X2Graph for Cancer Subtyping Prediction on Biological Tabular Data

Despite the transformative impact of deep learning on text, audio, and image datasets, its dominance in tabular data, especially in the medical domain where data are often scarce, remains less clear. In this paper, we propose X2Graph, a novel deep learning method that achieves strong performance on small biological tabular datasets. X2Graph leverages external knowledge about the relationships between table columns, such as gene interactions, to convert each sample into a graph structure. This transformation enables the application of standard message passing algorithms for graph modeling. Our X2Graph method demonstrates superior performance compared to existing tree-based and deep learning methods across three cancer subtyping datasets.

A Closer Look at Multimodal Representation Collapse

We aim to develop a fundamental understanding of modality collapse, a recently observed empirical phenomenon wherein models trained for multimodal fusion tend to rely only on a subset of the modalities, ignoring the rest. We show that modality collapse happens when noisy features from one modality are entangled, via a shared set of neurons in the fusion head, with predictive features from another, effectively masking out positive contributions from the predictive features of the former modality and leading to its collapse. We further prove that cross-modal knowledge distillation implicitly disentangles such representations by freeing up rank bottlenecks in the student encoder, denoising the fusion-head outputs without negatively impacting the predictive features from either modality. Based on the above findings, we propose an algorithm that prevents modality collapse through explicit basis reallocation, with applications in dealing with missing modalities. Extensive experiments on multiple multimodal benchmarks validate our theoretical claims. Project page: https://abhrac.github.io/mmcollapse/.

Learning Conditional Invariances through Non-Commutativity

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder $\varphi^*$ that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder $\Phi^*_\tau$. We prove that non-commutativity steers the optimization towards $\Phi^*_\tau$ instead of $\varphi^*$, bringing the $\mathcal{H}$-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning $\Phi^*_\tau$, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over $2\%$, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.