We introduce \textbf{Chebyshev Moment Regularization (CMR)}, a simple, architecture-agnostic loss that directly optimizes layer spectra. CMR jointly controls spectral edges via a log-condition proxy and shapes the interior via Chebyshev moments, with a decoupled, capped mixing rule that preserves task gradients. We prove strictly monotone descent for the condition proxy, bounded moment gradients, and orthogonal invariance. In an adversarial ``$κ$-stress'' setting (MNIST, 15-layer MLP), \emph{compared to vanilla training}, CMR reduces mean layer condition numbers by $\sim\!10^3$ (from $\approx3.9\!\times\!10^3$ to $\approx3.4$ in 5 epochs), increases average gradient magnitude, and restores test accuracy ( $\approx10\%\!\to\!\approx86\%$ ). These results support \textbf{optimization-driven spectral preconditioning}: directly steering models toward well-conditioned regimes for stable, accurate learning.

This approach allows predictions to be traced back to specific concept patterns that users can understand and potentially intervene on. However, existing CBMs' task predictors are not fully interpretable, preventing a thorough analysis and any form of

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes a new regression method, namely calibrated multivariate regression (CMR), for high dimensional data analysis. Besides proposing the CMR formulation, the paper focuses on (1) using a smoothed proximal gradient method to compute CMR's optimal solutions; (2) analyzing CMR' statical properties. One key contribution of the paper lies in the introduction of this CMR formulation; its loss term can be interpreted as calibrating each regression task's loss term with respect to its noise level. I am wondering whether there is any more intuitive interpretation behind the use of the noise level for calibration?

We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitive and achieves an improved finite-sample performance. Computationally, we develop an efficient smoothed proximal gradient algorithm which has a worst-case iteration complexity $O(1/\epsilon)$, where $\epsilon$ is a pre-specified numerical accuracy. Theoretically, we prove that CMR achieves the optimal rate of convergence in parameter estimation. We illustrate the usefulness of CMR by thorough numerical simulations and show that CMR consistently outperforms other high dimensional multivariate regression methods. We also apply CMR on a brain activity prediction problem and find that CMR is as competitive as the handcrafted model created by human experts.

An electrocardiogram (ECG) is a widely used, cost-effective tool for detecting electrical abnormalities in the heart. However, it cannot directly measure functional parameters, such as ventricular volumes and ejection fraction, which are crucial for assessing cardiac function. Cardiac magnetic resonance (CMR) is the gold standard for these measurements, providing detailed structural and functional insights, but is expensive and less accessible. To bridge this gap, we propose PTACL (Patient and Temporal Alignment Contrastive Learning), a multimodal contrastive learning framework that enhances ECG representations by integrating spatio-temporal information from CMR. PTACL uses global patient-level contrastive loss and local temporal-level contrastive loss. The global loss aligns patient-level representations by pulling ECG and CMR embeddings from the same patient closer together, while pushing apart embeddings from different patients. Local loss enforces fine-grained temporal alignment within each patient by contrasting encoded ECG segments with corresponding encoded CMR frames. This approach enriches ECG representations with diagnostic information beyond electrical activity and transfers more insights between modalities than global alignment alone, all without introducing new learnable weights. We evaluate PTACL on paired ECG-CMR data from 27,951 subjects in the UK Biobank. Compared to baseline approaches, PTACL achieves better performance in two clinically relevant tasks: (1) retrieving patients with similar cardiac phenotypes and (2) predicting CMR-derived cardiac function parameters, such as ventricular volumes and ejection fraction. Our results highlight the potential of PTACL to enhance non-invasive cardiac diagnostics using ECG. The code is available at: https://github.com/alsalivan/ecgcmr

How much of the improvement is coming from the implicit shape representation over meshes? The proposed approach of combining local and global information via CSM's consistency loss could have been done with meshes (CSM was mesh based). What does the result look like with meshes? Or CMR could have also used this implicit shape representation. This key ablative study is missing.

Cross-modal reasoning (CMR), the intricate process of synthesizing and drawing inferences across divergent sensory modalities, is increasingly recognized as a crucial capability in the progression toward more sophisticated and anthropomorphic artificial intelligence systems. Large Language Models (LLMs) represent a class of AI algorithms specifically engineered to parse, produce, and engage with human language on an extensive scale. The recent trend of deploying LLMs to tackle CMR tasks has marked a new mainstream of approaches for enhancing their effectiveness. This survey offers a nuanced exposition of current methodologies applied in CMR using LLMs, classifying these into a detailed three-tiered taxonomy. Moreover, the survey delves into the principal design strategies and operational techniques of prototypical models within this domain. Additionally, it articulates the prevailing challenges associated with the integration of LLMs in CMR and identifies prospective research directions. To sum up, this survey endeavors to expedite progress within this burgeoning field by endowing scholars with a holistic and detailed vista, showcasing the vanguard of current research whilst pinpointing potential avenues for advancement. An associated GitHub repository that collects the relevant papers can be found at https://github.com/ZuyiZhou/Awesome-Cross-modal-Reasoning-with-LLMs