# Bottom-Up and Top-Down Reasoning with Hierarchical Rectified Gaussians

arXiv: https://arxiv.org/abs/1507.05699 · HTML: https://mlsanity.com/paper/1507.05699/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2015.

## Built on by (most cited first, 14 of 14)

- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [Recent Advances in Monocular 2D and 3D Human Pose Estimation: A Deep Learning Perspective](https://mlsanity.com/paper/2104.11536/) (2021)
- [TFPose: Direct Human Pose Estimation with Transformers](https://mlsanity.com/paper/2103.15320/) (2021)
- [Virtual Correspondence: Humans as a Cue for Extreme-View Geometry](https://mlsanity.com/paper/2206.08365/) (2022)
- [OverLoCK: An Overview-first-Look-Closely-next ConvNet with Context-Mixing Dynamic Kernels](https://mlsanity.com/paper/2502.20087/) (2025)
- [Monocular 3D Multi-Person Pose Estimation by Integrating Top-Down and Bottom-Up Networks](https://mlsanity.com/paper/2104.01797/) (2021)
- [Dual networks based 3D Multi-Person Pose Estimation from Monocular Video](https://mlsanity.com/paper/2205.00748/) (2022)
- [Rethinking pose estimation in crowds: overcoming the detection information-bottleneck and ambiguity](https://mlsanity.com/paper/2306.07879/) (2023)
- [Human Pose-based Estimation, Tracking and Action Recognition with Deep Learning: A Survey](https://mlsanity.com/paper/2310.13039/) (2023)
- [TDAM: Top-Down Attention Module for Contextually Guided Feature Selection in CNNs](https://mlsanity.com/paper/2111.13470/) (2021)
- [Improving Multi-Person Pose Tracking with A Confidence Network](https://mlsanity.com/paper/2310.18920/) (2023)
- [FasterPose: A Faster Simple Baseline for Human Pose Estimation](https://mlsanity.com/paper/2107.03215/) (2021)
- [GatedUniPose: A Novel Approach for Pose Estimation Combining UniRepLKNet and Gated Convolution](https://mlsanity.com/paper/2409.07752/) (2024)
- [MamKPD: A Simple Mamba Baseline for Real-Time 2D Keypoint Detection](https://mlsanity.com/paper/2412.01422/) (2024)

## Abstract (arXiv)

Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a unidirectional bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores bidirectional architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs). We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks.