# Unbiased Gradient Estimation for Event Binning via Functional Backpropagation

arXiv: https://arxiv.org/abs/2602.12590 · HTML: https://mlsanity.com/paper/2602.12590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [High Speed and High Dynamic Range Video with an Event Camera](https://mlsanity.com/paper/1906.07165/) (2019)
- [DSEC: A Stereo Event Camera Dataset for Driving Scenarios](https://mlsanity.com/paper/2103.06011/) (2021)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [EV-FlowNet: Self-Supervised Optical Flow Estimation for Event-based Cameras](https://mlsanity.com/paper/1802.06898/) (2018)
- [The Event-Camera Dataset and Simulator: Event-based Data for Pose Estimation, Visual Odometry, and SLAM](https://mlsanity.com/paper/1610.08336/) (2016)
- [Event-based Vision meets Deep Learning on Steering Prediction for Self-driving Cars](https://mlsanity.com/paper/1804.01310/) (2018)
- [A Unifying Contrast Maximization Framework for Event Cameras, with Applications to Motion, Depth, and Optical Flow Estimation](https://mlsanity.com/paper/1804.01306/) (2018)
- [E-RAFT: Dense Optical Flow from Event Cameras](https://mlsanity.com/paper/2108.10552/) (2021)
- [TimeLens: Event-based Video Frame Interpolation](https://mlsanity.com/paper/2106.07286/) (2021)
- [Ultimate SLAM? Combining Events, Images, and IMU for Robust Visual SLAM in HDR and High Speed Scenarios](https://mlsanity.com/paper/1709.06310/) (2017)
- [Bringing a Blurry Frame Alive at High Frame-Rate with an Event Camera](https://mlsanity.com/paper/1811.10180/) (2018)
- [Event-based Stereo Visual Odometry](https://mlsanity.com/paper/2007.15548/) (2020)
- [Secrets of Event-Based Optical Flow](https://mlsanity.com/paper/2207.10022/) (2022)
- [Focus Is All You Need: Loss Functions For Event-based Vision](https://mlsanity.com/paper/1904.07235/) (2019)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [CMax-SLAM: Event-based Rotational-Motion Bundle Adjustment and SLAM System using Contrast Maximization](https://mlsanity.com/paper/2403.08119/) (2024)
- [The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data](https://mlsanity.com/paper/2106.06887/) (2021)
- [Motion-prior Contrast Maximization for Dense Continuous-Time Motion Estimation](https://mlsanity.com/paper/2407.10802/) (2024)
- [Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators](https://mlsanity.com/paper/2412.00088/) (2024)
- [Event-based Stereo Depth Estimation: A Survey](https://mlsanity.com/paper/2409.17680/) (2024)
- [EF-3DGS: Event-Aided Free-Trajectory 3D Gaussian Splatting](https://mlsanity.com/paper/2410.15392/) (2024)
- [Event-based Background-Oriented Schlieren](https://mlsanity.com/paper/2311.00434/) (2023)
- [A compact neuromorphic system for ultra-energy-efficient, on-device robot localization](https://mlsanity.com/paper/2408.16754/) (2024)
- [Event-based Asynchronous HDR Imaging by Temporal Incident Light Modulation](https://mlsanity.com/paper/2403.09392/) (2024)
- [MATE: Motion-Augmented Temporal Consistency for Event-based Point Tracking](https://mlsanity.com/paper/2412.01300/) (2024)
- [Learning Efficient Meshflow and Optical Flow from Event Cameras](https://mlsanity.com/paper/2510.04111/) (2025)

## Abstract (arXiv)

Event-based vision encodes dynamic scenes as asynchronous spatio-temporal spikes called events. To leverage conventional image processing pipelines, events are typically binned into frames. However, binning functions are discontinuous, which truncates gradients at the frame level and forces most event-based algorithms to rely solely on frame-based features. Attempts to directly learn from raw events avoid this restriction but instead suffer from biased gradient estimation due to the discontinuities of the binning operation, ultimately limiting their learning efficiency. To address this challenge, we propose a novel framework for unbiased gradient estimation of arbitrary binning functions by synthesizing weak derivatives during backpropagation while keeping the forward output unchanged. The key idea is to exploit integration by parts: lifting the target functions to functionals yields an integral form of the derivative of the binning function during backpropagation, where the cotangent function naturally arises. By reconstructing this cotangent function from the sampled cotangent vector, we compute weak derivatives that provably match long-range finite differences of both smooth and non-smooth targets. Experimentally, our method improves simple optimization-based egomotion estimation with 3.2% lower RMS error and 1.57× faster convergence. On complex downstream tasks, we achieve 9.4% lower EPE in self-supervised optical flow, and 5.1% lower RMS error in SLAM, demonstrating broad benefits for event-based visual perception. Source code can be found at https://github.com/chjz1024/EventFBP.