# A Geometric View of SRC: Learning Representations for Stable Residual Inference

arXiv: https://arxiv.org/abs/2605.29673 · HTML: https://mlsanity.com/paper/2605.29673/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [How catastrophic can catastrophic forgetting be in linear regression?](https://mlsanity.com/paper/2205.09588/) (2022)
- [Implicit differentiation of Lasso-type models for hyperparameter optimization](https://mlsanity.com/paper/2002.08943/) (2020)
- [One-step differentiation of iterative algorithms](https://mlsanity.com/paper/2305.13768/) (2023)
- [The Role of Principal Angles in Subspace Classification](https://mlsanity.com/paper/1507.04230/) (2015)
- [Deep Sparse Representation-based Classification](https://mlsanity.com/paper/1904.11093/) (2019)
- [Greedier is Better: Selecting Multiple Neighbors per Iteration for Sparse Subspace Clustering](https://mlsanity.com/paper/2204.02572/) (2022)

## Abstract (arXiv)

Reconstruction-based inference assigns a class by comparing class-wise reconstruction residuals; Sparse Representation Classification (SRC) is a canonical instance whose reliability depends on the geometry of the learned representation. We adopt a strict training-inference separation: SRC is used only as a fixed test-time rule and is never differentiated, unrolled, or optimized during training. In a span-level idealization based on class-conditional spans and their associated projection residuals, we formalize residual-ordering stability through a residual margin and characterize geometric obstructions -- span overlap, dominance, and near-overlap via small principal angles -- that can collapse this margin in worst-case directions. This span-level theory is primary: it specifies when the idealized residual family is well-separated, and it provides a conditional solver-level interpretation for practical residual approximations (e.g., OMP) insofar as they remain close to the span-level residual ordering. Under explicit coverage and separation assumptions, we derive a quantitative lower bound on the (idealized) residual margin. Guided by these targets, we propose geometry-shaping objectives that promote masked within-class self-expressiveness, discourage cross-class reconstruction pathways and inter-class span alignment, and prevent collapse -- without invoking SRC residuals or predictions during training. Experiments on images (COIL-100), text (TREC), and EEG connectivity evaluate all representations under identical fixed SRC/OMP inference and report residual margins and geometric diagnostics; cross-entropy is included only as a reference geometry under the same evaluation protocol.