Paper: arXiv 2509.25211

Authors: Remi Genet, Hugo Inzirillo

Abstract

This paper introduces Large Execution Models (LEMs), a novel deep learning framework that extends transformer-based architectures to address complex execution problems with flexible time boundaries and multiple execution constraints. Building upon recent advances in neural VWAP execution strategies, LEMs generalize the approach from fixed-duration orders to scenarios where execution duration is bounded between minimum and maximum time horizons, similar to share buyback contract structures. The proposed architecture decouples market information processing from execution allocation decisions: a common feature extraction pipeline using Temporal Kolmogorov-Arnold Networks (TKANs), Variable Selection Networks (VSNs), and multi-head attention mechanisms processes market data to create informational context, while independent allocation networks handle the specific execution logic for different scenarios (fixed quantity vs. fixed notional, buy vs. sell orders). This architectural separation enables a unified model to handle diverse execution objectives while leveraging shared market understanding across scenarios. Through comprehensive empirical evaluation on intraday cryptocurrency markets and multi-day equity trading using DOW Jones constituents, we demonstrate that LEMs achieve superior execution performance compared to traditional benchmarks by dynamically optimizing execution paths within flexible time constraints. The unified model architecture enables deployment across different execution scenarios (buy/sell orders, varying duration boundaries, volume/notional targets) through a single framework, providing significant operational advantages over asset-specific approaches.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics including Temporal Kolmogorov-Arnold Networks (TKANs), multi-head attention, and optimal control formulations, while providing comprehensive empirical evaluation on real-world datasets (cryptocurrency and DOW Jones) with reported performance improvements.

Research Flowchart

  flowchart TD
  A["Research Goal: Generalize VWAP Execution<br>to Flexible Time Constraints"] --> B["Methodology: LEM Architecture Design"]
  
  B --> C["Data Inputs:<br>Intraday Crypto & Multi-Day Equity Markets"]
  
  C --> D["Core Computation: Market Information Processing<br>TKANs + VSNs + Multi-Head Attention"]
  
  D --> E["Parallel Execution Allocation Networks<br>Fixed Qty vs. Fixed Notional | Buy vs. Sell"]
  
  E --> F["Key Findings:<br>1. Superior execution vs. traditional benchmarks<br>2. Dynamic optimization in flexible time horizons<br>3. Unified model for multi-scenario deployment"]

Cited References (111)

