Despite strong performance on vision-language tasks, Multimodal Large Language Models (MLLMs) struggle with mathematical problem-solving, with both open-source and state-of-the-art models falling short of human performance on visual-math benchmarks. To systematically examine visual-mathematical reasoning in MLLMs, we (1) evaluate their understanding of geometric primitives, (2) test multi-step reasoning, and (3) explore a potential solution to improve visual reasoning capabilities. Our findings reveal fundamental shortcomings in shape recognition, with top models achieving under 50% accuracy in identifying regular polygons. We analyze these failures through the lens of dual-process theory and show that MLLMs rely on System 1 (intuitive, memorized associations) rather than System 2 (deliberate reasoning). Consequently, MLLMs fail to count the sides of both familiar and novel shapes, suggesting they have neither learned the concept of sides nor effectively process visual inputs. Finally, we propose Visually Cued Chain-of-Thought (VC-CoT) prompting, which enhances multi-step mathematical reasoning by explicitly referencing visual annotations in diagrams, boosting GPT-4o's accuracy on an irregular polygon side-counting task from 7% to 93%. Our findings suggest that System 2 reasoning in MLLMs remains an open problem, and visually-guided prompting is essential for successfully engaging visual reasoning. Code available at: https://github.com/rsinghlab/Shape-Blind.

Drug discovery is a complex and time-intensive process that requires identifying and validating new therapeutic candidates. Computational approaches using large-scale biomedical knowledge graphs (KGs) offer a promising solution to accelerate this process. However, extracting meaningful insights from large-scale KGs remains challenging due to the complexity of graph traversal. Existing subgraph-based methods are tailored to graph neural networks (GNNs), making them incompatible with other models, such as large language models (LLMs). We introduce K-Paths, a retrieval framework that extracts structured, diverse, and biologically meaningful paths from KGs. Integrating these paths enables LLMs and GNNs to effectively predict unobserved drug-drug and drug-disease interactions. Unlike traditional path-ranking approaches, K-Paths retrieves and transforms paths into a structured format that LLMs can directly process, facilitating explainable reasoning. K-Paths employs a diversity-aware adaptation of Yen's algorithm to retrieve the K shortest loopless paths between entities in an interaction query, prioritizing biologically relevant and diverse relationships. Our experiments on benchmark datasets show that K-Paths improves the zero-shot performance of Llama 8.1B's F1-score by 12.45 points on drug repurposing and 13.42 points on interaction severity prediction. We also show that Llama 70B achieves F1-score gains of 6.18 and 8.46 points, respectively. K-Paths also improves the supervised training efficiency of EmerGNN, a state-of-the-art GNN, by reducing KG size by 90% while maintaining strong predictive performance. Beyond its scalability and efficiency, K-Paths uniquely bridges the gap between KGs and LLMs, providing explainable rationales for predicted interactions. These capabilities show that K-Paths is a valuable tool for efficient data-driven drug discovery.

Relational data occur in a variety of domains, such as social graphs [25], chemical structures [17], physical systems [25], gene-gene interactions [25], and epidemiological modeling [8]. These data are best represented by graphs that effectively model their relationships, such as chemical bonds in drug molecules that affect toxicity or treatment efficacy [25] or personal interactions in social networks indicating contact [17]. Although graph information represents these datasets more accurately by incorporating node features (i.e., chemical weight for molecules) and node interactions through edges (i.e., chemical bonds) [25], large-scale modeling to learn their patterns can be challenging if the graphs are complex [6, 22]. Embedding methods such as Graphlets[12] and DeepWalk[10] have been developed to address these challenges.

