KANFormer for Predicting Fill Probabilities via Survival Analysis in Limit Order Books

TL;DR

KANFormer introduces a survival-analysis-based framework for predicting limit-order fill probabilities by fusing agent actions, LOB snapshots, and queue position. It couples two KAN-Transformer encoders with a Dilated Causal Convolution front-end and a Weibull-based predictor to produce monotone survival functions, achieving superior calibration and discrimination on CAC 40 futures. The approach is complemented by SHAP-based, time-varying interpretability, revealing the evolving importance of queue priority, liquidity imbalances, and agent behavior. Empirical results show clear gains over deep-learning and classical baselines, highlighting the practical value of integrating market signals with advanced nonlinear architectures for real-time execution risk assessment.

Abstract

This paper introduces KANFormer, a novel deep-learning-based model for predicting the time-to-fill of limit orders by leveraging both market- and agent-level information. KANFormer combines a Dilated Causal Convolutional network with a Transformer encoder, enhanced by Kolmogorov-Arnold Networks (KANs), which improve nonlinear approximation. Unlike existing models that rely solely on a series of snapshots of the limit order book, KANFormer integrates the actions of agents related to LOB dynamics and the position of the order in the queue to more effectively capture patterns related to execution likelihood. We evaluate the model using CAC 40 index futures data with labeled orders. The results show that KANFormer outperforms existing works in both calibration (Right-Censored Log-Likelihood, Integrated Brier Score) and discrimination (C-index, time-dependent AUC). We further analyze feature importance over time using SHAP (SHapley Additive exPlanations). Our results highlight the benefits of combining rich market signals with expressive neural architectures to achieve accurate and interpretabl predictions of fill probabilities.

Figures (10)

• Figure 1: Two consecutive snapshots of a LOB. Each square represents a unit order; the purple bars denote ask (sell) orders, and the light green bars represent bid (buy) orders.
• Figure 2: KANFormer architecture with Dilated Causal Convolution (DCC). LOB snapshots $\mathbf{X}_{\text{LOB}}\in\mathbb{R}^{L\times(4n+4)}$ are processed by a DCC block followed by a KAN–Transformer to produce a LOB embedding. Agent actions $\mathbf{A}_{\text{actions}}\in\mathbb{R}^{L\times(d+5)}$ are encoded by a KAN–Transformer to produce an action embedding. The two embeddings are concatenated with the queue position $q$ and passed to the predictor, which outputs density and survival function.
• Figure 3: The evolution of Brier score and AUC over a set of 20 different prediction time points.
• Figure 4: The evolution of metrics over a set of 20 prediction time points.
• Figure 5: The evolution of metrics over a set of 20 prediction time points.