# Bilinear Input Normalization for Neural Networks in Financial Forecasting

arXiv: https://arxiv.org/abs/2109.00983 · HTML: https://mlsanity.com/paper/2109.00983/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methods](https://mlsanity.com/paper/1705.03233/) (2017)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [Data Normalization for Bilinear Structures in High-Frequency Financial Time-series](https://mlsanity.com/paper/2003.00598/) (2020)
- [Financial Series Prediction: Comparison Between Precision of Time Series Models and Machine Learning Methods](https://mlsanity.com/paper/1706.00948/) (2017)
- [Deep Adaptive Input Normalization for Time Series Forecasting](https://mlsanity.com/paper/1902.07892/) (2019)

## Built on by (most cited first, 2 of 2)

- [Augmented Bilinear Network for Incremental Multi-Stock Time-Series Classification](https://mlsanity.com/paper/2207.11577/) (2022)
- [The Inference-Compute Frontier and a Latency-Efficient Architecture for Limit Order Book Prediction](https://mlsanity.com/paper/2606.25986/) (2026)

## Abstract (arXiv)

Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic gradient descent is sensitive to the input variable range and prone to numerical issues. Different than other types of signals, financial time-series often exhibit unique characteristics such as high volatility, non-stationarity and multi-modality that make them challenging to work with, often requiring expert domain knowledge for devising a suitable processing pipeline. In this paper, we propose a novel data-driven normalization method for deep neural networks that handle high-frequency financial time-series. The proposed normalization scheme, which takes into account the bimodal characteristic of financial multivariate time-series, requires no expert knowledge to preprocess a financial time-series since this step is formulated as part of the end-to-end optimization process. Our experiments, conducted with state-of-the-arts neural networks and high-frequency data from two large-scale limit order books coming from the Nordic and US markets, show significant improvements over other normalization techniques in forecasting future stock price dynamics.