arXiv subjects

Matthew F Dixon

Publications and source records attributed to Matthew F Dixon.

5 recordsLinked to original sources

arXiv2026

Foundations of Stochastic Lexical Calculus: Semantic Descent and Random Dynamics on Probability Simplices

Large language models produce prompt-dependent probabilities over words, whereas scientific systems require uncertainty over meaningful states that can be updated as evidence arrives. We develop an observable framework for determining when language-derived probabilities support such a sequential state representation. Theoretically, we define typed measurable transformations of contextual language, construct a minimal closed representation, and give necessary and sufficient conditions for semantic updates to exist uniquely. We bound irreducible nonclosure and accumulated error, and under average contraction prove existence, uniqueness and stability of an external random recursion on a probability simplex. These results define a stochastic lexical calculus without attributing an internal calculus to the language model. Empirically, frozen experiments test the observable implications. Raw prompt-conditioned probabilities fail the prespecified invariance gate; after prompt-specific calibration, a common three-state representation passes the stability gates and covers 28 of 30 untouched eight-step paths, or 0.933 at nominal level 0.90. Accordingly, language probabilities support a stochastic state only conditionally on verified closure, stability and coverage within a declared operating domain.

cs.CL↗

arXiv2020

Industrial Forecasting with Exponentially Smoothed Recurrent Neural Networks

Time series modeling has entered an era of unprecedented growth in the size and complexity of data which require new modeling approaches. While many new general purpose machine learning approaches have emerged, they remain poorly understand and irreconcilable with more traditional statistical modeling approaches. We present a general class of exponential smoothed recurrent neural networks (RNNs) which are well suited to modeling non-stationary dynamical systems arising in industrial applications. In particular, we analyze their capacity to characterize the non-linear partial autocorrelation structure of time series and directly capture dynamic effects such as seasonality and trends. Application of exponentially smoothed RNNs to forecasting electricity load, weather data, and stock prices highlight the efficacy of exponential smoothing of the hidden state for multi-step time series forecasting. The results also suggest that popular, but more complicated neural network architectures originally designed for speech processing, such as LSTMs and GRUs, are likely over-engineered for industrial forecasting and light-weight exponentially smoothed architectures, trained in a fraction of the time, capture the salient features while being superior and more robust than simple RNNs and ARIMA models. Additionally uncertainty quantification of the exponential smoothed recurrent neural networks, provided by Bayesian estimation, is shown to provide improved coverage.

stat.ML↗

arXiv2017

A High Frequency Trade Execution Model for Supervised Learning

This paper introduces a high frequency trade execution model to evaluate the economic impact of supervised machine learners. Extending the concept of a confusion matrix, we present a 'trade information matrix' to attribute the expected profit and loss of the high frequency strategy under execution constraints, such as fill probabilities and position dependent trade rules, to correct and incorrect predictions. We apply the trade execution model and trade information matrix to Level II E-mini S&P 500 futures history and demonstrate an estimation approach for measuring the sensitivity of the P&L to the error of a Recurrent Neural Network. Our approach directly evaluates the performance sensitivity of a market making strategy to prediction error and augments traditional market simulation based testing.

q-fin.TR↗

arXiv2017

Sequence Classification of the Limit Order Book using Recurrent Neural Networks

Recurrent neural networks (RNNs) are types of artificial neural networks (ANNs) that are well suited to forecasting and sequence classification. They have been applied extensively to forecasting univariate financial time series, however their application to high frequency trading has not been previously considered. This paper solves a sequence classification problem in which a short sequence of observations of limit order book depths and market orders is used to predict a next event price-flip. The capability to adjust quotes according to this prediction reduces the likelihood of adverse price selection. Our results demonstrate the ability of the RNN to capture the non-linear relationship between the near-term price-flips and a spatio-temporal representation of the limit order book. The RNN compares favorably with other classifiers, including a linear Kalman filter, using S&P500 E-mini futures level II data over the month of August 2016. Further results assess the effect of retraining the RNN daily and the sensitivity of the performance to trade latency.

q-fin.TR↗

arXiv2006

Discrete Moser-Veselov Integrators for Spatial and Body Representations of Rigid Body Motions

The body and spatial representations of rigid body motion correspond, respectively, to the convective and spatial representations of continuum dynamics. With a view to developing a unified computational approach for both types of problems, the discrete Clebsch approach of Cotter and Holm for continuum mechanics is applied to derive (i) body and spatial representations of discrete time models of various rigid body motions and (ii) the discrete momentum maps associated with symmetry reduction for these motions. For these problems, this paper shows that the discrete Clebsch approach yields a known class of explicit variational integrators, called discrete Moser-Veselov (DMV) integrators. The spatial representation of DMV integrators are Poisson with respect to a Lie-Poisson bracket for the semi-direct product Lie algebra. Numerical results are presented which confirm the conservative properties and accuracy of the numerical solutions.

nlin.SI↗