Architecture ideas

Attention variants, state-space and recurrent cells, normalization and token-mixing schemes — each tested against the standard block it replaces.

✓✓ Beats tuned baseline 2026

Adaptive Physics-Lifted Koopman State Space

Replace a purely nonlinear recurrent transition with a learned observable map followed by an explicitly linear latent evolution model. Include the original latent state and a small set of nonlinear observables, and update the linear transition online with forgetting-factor recursive least squares when the environment or task dynamics change.

Useful8/10
Difficulty6/10
Novelty6/10
Paper: Physics-based Online Adaptive Koopman Model Predictive Attitude Control for Combined Spacecraft with Dynamic Uncertainties arXiv:2609.02534
✗ Failed on benchmark 2026

Differentially Passive Neural Blocks

Replace selected residual, recurrent, or state-space blocks by modules whose input-output Jacobians satisfy an IODP inequality throughout a prescribed activation domain. The constraint controls incremental amplification between two trajectories without requiring either trajectory to remain near one fixed equilibrium, so it should improve robustness to changing contexts and prevent exploding long-horizon sensitivities.

Useful8/10
Difficulty6/10
Novelty6/10
Paper: Decentralized and Equilibrium-Set-Oriented Stability Analysis and Control for Power Systems arXiv:2609.00497
✓✓ Beats tuned baseline 2026

Conservative Flux Neural Operator

Replace pointwise prediction of the next field with prediction of a learned flux followed by a discrete divergence. Combine Fourier spatial mixing with a causal temporal kernel over the recent resolved-history slab, so the model learns finite-memory closure effects while preserving local conservation exactly under periodic or compatible boundary conditions. The architecture should reduce spurious mass drift and improve autoregressive rollout stability on coarse-grained PDE data.

Useful8/10
Difficulty5/10
Novelty6/10
Paper: Flux-form spatiotemporal neural operators for coarse-grained dynamics of multiscale PDEs arXiv:2608.18148
✓✓ Beats tuned baseline 2026

Power-Balanced Modular Neural Block

Represent each neural module as a Hamiltonian storage system and connect modules through a state-dependent skew or Dirac interconnection instead of arbitrary residual additions. The coupling may change with the hidden state, but its internal power contribution cancels exactly, so total stored energy is controlled only by external inputs and explicitly added dissipation.

Useful8/10
Difficulty5/10
Novelty5/10
Paper: Port-Hamiltonian modelling of coupled rigid/flexible multibody systems arXiv:2608.05143
✗ Failed on benchmark 2026

Generator-Flow Equivariance Training

Use discovered infinitesimal generators to create small continuous transformations of hidden states and force a neural predictor to commute with those transformations. This converts symmetry discovery into self-supervised augmentation without prespecifying a group, canonical coordinates, or hand-designed equivariant layers.

Useful8/10
Difficulty5/10
Novelty6/10
Paper: LieStoNet: Learning Lie Symmetries from Spatiotemporal Data for Stochastic Dynamical Systems arXiv:2608.01582
△ Mechanism confirmed, baseline not beaten 2026

Stable Modal State-Space Bottleneck

Insert a continuous spatial trunk and a pole-constrained modal state-space branch into a spatiotemporal predictor. The model represents a field as a sum of learned spatial modes and exponentially evolving modal coordinates, so long-horizon behavior is controlled by explicit poles rather than by an unconstrained recurrent transition matrix.

Useful8/10
Difficulty6/10
Novelty7/10
Paper: Learning Structural Eigenmodes with Modal Operator Network (ModalONet) arXiv:2607.28926
✗ Mechanism failed 2026

Permutation-family residual network

Replace direct learning of a highly cancelling signed observable with a quotient-space model over symmetry orbits of inputs. Predict a physically constrained baseline for each family and use an LSTM or set/graph encoder only for the residual many-body correlation, then aggregate family predictions with known signed weights instead of forming a noisy sample-level ratio.

Useful8/10
Difficulty5/10
Novelty7/10
Paper: Learning the Fermion sign structure in path-integral Monte Carlo arXiv:2607.15060
△ Mechanism confirmed, baseline not beaten 2026

Certified Bi-Lipschitz Recurrent Cell

Replace an unconstrained RNN or state-space layer with an implicit recurrent cell whose nonlinear algebraic loop is well posed and whose forward dynamics are contracting and strongly input-output monotone. The same certificate guarantees a causal inverse with bounded gain, so sequence predictions should be insensitive to initial-state mismatch while remaining responsive to input perturbations.

