated with an FFT and should be combined with explicit top-k gating so that the sparse-input assumption is enforced.
Useful6/10
Difficulty4/10
Novelty5/10
Unverified
2026
Replace a dense order-p tensorized neural layer with a sparse random hypergraph tensor whose support probability is alpha = c/N^{p-1}. Assign independent zero-mean marks to active hyperedges, so every tensor moment scales as N^{-(p-1)} while the total variance entering each output remains controlled. The resulting locally tree-like computation graph should reduce parameters and multiply-adds without immediately destroying signal propagation.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Use the paper's effective-rank and eigengap-dependent covariance estimation rates to construct a confidence-aware low-rank bottleneck for transformer activations or key/value tensors. The bottleneck is enabled only when the top-p empirical eigenspace can be estimated more accurately than the desired compression error; otherwise the layer remains full-rank.
Useful6/10
Difficulty5/10
Novelty5/10
Unverified
2026
Use the paper's correspondence between KAN splines and finite-element or isogeometric shape functions to build coordinate-separable tensor-product trial layers. Replace additive coordinate aggregation with a multiplicative contraction of one-dimensional spline expansions, yielding an explicit tensor-product basis without storing a dense multidimensional grid.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Replace a dense channel-mixing matrix by a sparse complex generalised weighing matrix W with exactly w nonzero entries in every row and column, then use U=W divided by square root of w as a norm-preserving mixer. Restricting to k=2 gives a real matrix with entries in {+1,-1}; k=4 supports signed phase rotations. The exact isometry should preserve signal and gradient norms while reducing channel-mixing cost.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Build a sparse graph by thresholding normalized token or item inner products, then use the leading eigenvectors of its centered adjacency matrix as geometric features or a low-rank attention-logit bias. The graph avoids storing all pairwise similarities, while the paper's spectral bound supplies a concrete signal-to-noise test for deciding whether the resulting embedding is trustworthy.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Replace a dense token-mixing matrix in a sequence model with a fixed or learnable SBP derivative operator D=P^{-1}Q. The discrete integration-by-parts identity makes the interior mixing energy-neutral or boundary-dissipative, reducing exploding activations in deep residual stacks while preserving directional information along the sequence.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Train a square orthogonal neural mixer while maximizing its entrywise fourth-power concentration. When optimization reaches a non-permutation stationary configuration, explicitly test rank-two row or column rotations and take a rotation with positive exact second variation, using the paper's constructive saddle-escape mechanism.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Use the paper's explicitly solved SU(2)-based extremal flow as a structured recurrent transition instead of learning an unconstrained dense recurrent matrix. The transition has only two scalar parameters, a radius/frequency r and phase phi, while its rotating coefficient pattern continuously mixes four real state coordinates and can be integrated with a norm-preserving Cayley transform.
Useful6/10
Difficulty5/10
Novelty6/10
✗ Mechanism failed
2026
Replace a dense recurrent transition matrix with a periodic CMV-style product of alternating local 2x2 unitary cores. The transition is exactly norm-preserving, has O(n) trainable parameters under periodic tying, and can be applied through local factor operations rather than stored as an n-by-n matrix. Use turnover refactorization when changing the ordering or boundary connection of cores, enabling a compact cyclic unitary state-space layer.
Useful6/10
Difficulty5/10
Novelty5/10
✗ Mechanism failed
2026
Replace a dense channel or token-mixing matrix with a product of positive bidiagonal factors, so information propagates through a controlled sequence of local couplings rather than arbitrary signed interactions. Initialize the factors from the paper's barycentric-subdivision factorization, then learn positive diagonal and off-diagonal parameters; the resulting map is structured, parameter-efficient, and constrained to remain totally positive.
Useful6/10
Difficulty5/10
Novelty8/10
Unverified
2026
Treat a finite shallow network as a discrete signed measure over ridge atoms and grow or prune neurons according to their contribution to total variation. This turns width selection into an atomic approximation procedure: add neurons correlated with the current residual and remove coefficients that consume budget without contributing materially.
Useful5/10
Difficulty5/10
Novelty5/10
Unverified
2026
Replace ordinary per-coordinate activation normalization or covariance whitening with a learned or frozen affine map based on a minimum-volume ellipsoid calibrated to the activation convex hull. Estimate the hull's Minkowski symmetry and use the bound \(\rho=\sqrt{d/\alpha}\) to set a principled clipping radius, where \(d\) is feature dimension and \(\alpha\) is the measured symmetry. This should reduce worst-case clipping of asymmetric activation distributions without requiring a much larger…
Useful5/10
Difficulty6/10
Novelty4/10