# Breaking the Correlation Plateau: On the Optimization and Capacity Limits of Attention-Based Regressors

arXiv: https://arxiv.org/abs/2602.17898 · HTML: https://mlsanity.com/paper/2602.17898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Multimodal Transformer for Unaligned Multimodal Language Sequences](https://mlsanity.com/paper/1906.00295/) (2019)
- [Tensor Fusion Network for Multimodal Sentiment Analysis](https://mlsanity.com/paper/1707.07250/) (2017)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Efficient Low-rank Multimodal Fusion with Modality-Specific Factors](https://mlsanity.com/paper/1806.00064/) (2018)
- [MISA: Modality-Invariant and -Specific Representations for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2005.03545/) (2020)
- [Learning Modality-Specific Representations with Self-Supervised Multi-Task Learning for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2102.04830/) (2021)
- [Breaking the Softmax Bottleneck: A High-Rank RNN Language Model](https://mlsanity.com/paper/1711.03953/) (2017)
- [Low-Rank Bottleneck in Multi-head Attention Models](https://mlsanity.com/paper/2002.07028/) (2020)
- [Learning Relationships between Text, Audio, and Video via Deep Canonical Correlation for Multimodal Language Analysis](https://mlsanity.com/paper/1911.05544/) (2019)
- [Regression Transformer: Concurrent sequence regression and generation for molecular language modeling](https://mlsanity.com/paper/2202.01338/) (2022)
- [BasisFormer: Attention-based Time Series Forecasting with Learnable and Interpretable Basis](https://mlsanity.com/paper/2310.20496/) (2023)
- [Sparse and Continuous Attention Mechanisms](https://mlsanity.com/paper/2006.07214/) (2020)
- [Exemplar Guided Deep Neural Network for Spatial Transcriptomics Analysis of Gene Expression Prediction](https://mlsanity.com/paper/2210.16721/) (2022)
- [Patch-wise Structural Loss for Time Series Forecasting](https://mlsanity.com/paper/2503.00877/) (2025)
- [Learning Language-guided Adaptive Hyper-modality Representation for Multimodal Sentiment Analysis](https://mlsanity.com/paper/2310.05804/) (2023)
- [DLF: Disentangled-Language-Focused Multimodal Sentiment Analysis](https://mlsanity.com/paper/2412.12225/) (2024)
- [Sigsoftmax: Reanalysis of the Softmax Bottleneck](https://mlsanity.com/paper/1805.10829/) (2018)
- [MHAttnSurv: Multi-Head Attention for Survival Prediction Using Whole-Slide Pathology Images](https://mlsanity.com/paper/2110.11558/) (2021)
- [MagNet: Multi-Level Attention Graph Network for Predicting High-Resolution Spatial Transcriptomics](https://mlsanity.com/paper/2502.21011/) (2025)
- [The Many-to-Many Mapping Between the Concordance Correlation Coefficient and the Mean Square Error](https://mlsanity.com/paper/1902.05180/) (2019)
- [A circumcentered-reflection method for finding common fixed points of firmly nonexpansive operators](https://mlsanity.com/paper/2203.02410/) (2022)

## Abstract (arXiv)

Attention-based regression models are often trained by jointly optimizing Mean Squared Error (MSE) loss and Pearson correlation coefficient (PCC) loss, emphasizing the magnitude of errors and the order or shape of targets, respectively. A common but poorly understood phenomenon during training is the PCC plateau: PCC stops improving early in training, even as MSE continues to decrease. We provide the first rigorous theoretical analysis of this behavior, revealing fundamental limitations in both optimization dynamics and model capacity. First, in regard to the flattened PCC curve, we uncover a critical conflict where lowering MSE (magnitude matching) can paradoxically suppress the PCC gradient (shape matching). This issue is exacerbated by the softmax attention mechanism, particularly when the data to be aggregated is highly homogeneous. Second, we identify a limitation in the model capacity: we derived a PCC improvement limit for any convex aggregator (including the softmax attention), showing that the convex hull of the inputs strictly bounds the achievable PCC gain. We demonstrate that data homogeneity intensifies both limitations. Motivated by these insights, we propose the Extrapolative Correlation Attention (ECA), which incorporates novel, theoretically-motivated mechanisms to improve the PCC optimization and extrapolate beyond the convex hull. Across diverse benchmarks, including challenging homogeneous data setting, ECA consistently breaks the PCC plateau, achieving significant improvements in correlation without compromising MSE performance.