Scale-Equivariant Generative Forecasting: Weight-Tied Dilated Convolutions, Wavelet Scattering Inputs, and Spectral-Consistency Training for Self-Similar Time Series
Many natural and engineered time series -- equity returns, climate anomalies, turbulent velocities, neural recordings, packet-level network traffic -- are approximately self-similar: their horizon-$T$ distribution is tied to the horizon-$1$ distribution by one scaling exponent $H$. Standard deep generative sequence models (transformers, dilated TCNs, the WaveNet family) ignore this. Their receptive fields are wide, but kernel parameters live independently at every dilation level, yielding a multi-scale architecture, not a scale-equivariant one. We make three contributions. First, we give a precise definition of discrete scale equivariance for 1D causal networks and prove that dyadic dilation commutes (up to boundary effects) with any dilated-convolution stack whose kernel weights are shared across levels. Tying the kernel shrinks the convolutional parameter budget by an $L$-fold factor (where $L$ is depth) and hard-wires self-similarity in as an inductive bias. Second, we wrap this Scale-Equivariant WaveNet (SE-WaveNet) backbone in three components that carry the same prior: a one-level Daubechies-4 wavelet input, a Hurst-FiLM block exposing the local scaling exponent, and a spectral-consistency training term targeting the $|f|^{-(2H+1)}$ power-law spectrum. The head is a conditional normalising flow, chosen to preserve equivariance. Third, on 30 years of S&P 500 daily log-returns, SE-WaveNet samples reproduce the empirical scaling-collapse diagnostic on the Allan-Variance top-25 universe (median $\mathcal{C}^\star = 0.020$), while a vanilla WaveNet at matched capacity does not ($\geq 0.06$). NLL, KS-calibration, and tail energy distance tie or beat the baseline, with $L\times$ fewer convolutional parameters.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks
Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes. We …
No Equivariant Architecture Covers All Equivariant Attention
We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$ can only act by permuting head-clusters, with QK and OV matrices sati…
T-LLM: Teaching Large Language Models to Forecast Time Series via Temporal Distillation
Time series forecasting plays a critical role in decision-making across many real-world applications. Unlike data in vision and language domains, time series data is inherently tied to the evolution of underlying process…
Time Series ForecastingEquivariant Graph Neural Networks for 3D Macromolecular Structure
Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural net…
Atom3D benchmarkBIG-bench Machine LearningTransfer LearningFlowState: Sampling-Rate-Equivariant Time-Series Forecasting
Existing time series foundation models (TSFMs), often based on transformer variants, lack adaptability to different sampling rates, struggle with generalization across varying context and target lengths, and are computat…