Useful8/10
Difficulty6/10
Novelty7/10
Paper: Robustly Invertible Nonlinear Dynamics and the BiLipREN: From Inversion-Based Control to Generative Trajectory Modelling arXiv:2607.10026
✗ Failed on benchmark 2026

Holonomy-designed recurrent memory

Build a recurrent module from two finite-state factors: a normalization state and a winner-selection state. Choose or learn their coupling so that the joint transition system contains a certified composite two-cycle, giving the network a small robust memory state, while every fixed-input generator still collapses most states toward attractors. The module can be embedded in a continuous RNN using soft state assignments during training and straight-through discretization for algebraic auditing.

Useful7/10
Difficulty5/10
Novelty8/10
Paper: "More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks arXiv:2608.30231
△ Mechanism confirmed, baseline not beaten 2026

Positive-Regime Observable ReLU State Space

Constrain recurrent preactivations to remain nonnegative so that ReLU acts as the identity along realized trajectories. The hidden dynamics then admit a classical linear observability matrix, allowing principled hidden-coordinate selection and conditioning control instead of relying on potentially destructive activation masks.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: On the Number of Observation Nodes in Recurrent Neural Networks with Linear Threshold and ReLU Functions arXiv:2608.29650
✗ Failed on benchmark 2026

Hyperplane-Gated Piecewise Neural Dynamics

Replace a single smooth neural vector field with a finite collection of smooth subnetworks selected by learned affine hyperplanes. The architecture exposes switching geometry directly, allowing it to represent friction-like or threshold dynamics without approximating discontinuities using excessively steep activations.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: Learning piecewise-smooth dynamical systems arXiv:2608.19785
△ Mechanism confirmed, baseline not beaten 2026

Koopman Hankel Dual Autoencoder

Replace pointwise sequence reconstruction with reconstruction of overlapping past and future Hankel windows in a shared latent manifold. A first encoder compresses the delay-coordinate trajectory, while a second decoder or predictor reconstructs the future block from the latent state; training therefore penalizes representations that fit observations but do not preserve dynamical evolution.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: Fault detection on manifolds of nonlinear dynamical systems with dual autoencoders arXiv:2608.17698
✗ Failed on benchmark 2026

Sensitivity-Conditioned Neural ODE Pruning

Use trajectory sensitivities to remove neural units or parameter groups whose effects are redundant over the available data support. A parameter group is pruned when its Fisher contribution is small or its sensitivity is nearly collinear with other groups, producing a compact neural ODE without relying only on parameter magnitude.

Useful7/10
Difficulty5/10
Novelty8/10
Paper: Identifiability-aware neural ordinary differential equations for parsimonious and reliable dynamic modelling arXiv:2608.13044
✗ Mechanism failed 2026

Volume-Threshold Contracting State Layer

Construct a recurrent or state-space layer as a skew product: an expanding bounded feature coordinate drives a linearly contracting hidden state. Constrain the hidden transition matrix A to have spectral radius below one, and monitor the predicted transition ell times the absolute determinant of A equals one: below it, hidden trajectories should occupy a thin or fractal set, while above it they should have substantially higher-dimensional state coverage without losing local contraction.

Useful7/10
Difficulty5/10
Novelty7/10
Paper: Geometric Properties of Higher Dimensional Solenoidal Attractors arXiv:2607.27089
✗ Failed on benchmark 2026

Nonlinear Noise-Tightening Drift

Replace a linear restoring drift in score-based sampling, latent dynamics, or stochastic regularization with a state-dependent nonlinear restoring term that is at least as contractive globally and more contractive away from the origin. This should reduce stationary variance without changing the worst-case local contraction certificate.

Useful7/10
Difficulty5/10
Novelty7/10
Paper: Wasserstein Stability of Contracting Flows: Effective Rates, Euler Self-Correction, and Noise Tightening arXiv:2607.14291
✗ Failed on benchmark 2026

ISS-Constrained Modular Recurrent Network

Replace an unconstrained recurrent block with two coupled modules: a contractive perceptual estimator and an input-to-state-stable cognitive state transition. Spectral normalization and a controlled Euler residual step enforce a quantitative gain condition, preventing hidden-state explosion while retaining long memory when the contraction factor is chosen close to one.

