Temporal Kolmogorov-Arnold Networks (T-KAN) for High-Frequency Limit Order Book Forecasting: Efficiency, Interpretability, and Alpha Decay

AI summary

Overview

Research area: Machine learning for financial markets — specifically deep learning applied to high-frequency limit order book (LOB) forecasting, model interpretability, and hardware-efficient neural architecture design.

Technical level: Advanced. The paper assumes familiarity with LSTMs, B-spline parameterization, limit order book microstructure, backtesting under transaction costs, and FPGA/high-level synthesis workflows.

Scope: The paper introduces Temporal Kolmogorov-Arnold Networks (T-KAN), which swap the fixed linear weights of standard LSTMs for learnable B-spline activation functions, and evaluates them on the FI-2010 limit order book dataset for horizon-degradation ("alpha decay"), interpretability, and suitability for low-latency hardware.

What This Paper Is About

High-frequency limit order book data is large, noisy, and non-linear, and predictive models tend to lose accuracy as the forecast horizon stretches further into the future — a phenomenon the paper calls alpha decay. The authors propose T-KAN, a recurrent architecture that learns the shape of market signals through learnable spline functions rather than only their magnitude, aiming to hold predictive power at longer horizons while remaining interpretable and cheap enough to run on low-latency hardware.

Key Contributions

1. Introduction of Temporal Kolmogorov-Arnold Networks (T-KAN): Replaces the fixed, linear weights of standard LSTMs with learnable B-spline activation functions, enabling the model to represent the shape of market signals rather than only their magnitude.
2. Demonstration of reduced alpha decay: Reports a 19.1% relative improvement in F1-score at the k = 100 forecasting horizon on the FI-2010 dataset, addressing the loss of predictive power that affects models such as DeepLOB as the horizon grows.
3. Backtested performance comparison under transaction costs: Reports a 132.48% return for T-KAN versus a -82.76% DeepLOB drawdown under 1.0 bps transaction costs.
4. Interpretability and hardware orientation: Shows that "dead-zones" are clearly visible in the learned splines, and states that the architecture is optimized for low-latency FPGA implementation via High Level Synthesis (HLS).

Main Findings

• Longer-horizon accuracy improves: T-KAN yields a 19.1% relative F1-score improvement at the k = 100 horizon, framed as a direct counter to the alpha decay that erodes DeepLOB's predictive power as the time horizon increases.
• Backtest outcome diverges sharply from the baseline: Under 1.0 bps transaction costs, the abstract reports a 132.48% return for T-KAN against a -82.76% DeepLOB drawdown. The abstract does not specify the backtest period, universe, or sample length.
• Interpretability is a byproduct of the architecture: The learned B-splines expose visible "dead-zones" — regions where the model's response flattens — giving a readable view of where the network is effectively inactive. The abstract does not detail how these dead-zones were quantified or analyzed.
• Hardware deployment is a design goal: The architecture is described as uniquely optimized for low-latency FPGA implementation through High Level Synthesis, positioning it for latency-sensitive trading environments. No latency or resource-utilization figures are given in the abstract.
• Reproducibility: The experiment code is released at a public GitHub repository (github.com/AhmadMak/Temporal-Kolmogorov-Arnold-Networks-T-KAN-for-High-Frequency-Limit-Order-Book-Forecasting).

Methodology in Plain English

Standard recurrent networks such as LSTMs apply fixed, linear transformations to their inputs, with a fixed non-linear activation applied afterward. The authors keep the recurrent structure but replace those fixed pieces with learnable B-spline activation functions — flexible curves whose shape is fitted during training. This lets the model capture non-linear market relationships by learning the form of the response, rather than scaling a signal linearly and hoping a fixed activation captures the rest.

They evaluate this on the FI-2010 limit order book dataset, comparing against DeepLOB, and measure both classification quality across prediction horizons (the k = 100 horizon being the headline case) and economic performance via a backtest that charges 1.0 bps in transaction costs. Because splines are piecewise curves, the trained functions can be inspected directly — the authors use this to point to "dead-zones" in the learned responses. Finally, the spline formulation is chosen partly because it maps cleanly onto FPGA hardware through High Level Synthesis, targeting low-latency deployment.

