# Detecting Toxic Flow

arXiv: https://arxiv.org/abs/2312.05827 · HTML: https://mlsanity.com/paper/2312.05827/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 10 Dec 2023.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [Do Bayesian Neural Networks Need To Be Fully Stochastic?](https://mlsanity.com/paper/2211.06291/) (2022)
- [How many degrees of freedom do we need to train deep networks: a loss landscape perspective](https://mlsanity.com/paper/2107.05802/) (2021)
- [Online Natural Gradient as a Kalman Filter](https://mlsanity.com/paper/1703.00209/) (2017)
- [Stein's Lemma for the Reparameterization Trick with Exponential Family Mixtures](https://mlsanity.com/paper/1910.13398/) (2019)
- [Efficient Online Bayesian Inference for Neural Bandits](https://mlsanity.com/paper/2112.00195/) (2021)

## Built on by (most cited first, 3 of 3)

- [Rough Transformers: Lightweight and Continuous Time Series Modelling through Signature Patching](https://mlsanity.com/paper/2405.20799/) (2024)
- [Martingale Posterior Neural Networks for Fast Sequential Decision Making](https://mlsanity.com/paper/2506.11898/) (2025)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

This paper develops a framework to predict toxic trades that a broker receives from her clients. Toxic trades are predicted with a novel online learning Bayesian method which we call the projection-based unification of last-layer and subspace estimation (PULSE). PULSE is a fast and statistically-efficient Bayesian procedure for online training of neural networks. We employ a proprietary dataset of foreign exchange transactions to test our methodology. Neural networks trained with PULSE outperform standard machine learning and statistical methods when predicting if a trade will be toxic; the benchmark methods are logistic regression, random forests, and a recursively-updated maximum-likelihood estimator. We devise a strategy for the broker who uses toxicity predictions to internalise or to externalise each trade received from her clients. Our methodology can be implemented in real-time because it takes less than one millisecond to update parameters and make a prediction. Compared with the benchmarks, online learning of a neural network with PULSE attains the highest PnL and avoids the most losses by externalising toxic trades.