Useful7/10
Difficulty5/10
Novelty6/10
Paper: A modular state-space model of human perception, cognition, and decision dynamics arXiv:2607.14078
✓✓ Beats tuned baseline 2026

Cyclic Momentum Latents

Add a learnable cyclic-coordinate mechanism to latent dynamics so that selected latent coordinates do not enter the Hamiltonian and their conjugate momenta become conserved. This provides an explicit dimensionality-discovery and invariance bias, encouraging the model to represent nuisance or symmetry directions compactly instead of spending independent dynamics capacity on them.

Useful7/10
Difficulty6/10
Novelty7/10
Paper: Generating Physically Plausible Parachute Dynamics with Deep Generative Modeling arXiv:2607.12143
✗ Mechanism failed 2026

Canonical Tropical Segment State

Build a sequence or graph module whose state is a canonical set of affine tropical pieces rather than an opaque hidden vector. Compose consecutive segments by Minkowski addition of their lifted supports, merge alternatives by union followed by lower-hull reduction, and evaluate the resulting piecewise-linear function with a minimum.

Useful7/10
Difficulty7/10
Novelty8/10
Paper: On the Representational Geometry of Dynamic Programs arXiv:2608.25034
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

Sector-Parametrized Neural Operator

Replace a recurrent, SSM, or residual linear operator W by an exact affine image of a contractive matrix sigma. The resulting W lies in a prescribed matrix ball and, for the positive-real choice of parameters, satisfies a sector inequality such as W+W^* >= 0. This gives an anisotropic, learnable alternative to plain spectral normalization: the allowable operator set is convex and its center and left/right radii can encode known directional scales.

Useful6/10
Difficulty5/10
Novelty6/10
Paper: Hyperpositive functions, sector bounded functions and a trace formula arXiv:2609.03403
Unverified 2026

Marginal Fractional Coupling Layer

Replace a local smoothness penalty or local state transition along a sequence or depth coordinate by a marginal fractional quadratic energy with Fourier multiplier |k|. The sigma=1 kernel is nonlocal and scale-free, so it can preserve long-range correlations while suppressing high-frequency instability more selectively than an ordinary Laplacian penalty.

Useful6/10
Difficulty5/10
Novelty7/10
Paper: BKT-like Correlation Scaling and Twist Responses in a One-Dimensional Fractional $U(1)$ Ginzburg--Landau Model arXiv:2609.00721
Unverified 2026

Pressure-Controlled Neural IFS

Construct a generative or recurrent neural architecture with several contractive or mildly expanding branches, and explicitly control the geometric complexity of its invariant set using the sub-additive singular-value pressure of branch-Jacobian products. Instead of regularizing only the operator norm, the model can preserve anisotropic directions while targeting a desired attractor dimension, potentially improving coverage of structured data without uncontrolled folding or collapse.

Useful6/10
Difficulty6/10
Novelty8/10
Paper: Dimensions of surface repellers and attractors of non-linear planar IFSs arXiv:2608.30744
Unverified 2026

Composite-cycle interface search

Use exhaustive finite-state analysis as an architecture-search objective for coupled recurrent motifs. Instead of independently tuning a normalization gate and a WTA gate, enumerate their possible interfaces and select couplings that create group action only on a small joint image set, yielding controlled reversible subdynamics embedded in an otherwise dissipative system.

Useful6/10
Difficulty6/10
Novelty9/10
Paper: "More Is Different'' in Neural Circuits: Algebraic Emergence of Effective Theories in Canonical Recurrent Motifs of Biological Neuronal Networks arXiv:2608.30231
Unverified 2026

Bures-Shaped Latent State Space

Add a stable linear latent state-space block whose controllability Gramian is trained toward a chosen positive-definite target using squared Bures–Wasserstein distance. Direction-specific semidefinite constraints can suppress disturbance amplification in nuisance coordinates while preserving controllability in coordinates needed for prediction.

Useful6/10
Difficulty6/10
Novelty7/10
Paper: A Controllability Gramain Shaping with LMI Constraints under Bures--Wasserstein Distance arXiv:2608.19754