Taylantay/fading-flash

Fading Flash

A compact diagnostic for sequence models that jointly tests input-dependent dynamics and extrapolation to unseen step sizes Δ, from the paper TIDES: Implicit Time-Awareness in Selective State Space Models (code: https://github.com/TaylanSoydan/TIDES).

Each sequence has 40 steps split into 2-3 zones. Every zone has its own decay rate λ ∈ {1, 1.5, 2} and 2-4 unit "flashes" occur at random steps. The target is the glow

h_j = α_j h_{j-1} + β_j x_j,   α_j = exp(-λ_j Δ),   β_j = (1 - α_j) / λ_j,

the exact zero-order-hold discretisation of dh/dt = -λ h + x at step size Δ (one Δ per sequence). A model must read the zone's rate from the input (input-dependence) and apply it at the right Δ. Training uses Δ ~ U[0.5, 1.5]; the test split sweeps Δ ∈ {0.1, 0.2, 0.3, 0.5, 0.8, 1, 1.2, 1.5, 1.8, 2}, so Δ < 0.5 and Δ > 1.5 are out of distribution.

Fields

column	type	meaning
flash	float32[40]	input x_j: 1 at a flash, else 0
rate	int8[40]	zone rate index per step (λ = 1, 1.5, 2 for 0, 1, 2)
dt	float32	step size Δ of the sequence
glow	float32[40]	target h_j

The model input used in the paper is, per step, [flash, one_hot(rate)] (4 features) plus Δ.

Splits

split	sequences	Δ
train	100,000	U[0.5, 1.5]
validation	5,000	U[0.5, 1.5]
test	20,000	2,000 at each of the 10 values above

The paper trains on freshly sampled batches from the same generator (3000 Adam steps of 32 sequences, ≈ 96k sequences); this static train split is that distribution frozen. Metric: relative error 100 · sqrt(MSE / Var(glow)) per Δ.

Usage

import torch
from datasets import load_dataset

test = load_dataset("Taylantay/fading-flash", split="test").with_format("torch")[:]
x = torch.cat([test["flash"].unsqueeze(-1),
               torch.nn.functional.one_hot(test["rate"].long(), 3).float()], dim=-1)
dt, y = test["dt"], test["glow"]      # x: (N, 40, 4), dt: (N,), y: (N, 40)

Provenance

Generated by fading_flash/make_hf_dataset.py (seeds: train 1, validation 2, test 3000 + i for the i-th Δ). MIT licensed, like the code.

Citation

@article{soydan2026tides,
  title   = {{TIDES}: Implicit Time-Awareness in Selective State Space Models},
  author  = {Soydan, Taylan and Bessa, Miguel A. and Mohr, Dirk and Barreira, Rui},
  journal = {arXiv preprint arXiv:2605.09742},
  year    = {2026}
}