Taming Volatility with Oscillating Networks

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Author: Denis Avetisyan

A new deep learning approach leverages the power of chaotic oscillators to improve forecasting in unpredictable systems.

The system leverages the temporal dynamics of a Lee Oscillator, distilling its oscillatory behavior into a meta-activation function through Max-over-Time pooling—a process that suggests any attempt at static definition inevitably loses information inherent in the system’s evolving state.
The system leverages the temporal dynamics of a Lee Oscillator, distilling its oscillatory behavior into a meta-activation function through Max-over-Time pooling—a process that suggests any attempt at static definition inevitably loses information inherent in the system’s evolving state.

This research introduces COTN, a novel architecture integrating Lee Oscillators into Transformer networks for enhanced time series forecasting, particularly under extreme and volatile conditions.

Accurate forecasting remains a persistent challenge in complex systems like financial and electricity markets, particularly when confronted with extreme volatility and nonlinear dynamics. This paper introduces ‘COTN: A Chaotic Oscillatory Transformer Network for Complex Volatile Systems under Extreme Conditions’, a novel deep learning architecture designed to address these limitations. By integrating Lee Oscillators into a Transformer network, COTN effectively captures chaotic patterns and improves responsiveness during periods of heightened fluctuation, demonstrably outperforming state-of-the-art models. Could this approach unlock more robust and reliable forecasting capabilities for navigating increasingly uncertain real-world systems?

The Illusion of Predictability

Traditional time series models, such as ARIMA and GARCH, often falter when confronted with real-world data, struggling to represent the non-linear dynamics inherent in complex systems. Their assumptions of stationarity and simplified volatility prove inadequate for capturing chaotic behaviors. Existing deep learning architectures, including LSTMs and Transformers, similarly struggle with long-range dependencies and unpredictable fluctuations, limited by their inability to extrapolate from complex, sensitive data. These persistent limitations necessitate novel approaches, acknowledging that forecasts are fleeting illusions of control.

Resonance and the Oscillatory Network

The Chaotic Oscillatory Transformer Network (COTN) integrates the Lee Oscillator—a discrete-time model of chaotic dynamics—with the Transformer architecture. This fusion aims to imbue the Transformer with the capacity to model complex temporal dependencies, surpassing the limitations of recurrent or convolutional approaches.

A λ-Gating Mechanism dynamically modulates the Lee Oscillator’s influence, allowing the network to adaptively capture chaotic behavior at different timescales. The gating parameter, λ, is learned during training, balancing stability and responsiveness.

The neural architecture of the Lee Oscillator demonstrates a recurrent network structure designed to model and replicate oscillatory behavior.
The neural architecture of the Lee Oscillator demonstrates a recurrent network structure designed to model and replicate oscillatory behavior.

Max-over-Time Pooling compresses the Lee Oscillator’s temporal output, reducing computational complexity and facilitating long-range dependency modeling. This fixed-length representation is fed into the Transformer’s attention mechanism, capturing relationships across extended temporal sequences.

Performance Under Duress

The COTN demonstrates enhanced performance on datasets characterized by extreme conditions, particularly the ETT dataset (electricity transformer temperature prediction) and high-frequency A-Share stock data. Evaluations reveal COTN’s capability to capture non-stationarity and accurately forecast periods of high volatility, achieving up to a 9% average Mean Squared Error (MSE) improvement over Informer and standard Transformers.

The λλ-Gated Lee Activation Module contributes a 5%-8% accuracy improvement over a baseline Transformer utilizing GELU activation. Preprocessing with an Autoencoder Self-Regressive Model further enhances COTN’s ability to extract relevant features and improve forecasting accuracy.

Beyond Prediction: Echoes of the System

Integrating biologically inspired oscillators, like the Lee Oscillator, into time series modeling shifts toward more interpretable and robust forecasting methods, mirroring retrograde signaling pathways where past states influence current dynamics. The oscillatory nature provides inherent regularization, mitigating overfitting and enhancing generalization.

COTN addresses computational limitations through Distilled Attention, facilitating real-time forecasting and deployment on resource-constrained devices. Empirical evaluations demonstrate COTN’s efficacy, outperforming a baseline model in 77% of trials. Future research will explore applications to anomaly detection and predictive maintenance, synergizing with other advanced machine learning techniques to further enhance predictive power.

Every architecture promises control, but time, like a river, finds its own course.

The pursuit of predictable control within complex systems is, predictably, an exercise in futility. This work, detailing COTN and its integration of chaotic oscillators, acknowledges this inherent unpredictability. It doesn’t seek to eliminate volatility, but to model it, to dance with the oscillations rather than attempt to suppress them. As Barbara Liskov observed, “Programs must be correct, but we can never be sure.” COTN embodies this sentiment; it doesn’t promise perfect forecasts, especially under extreme conditions, but offers a robust framework for navigating inherent uncertainty. Every dependency, in this case the interplay between transformer networks and Lee oscillators, is a promise made to the past – a commitment to a specific model of volatility. The architecture understands that everything built will one day start fixing itself, adapting to the inevitable shifts in chaotic dynamics.

What’s Next?

The pursuit of forecasting accuracy, as demonstrated by this work with COTN, invariably reveals the inherent limitations of any predictive model. A system that perfectly anticipates volatility is, by definition, a system that ceases to learn from it. The integration of chaotic oscillators into a Transformer network is not a solution, but a carefully constructed invitation to failure – a failure that, when it arrives, will illuminate the next architectural iteration. The true metric of success will not be minimized error, but maximized responsiveness to unforeseen breakdown.

Future work will undoubtedly focus on expanding the repertoire of oscillators employed, and exploring the interplay between oscillator dynamics and the attention mechanisms within the Transformer. However, a more fruitful line of inquiry may lie in accepting the inevitability of prediction errors, and designing systems that gracefully degrade under extreme conditions. A network that anticipates its own limitations is, paradoxically, more resilient than one striving for impossible perfection.

Ultimately, the COTN architecture, and those like it, should not be viewed as attempts to conquer volatility, but to coexist with it. The goal isn’t to eliminate the unpredictable, but to build systems that learn from the unpredictable – systems that thrive not in spite of failure, but because of it. Perfection, after all, leaves no room for people—or for learning.

Original article: https://arxiv.org/pdf/2511.06273.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-11-11 18:00