# Sparse Latent Factor Forecaster (SLFF) with Iterative Inference for Transparent Multi-Horizon Commodity Futures Prediction

arXiv: https://arxiv.org/abs/2505.06795 · HTML: https://mlsanity.com/paper/2505.06795/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 134 references that are in the map.
- First posted on arXiv 11 May 2025.

## Builds on (most cited first, 23 of 23)

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- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [Character-Aware Neural Language Models](https://mlsanity.com/paper/1508.06615/) (2015)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Iterative Amortized Inference](https://mlsanity.com/paper/1807.09356/) (2018)
- [Semi-Amortized Variational Autoencoders](https://mlsanity.com/paper/1802.02550/) (2018)
- [Structured Prediction Energy Networks](https://mlsanity.com/paper/1511.06350/) (2015)

## Abstract (arXiv)

Amortized variational inference in latent-variable forecasters creates a deployment gap: the test-time encoder approximates a training-time optimization-refined latent, but without access to future targets. This gap introduces unnecessary forecast error and interpretability challenges. In this work, we propose the Sparse Latent Factor Forecaster with Iterative Inference (SLFF), addressing this through (i) a sparse coding objective with L1 regularization for low-dimensional latents, (ii) unrolled proximal gradient descent (LISTA-style) for iterative refinement during training, and (iii) encoder alignment to ensure amortized outputs match optimization-refined solutions. Under a linearized decoder assumption, we derive a design-motivating bound on the amortization gap based on encoder-optimizer distance, with convergence rates under mild conditions; empirical checks confirm the bound is predictive for the deployed MLP decoder. To prevent mixed-frequency data leakage, we introduce an information-set-aware protocol using release calendars and vintage macroeconomic data. Interpretability is formalized via a three-stage protocol: stability (Procrustes alignment across seeds), driver validity (held-out regressions against observables), and behavioral consistency (counterfactuals and event studies). Using commodity futures (Copper, WTI, Gold; 2005--2025) as a testbed, SLFF demonstrates significant improvements over neural baselines at 1- and 5-day horizons, yielding sparse factors that are stable across seeds and correlated with observable economic fundamentals (interpretability remains correlational, not causal). Code, manifests, diagnostics, and artifacts are released.