Why This Matters

Impact on research: Most work on financial deep learning optimizes for accuracy without asking whether the model degrades gracefully as the forecast horizon extends. This paper frames alpha decay as a first-class architectural problem and proposes that the shape of the non-linearity — not just the weights — is a lever worth pulling. It also bridges two normally separate literatures: Kolmogorov-Arnold-style spline networks and market microstructure forecasting, while adding an interpretability argument and a hardware-deployment argument that pure-accuracy papers typically omit.

Real-world applications:

• Latency-sensitive algorithmic trading: An architecture designed for FPGA/HLS deployment is directly relevant to execution and market-making systems where microseconds of inference latency matter.
• Risk and inventory management at longer horizons: If predictive power holds up at k = 100 as claimed, signals remain usable further into the future, which is useful for managing positions over seconds-long windows rather than tick-by-tick.
• Model risk and compliance review: Learned splines with visible dead-zones give quants and risk reviewers a way to inspect a model's response surface, which is more tractable than auditing an opaque LSTM's weight matrices.
• Signal research and feature diagnostics: Dead-zone analysis can reveal which input regimes the model effectively ignores, informing feature engineering and data-quality work on order book feeds.

Industry relevance: The combination of a claimed economic edge under realistic transaction costs, an interpretability story, and a hardware path is the profile trading firms care about. The transaction-cost framing (1.0 bps) and the drawdown metric speak to practitioners rather than purely to academic benchmarks.

Future Directions

• Independent replication and breadth of evaluation: The abstract reports results on one dataset (FI-2010) at a headline horizon. Whether the gains hold across other venues, asset classes, and market regimes — and across additional horizons besides k = 100 — is not addressed in the abstract.
• Closing the gap between backtest and deployment: The paper claims FPGA/HLS optimization, but the abstract reports no measured latency, throughput, or resource utilization. Demonstrating realized gains on actual hardware is the natural next step.
• Turning interpretability into a method: "Dead-zones" are reported as an observation. Formalizing what they mean for market microstructure — and whether they can drive pruning, regularization, or feature selection — is an open question.
• Scaling and cost of spline parameterization: Learnable B-splines add parameters and computation relative to fixed activations. How T-KAN behaves with larger order book histories, deeper stacks, or limited training data is not specified in the abstract.

Target Audience

Quantitative researchers and machine learning engineers working on high-frequency trading and market microstructure; practitioners evaluating architectures for latency-critical inference on FPGAs; and researchers interested in Kolmogorov-Arnold networks or spline-based activation functions looking for a domain application with an interpretability and deployment angle. Readers focused on economic backtesting will find the transaction-cost framing relevant, though the abstract alone does not supply enough detail to assess the backtest's robustness.

Authors’ abstract

High-Frequency trading (HFT) environments are characterised by large volumes of limit order book (LOB) data, which is notoriously noisy and non-linear. Alpha decay represents a significant challenge, with traditional models such as DeepLOB losing predictive power as the time horizon (k) increases. In this paper, using data from the FI-2010 dataset, we introduce Temporal Kolmogorov-Arnold Networks (T-KAN) to replace the fixed, linear weights of standard LSTMs with learnable B-spline activation functions. This allows the model to learn the 'shape' of market signals as opposed to just their magnitude. This resulted in a 19.1% relative improvement in the F1-score at the k = 100 horizon. The efficacy of T-KAN networks cannot be understated, producing a 132.48% return compared to the -82.76% DeepLOB drawdown under 1.0 bps transaction costs. In addition to this, the T-KAN model proves quite interpretable, with the 'dead-zones' being clearly visible in the splines. The T-KAN architecture is also uniquely optimized for low-latency FPGA implementation via High level Synthesis (HLS). The code for the experiments in this project can be found at https://github.com/AhmadMak/Temporal-Kolmogorov-Arnold-Networks-T-KAN-for-High-Frequency-Limit-Order-Book-Forecasting.