SPECTRA: Sparse Periodic Extraction for Conditional Time-series Retrieval Augmentation

This repository contains the layout, performance evaluations, and theoretical framework for SPECTRA (Sparse Periodic Extraction for Conditional Time-series Retrieval Augmentation).

SPECTRA introduces a lightweight, end-to-end architecture that solves the scalability, memory, and latency bottlenecks of conventional Retrieval-Augmented Forecasting (RAFT) methods without compromising on predictive precision.

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👥 Authors & Affiliations

• Elhoussaine Gangouch (elhoussainegangouch@gmail.com) — UM6P (Université Mohammed VI Polytechnique)
• Issam Ait Yahia — Université Mohammed VI Polytechnique
• Abdelkader El Mahdaouy — Mohammed VI Polytechnique University
• Ismail Berrada — Université Mohammed VI Polytechnique

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🚀 Core Contributions

• Data-Domain Sparsity: Shifts the time-series retrieval paradigm away from traditional data-point retrieval to periodic-motif retrieval.
• 100× Storage Reduction: Replaces dense, overlapping historical sliding windows ($O(N)$) with a highly compressed Sparse Periodic Dictionary ($O(N/L)$).
• 10× Inference Speedup: Achieves an inference throughput of 200 samples/second, matching the speeds of non-retrieval linear baselines while keeping high-fidelity retrieval capacity.
• Mathematical Justification: Leverages the Nyquist-Shannon Sampling Theorem via frequency-domain constraint rules. The learnable Spectral Extractor (Conv1D + Pooling) band-limits raw inputs to perform strided sampling without aliasing.

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📊 Performance & Efficiency Benchmarks (ETTh1 Summary)

SPECTRA establishes a new Pareto-Optimal Frontier, yielding lower overall error thresholds compared to dense baselines while cutting operational overhead.

Retrieval Strategy	Database Management Strategy	Evaluation MSE	Inference Latency	Throughput
Dense RAFT	Full Sliding History ($S = 1$)	0.367	145 ms	19 samp/s
Random Sparse	Naive Unstructured Subsampling	0.412	—	—
SPECTRA (Ours)	Periodic Stride ($S = T$)	0.361	14 ms	200 samp/s

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🧠 Extended Empirical Insights (From Appendix)

1. Robust Denoising Mechanics

Standard dense retrieval relies on raw Euclidean space metrics, making it highly sensitive to high-frequency stochastic noise. As shown via query injection experiments, SPECTRA projects values into a lower-dimensional periodic motif space, successfully filtering out anomalies and showing a shallow, linear noise degradation curve.

2. Manifold Topology Verification

Applying t-SNE dimensional scaling to our stored keys confirms that the embeddings form a clean, stable circular topology (Limit Cycle). This geometric phase coherence allows the model to interpolate smoothly and accurately across sparse historical anchors.

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🛠️ Operational Architecture