Inject weak, unpostselected stochastic perturbations into activations, attention links, or recurrent transitions, but scale their strength according to effective computational size. The schedule is designed so that noise is initially a weak perturbation and becomes dominant only beyond a controlled depth or sequence length, producing a measurable crossover rather than uncalibrated constant dropout.
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.
Replace dense pairwise interactions between all forecast horizons with nested time-shell summaries. For sorted horizons, the readout at shell j receives a cumulative embedding of all coefficients or queries assigned to later horizons, reproducing the paper's dependence on products such as \(\Pi_j=\prod_{l>j}e^{\alpha_l}=e^{\sum_{l>j}\alpha_l}\). This gives an \(O(Kd)\) multi-horizon interaction instead of an \(O(K^2d)\) temporal attention block and should work best for weak-memory…
Augment a sequence model with a scalar phase-like latent field and several coupled channel fields, then add a KPZ-style nonlinear gradient drift between neighboring sequence positions. The coupling is made dimension-aware: it can remain active in effectively one- or two-dimensional latent dynamics, but is annealed toward zero in higher-dimensional dynamics where the paper predicts that weak nonequilibrium perturbations become irrelevant.
Construct a 2D recurrent or residual neural lattice with slowly varying local couplings, while parameterizing those couplings so that an anisotropy invariant remains constant across all spatial and depth locations. The network obtains controlled local propagation velocities rather than arbitrary inhomogeneous amplification, enabling depth-dependent receptive fields while preserving near-critical signal propagation.
Construct a residual network with two coupled feature streams and deliberately non-reciprocal cross-stream interactions represented by a skew-symmetric coupling matrix. Decay the coupling strength with depth according to the RG picture of an irrelevant perturbation, allowing early layers to exploit rotational mixing while forcing deep layers toward reciprocal equilibrium-like dynamics. This should preserve transient expressivity without producing depth-dependent amplification or oscillatory…
Construct augmented sequences by tiling long contexts with large finite blocks sampled from a library whose local-pattern frequencies match a target dataset, replacing only block interiors and leaving boundary zones untouched. This produces globally coherent synthetic contexts while controlling the distortion of short-range statistics through an explicit boundary-to-volume ratio.