△ Mechanism confirmed, baseline not beaten
2026
Replace dense continuous action search during neural-controller verification with a finite set of representative inputs induced by affine pieces of the interval neural dynamics. This makes safety checking parallel over state cells and candidate actions, enabling much cheaper certification or repeated safe-set updates.
Useful7/10
Difficulty7/10
Novelty8/10
△ Mechanism confirmed, baseline not beaten
2026
Replace a fixed-order polynomial or recurrent state-space block by an Arnoldi basis built from a learned operator and the current input, and use subdiagonal coefficients as geometry-aware gates over Krylov depth. The gates quantify how much genuinely new direction each operator application contributes, allowing the layer to stop early near Krylov breakdown and suppress redundant or unstable directions.
Useful7/10
Difficulty5/10
Novelty7/10
✗ Failed on benchmark
2026
Train a cheap shared multi-task probe briefly, extract one semantic embedding per task, and use density-based clustering to determine which tasks should share a neural trunk. After clustering, replace the globally shared trunk by one trunk per discovered cluster, with task heads remaining separate; this preserves cooperation among related tasks while isolating destructive task interactions.
Useful7/10
Difficulty5/10
Novelty5/10
✓✓ Beats tuned baseline
2026
Build a positively homogeneous convex network by representing every intermediate unit as a compact polytope and composing units with Minkowski sums, convex-hull unions, and positive dilations. This gives an explicitly convex and monotone architecture whose geometric complexity can be controlled independently of the number of sampled linear pieces, potentially producing smaller ICNNs for structured convex functions.
Useful7/10
Difficulty7/10
Novelty7/10
△ Mechanism confirmed, baseline not beaten
2026
Replace a dense multiresolution voxel or hash-grid encoder with an omnitree-like anisotropic feature partition. Each cell stores a vector-valued scaling feature and its children are introduced only when local Haar detail energy is large; coarsening replaces children by their mean, so compression does not introduce an arbitrary offset. Splitting can be restricted to the coordinate whose one-dimensional detail coefficient is largest, allowing thin structures to receive resolution only in the…
Useful7/10
Difficulty5/10
Novelty7/10
Unverified
2026
Propagate uncertain inputs or parameter perturbations through a neural network with zonotopes, and choose the reduction rule after each layer using short lookahead that predicts downstream certified-bound error. Candidate reducers can include largest-generator retention, box conversion, and norm-based merging; unlike a fixed policy, the chosen rule depends on the current generator geometry and remaining network depth. The goal is tighter robustness bounds at the same generator budget, or the…
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Replace a dense directional feature map with a finite stable-zonotope layer: a small set of large random vectors creates a hyperplane arrangement over the input sphere, while a cheaper small-jump residual gives continuous features inside each cell. The layer exposes an explicit compute-versus-resolution knob through the jump cutoff and can be used either as an embedding before an MLP or as a lightweight router for mixture-of-experts blocks.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Represent adaptive computation or MoE routing as a continuous latent trajectory that crosses convex mode walls, with a Minkowski norm defining computational speed. At a wall, choose the outgoing latent velocity by the same constrained variational rule as billiard reflection, and use the local path-length certificate to detect or prevent pathological accumulation of infinitely many routing events in finite depth.
Useful6/10
Difficulty7/10
Novelty8/10
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
Build a recurrent ReLU module that evaluates a binary refinement cascade using a fixed-dimensional state and shared cell weights. Replace hard binary digit selection with two overlapping circle coordinates; switch between their affine state updates only at points where the two candidate updates agree, so the switch is an exact continuous piecewise-linear ReLU operation rather than a multiplicative gate.
Useful6/10
Difficulty6/10
Novelty7/10
Unverified
2026
Build a sparse expert cascade whose router uses empirical progress, uncertainty, and compute cost to construct an efficient frontier of experts. Instead of always choosing the expert with the largest immediate gain per FLOP, route different confidence states through an ordered sequence of frontier experts, allowing cheap high-variance experts early and safer or more cost-effective experts near the final decision.
Useful6/10
Difficulty5/10
Novelty6/10
Unverified
2026
Construct a sparse routing or graph-neural architecture whose activation gates satisfy a hard-core constraint: neighboring sites, experts, or token groups cannot be active simultaneously. Compare the same local routing rule on bipartite and random regular interaction graphs; the graph structure should change the maximum usable activation dimension and may also change optimization stability.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Replace a $K$-class softmax with $N$ binary hyperplane heads, where each class is represented by the signs of its projections onto fixed random directions. Train the embedding to reproduce these codewords and decode by nearest Hamming codeword. The paper's guarantee suggests that $N\approx 2\log_2 K+\log_2(1/\delta)$ can separate all class centers with high probability in sufficiently high dimension, giving a concrete width rule rather than choosing the number of binary heads heuristically.
Useful6/10
Difficulty4/10
Novelty5/10
Unverified
2026
Use the trace representation of a maxout network to regularize the geometry of its generated coefficient vectors. Encourage active traces to be diverse and nonredundant, so the model spends parameters on genuinely different supporting hyperplanes rather than branches that collapse to the same linear function.
Useful6/10
Difficulty5/10
Novelty8/10
✗ Mechanism failed
2026
Represent every mesh interface degree of freedom by one feature copy per incident cell, and apply local neural blocks directly to these cell tensors. Enforce inter-cell consistency with valence-weighted averaging only after selected layers or hierarchy transitions, avoiding repeated construction of a global sparse graph or assembled feature vector. This is suited to adaptive quadtrees, octrees, and finite-element neural operators.
Useful6/10
Difficulty5/10
Novelty7/10
Unverified
2026
Prune higher-order tensor or polynomial interactions while preserving an exchange-closed support instead of independently retaining the largest weights. The resulting sparse interaction pattern avoids arbitrary holes and retains structured substitutions between coordinates, potentially improving parameter efficiency and robustness after pruning.
Useful5/10
Difficulty5/10
Novelty9/10
Unverified
2026
Construct a Fourier layer whose active frequencies lie on several nonparallel polygonal patches or thin annular sectors, and cap repeated difference vectors generated by pairs of patches. The bounded-multiplicity geometry limits how many input frequency pairs can contribute to the same output frequency, potentially reducing spectral aliasing and gradient variance in nonlinear Fourier mixing.
Useful5/10
Difficulty6/10
Novelty7/10
Unverified
2026
Use the layer at which persistent connected components and holes disappear to allocate capacity nonuniformly across a network. If representations simplify much earlier than desired, widen the responsible layers or insert an additional block; if simplification is excessively delayed, avoid spending parameters there. This turns persistent-homology COM into an actionable architecture-search signal rather than a post-hoc visualization.
Useful5/10
Difficulty6/10
Novelty7/10
Unverified
2026
Estimate the simplex-based ratio of a target or learned convex piecewise-linear polytope and use the theorem \(\rho_\Delta(P)\le 2^d-1\) to choose a minimum useful ReLU depth. During training, monitor whether the learned polytope is approaching a high-\(\rho\) target; if it is, widen the model without increasing depth only when the diagnostic indicates that depth is the bottleneck.
Useful5/10
Difficulty5/10
Novelty9/10