  1. The Kolmogorov–Arnold representation theorem revisited (2021)
  2. Semi-supervised classification with graph convolutional networks (2016) — link
  3. Wav-kan: Wavelet kolmogorov-arnold networks, 2024 — link
  4. Optimal slice of a VWAP trade (2002) — link
  5. Optimal VWAP Trading Strategy and Relative Volume (2007) — link
  6. Non-linear time series: a dynamical system approach (1990)
  7. Concave Cross Impact (2024) — link
  8. Measuring the Information Content of Stock Trades (1991)
and 103 more
  1. Trading Cost: The Critical Link Between Investment Information and Results (1983)
  2. Optimal Execution Strategies in Limit Order Books with General Shape Functions (2010)
  3. Fluctuations and Response in Financial Markets: The Subtle Nature of Random Price Changes (2004)
  4. Temporal fusion transformers for interpretable multi-horizon time series forecasting (2021)
  5. TimesKAN: A Generic Backbone Network for Time Series Prediction Based on Kolmogorov-Arnold Networks (2024)
  6. Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting (2023)
  7. Integrating Kolmogorov–Arnold Networks with Time Series Prediction Framework in Electricity Demand Forecasting (2025)
  8. Gkan: Graph kolmogorov-arnold networks (2024) — link
  9. Deep residual learning for image recognition (2016)
  10. Informer: Beyond efficient transformer for long sequence time-series forecasting (2021)
  11. LPSNet: a novel log path signature feature based hand gesture recognition framework (2017)
  12. Extracting information from the signature of a financial data stream (2013) — link
  13. Deep signature statistics for likelihood-free time-series models (2021)
  14. Embedding and learning with signatures (2021)
  15. Chebyshev polynomial-based kolmogorov-arnold networks: An efficient architecture for nonlinear function approximation (2024) — link
  16. Smooth Kolmogorov Arnold networks enabling structural knowledge representation (2024) — link
  17. Graphkan: Enhancing feature extraction with graph kolmogorov arnold networks (2024) — link
  18. Time series analysis: forecasting and control (2015)
  19. Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting (2019)
  20. Hippo-kan: Efficient kan model for time series analysis (2024) — link
  21. Tsmixer: An all-mlp architecture for time series forecasting (2023) — link
  22. KAN: Kolmogorov-Arnold Networks (2024) — link
  23. Sigmoid-weighted linear units for neural network function approximation in reinforcement learning (2018)
  24. Vector autoregressive models for multivariate time series (2006)
  25. Layer Normalization (2016) — link
  26. Vector autoregressive models (2013)
  27. State-space models (1994)
  28. Dynamic linear models with Markov-switching (1994)
  29. Time series forecasting using neural networks vs. Box-Jenkins methodology (1991)
  30. Connecting the dots: Multivariate time series forecasting with graph neural networks (2020)
  31. Multiple convolutional neural networks for multivariate time series prediction (2019)
  32. Neural networks: a comprehensive foundation (1998)
  33. Approximation by superpositions of a sigmoidal function (1989)
  34. Autoregressive convolutional neural networks for asynchronous time series (2018)
  35. A novel LSTM approach for asynchronous multivariate time series prediction (2019)
  36. Multilayer feedforward networks are universal approximators (1989)
  37. The vanishing gradient problem during learning recurrent neural nets and problem solutions (1998)
  38. Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling (2014)
  39. Learning long-term dependencies with gradient descent is difficult (1994) — link
  40. Backpropagation through time: what it does and how to do it (1990)
  41. A learning algorithm for continually running fully recurrent neural netwokrs (1989)
  42. Long short-term memory (1997)
  43. On the Properties of Neural Machine Translation: Encoder-Decoder Approaches (2014)
  44. A simple way to initialize recurrent networks of rectified linear units (2015) — link
  45. Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) (2016)
  46. Multi-horizon time series forecasting with temporal attention learning (2019)
  47. Financial time series forecasting with deep learning: A systematic literature review: 2005–2019 (2020)
  48. Study of effectiveness of time series modeling (ARIMA) in forecasting stock prices (2014)
  49. ARMA models and the Box–Jenkins methodology (1997)
  50. Recurrent neural networks (2001)
  51. Recurrent neural networks for time series forecasting: Current status and future directions (2021)
  52. On the representation of continuous functions of several variables by superpositions of continuous functions of a smaller number of variables (1961)
  53. The perceptron: A probabilistic model for information storage and organization in the brain. (1958)
  54. Understanding LSTM–a tutorial into long short-term memory recurrent neural networks (2019) — link
  55. Learning phrase representations using RNN encoder-decoder for statistical machine translation (2014) — link
  56. Deep learning for time series forecasting: a survey (2021)
  57. Time-series forecasting with deep learning: a survey (2021)
  58. Attention is all you need (2017)
  59. Fast and accurate deep network learning by exponential linear units (elus) (2015) — link
  60. Language modeling with gated convolutional networks (2017)
  61. Kolmogorov-arnold networks for time series: Bridging predictive power and interpretability (2024) — link
  62. seqKAN: Sequence processing with Kolmogorov-Arnold Networks (2025) — link
  63. Tkan: Temporal kolmogorov-arnold networks (2024) — link
  64. C-kan: A new approach for integrating convolutional layers with kolmogorov–arnold networks for time-series forecasting (2024)
  65. Sigkan: Signature-weighted kolmogorov-arnold networks for time series (2024) — link
  66. KAN-AD: Time series anomaly detection with Kolmogorov-Arnold networks (2024) — link
  67. Kolmogorov-arnold networks (kan) for time series classification and robust analysis (2024)
  68. Kolmogorov-arnold networks (kans) for time series analysis (2024) — link
  69. Abnormality Detection in Time-Series Bio-Signals using Kolmogorov-Arnold Networks for Resource-Constrained Devices (2024)
  70. Kolmogorov–Arnold recurrent network for short term load forecasting across diverse consumers (2025)
  71. TSKANMixer: Kolmogorov-Arnold Networks with MLP-Mixer Model for Time Series Forecasting (2025) — link
  72. Kolmogorov-Arnold Networks for Time Series Granger Causality Inference (2025) — link
  73. An algorithm for the machine calculation of complex Fourier series (1965)
  74. Zero Shot Time Series Forecasting Using Kolmogorov Arnold Networks (2024) — link
  75. Exploring kolmogorov-arnold networks for interpretable time series classification (2024) — link
  76. Integration of paths–A faithful representation of paths by noncommutative formal power series (1958)
  77. Rough paths, signatures and the modelling of functions on streams (2014) — link
  78. Differential equations driven by rough signals (1998)
  79. A primer on the signature method in machine learning (2016) — link
  80. Chebyshev polynomials (2002)
  81. Hippo: Recurrent memory with optimal polynomial projections (2020)
  82. Developing the path signature methodology and its application to landmark-based human action recognition (2022)
  83. N-BEATS: Neural basis expansion analysis for interpretable time series forecasting (2019) — link
  84. Domain-adversarial training of neural networks (2016)
  85. A CNN–LSTM model for gold price time-series forecasting (2020)
  86. Shape and time distortion loss for training deep time series forecasting models (2019)
  87. Recurrent Fourier-Kolmogorov Arnold Networks for photovoltaic power forecasting (2025)
  88. TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting (2025) — link
  89. A gated residual kolmogorov-arnold networks for mixtures of experts (2024) — link
  90. Dispensing with optimal control: a new approach for the pricing and management of share buyback contracts — → 2404.13754
  91. A new method for the pricing of share buy-back programmes (2024)
  92. Optimal execution of accelerated share repurchase contracts with fixed notional (2017)
  93. Accelerated share repurchase: pricing and execution strategy (2015)
  94. Optimal accelerated share repurchase (2017)
  95. Valuing american options by simulation: a simple least-squares approach (2001)
  96. Deep Learning for VWAP Execution in Crypto Markets: Beyond the Volume Curve — → 2502.13722
  97. VWAP Execution with Signature-Enhanced Transformers: A Multi-Asset Learning Approach — → 2503.02680
  98. Recurrent neural networks for dynamic vwap execution: Adaptive trading strategies with temporal kolmogorov-arnold networks — → 2502.18177
  99. A temporal kolmogorov-arnold transformer for time series forecasting (2024) — link
  100. Sigkan: Signature-weighted kolmogorov-arnold networks for time series (2024) — link
  101. Optimal slice of a vwap trade (2002)
  102. Optimal VWAP trading under noisy conditions (2011)
  103. Improving VWAP strategies: A dynamic volume approach (2008)

4 of 111 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.