# Task-Directed Residual AddUNet:Perfect-Reconstruction Routing for Full-Rate Representations

arXiv: https://arxiv.org/abs/2609.15857 · HTML: https://mlsanity.com/paper/2609.15857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [i-RevNet: Deep Invertible Networks](https://mlsanity.com/paper/1802.07088/) (2018)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)

## Abstract (arXiv)

This paper establishes a perfect-reconstruction (PR) interpretation of AddUNet and its full-rate realization, and introduces a Residual Full-Rate PR architecture for task-directed representation learning. The survivor--skip structure of a constrained additive U-Net is shown to be exactly equivalent to a critically sampled multirate PR filter bank. The full-rate formulation removes the complementary-subband restrictions of the critically sampled system while preserving PR. A Residual Full-Rate PR architecture is then proposed to progressively route task-irrelevant, nuisance, or redundant structure away from the task-facing survivor while retaining the routed information explicitly. Exact reconstruction is guaranteed for arbitrary shape-compatible linear or nonlinear routing operators, without requiring invertibility, a matched synthesis bank, reconstruction loss, or learned decoder. The resulting architecture decouples representation design from reconstruction design: conservation is structural, while learning is devoted to task-directed routing. The same formulation identifies an identity-shortcut ResNet with its residual output retained as a full-rate PR system. Experiments verify exact single-channel routing of linearly separable factors to machine precision. On TIMIT, the proposed front-end improves test PER from 28.60±2.09% to 25.76±0.41% with the recognizer and training protocol held fixed, while maintaining exact reconstruction. Speaker probing further shows that structural conservation does not itself imply task-specific invariance.