# QFCQT: A Chaotically Gated Quantformer Framework for Volatile Time-Series Forecasting

arXiv: https://arxiv.org/abs/2608.07363 · HTML: https://mlsanity.com/paper/2608.07363/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [Deep Transformer Models for Time Series Forecasting: The Influenza Prevalence Case](https://mlsanity.com/paper/2001.08317/) (2020)
- [Quantformer: from attention to profit with a quantitative transformer trading strategy](https://mlsanity.com/paper/2404.00424/) (2024)
- [COTN: A Chaotic Oscillatory Transformer Network for Complex Volatile Systems under Extreme Conditions](https://mlsanity.com/paper/2511.06273/) (2025)

## Abstract (arXiv)

Forecasting non-stationary time series remains difficult due to long-range dependencies, local volatility bursts, structural shifts, and nonlinear oscillatory behaviors. Although Transformer-based forecasters are effective for modeling long-term temporal dependencies, their feed-forward blocks typically rely on smooth static activations that are insufficiently sensitive to abrupt regime changes. Motivated by quantitative Transformer designs and oscillator-based nonlinear activations, we propose QFCQT, short for Quantum-Fractal-inspired Chaotically Gated Quantformer, for robust forecasting under complex volatile dynamics. Here, "quantum-fractal-inspired" denotes a computational analogy based on soft oscillator superposition and multi-scale nonlinear responses, rather than a formal quantum-mechanical or fractal-theoretic derivation. QFCQT consists of three main components: (1) a Quantformer-style numerical encoder that directly processes multivariate inputs via linear embedding; (2) a learnable Lee-oscillator activation module that maps scalar pre-activations to dynamic oscillatory responses and summarizes them through Max-over-Time pooling; and (3) a smooth-chaotic gated fusion mechanism that adaptively balances conventional smooth activations and chaos-sensitive responses. Furthermore, instead of using a single fixed oscillator, QFCQT employs a soft superposition of eight parameterized Lee oscillator families to adaptively capture different nonlinear response patterns across regimes. Experiments on ETTh1, ETTh2, and A-share Stock Index benchmarks show that QFCQT consistently outperforms strong baselines, including Informer, LogTrans, LSTMa, HAT, and COTN.