Multimodal learning models have become increasingly important as they surpass single-modality approaches on diverse tasks ranging from question-answering to autonomous driving. Despite the importance of multimodal learning, existing efforts focus on NLP applications, where the number of modalities is typically less than four (audio, video, text, images). However, data inputs in other domains, such as the medical field, may include X-rays, PET scans, MRIs, genetic screening, clinical notes, and more, creating a need for both efficient and accurate information fusion. Many state-of-the-art models rely on pairwise cross-modal attention, which does not scale well for applications with more than three modalities. For $n$ modalities, computing attention will result in $n \choose 2$ operations, potentially requiring considerable amounts of computational resources. To address this, we propose a new domain-neutral attention mechanism, One-Versus-Others (OvO) attention, that scales linearly with the number of modalities and requires only $n$ attention operations, thus offering a significant reduction in computational complexity compared to existing cross-modal attention algorithms. Using three diverse real-world datasets as well as an additional simulation experiment, we show that our method improves performance compared to popular fusion techniques while decreasing computation costs.

Gromov-Wasserstein distance has found many applications in machine learning due to its ability to compare measures across metric spaces and its invariance to isometric transformations. However, in certain applications, this invariance property can be too flexible, thus undesirable. Moreover, the Gromov-Wasserstein distance solely considers pairwise sample similarities in input datasets, disregarding the raw feature representations. We propose a new optimal transport-based distance, called Augmented Gromov-Wasserstein, that allows for some control over the level of rigidity to transformations. It also incorporates feature alignments, enabling us to better leverage prior knowledge on the input data for improved performance. We present theoretical insights into the proposed metric. We then demonstrate its usefulness for single-cell multi-omic alignment tasks and a transfer learning scenario in machine learning.

Optimal transport (OT) compares probability distributions by computing a meaningful alignment between their samples. CO-optimal transport (COOT) takes this comparison further by inferring an alignment between features as well. While this approach leads to better alignments and generalizes both OT and Gromov-Wasserstein distances, we provide a theoretical result showing that it is sensitive to outliers that are omnipresent in real-world data. This prompts us to propose unbalanced COOT for which we provably show its robustness to noise in the compared datasets. To the best of our knowledge, this is the first such result for OT methods in incomparable spaces. With this result in hand, we provide empirical evidence of this robustness for the challenging tasks of heterogeneous domain adaptation with and without varying proportions of classes and simultaneous alignment of samples and features across single-cell measurements.

The past decade has seen a revolution in genomic technologies that enabled a flood of genome-wide profiling of chromatin marks. Recent literature tried to understand gene regulation by predicting gene expression from large-scale chromatin measurements. Two fundamental challenges exist for such learning tasks: (1) genome-wide chromatin signals are spatially structured, high-dimensional and highly modular; and (2) the core aim is to understand what are the relevant factors and how they work together. Previous studies either failed to model complex dependencies among input signals or relied on separate feature analysis to explain the decisions. This paper presents an attention-based deep learning approach; AttentiveChrome, that uses a unified architecture to model and to interpret dependencies among chromatin factors for controlling gene regulation.

Computational methods that predict differential gene expression from histone modification signals are highly desirable for understanding how histone modifications control the functional heterogeneity of cells through influencing differential gene regulation. Recent studies either failed to capture combinatorial effects on differential prediction or primarily only focused on cell type-specific analysis. In this paper, we develop a novel attention-based deep learning architecture, DeepDiff, that provides a unified and end-to-end solution to model and to interpret how dependencies among histone modifications control the differential patterns of gene regulation. DeepDiff uses a hierarchy of multiple Long short-term memory (LSTM) modules to encode the spatial structure of input signals and to model how various histone modifications cooperate automatically. We introduce and train two levels of attention jointly with the target prediction, enabling DeepDiff to attend differentially to relevant modifications and to locate important genome positions for each modification. Additionally, DeepDiff introduces a novel deep-learning based multi-task formulation to use the cell-type-specific gene expression predictions as auxiliary tasks, encouraging richer feature embeddings in our primary task of differential expression prediction. Using data from Roadmap Epigenomics Project (REMC) for ten different pairs of cell types, we show that DeepDiff significantly outperforms the state-of-the-art baselines for differential gene expression prediction. The learned attention weights are validated by observations from previous studies about how epigenetic mechanisms connect to differential gene expression. Codes and results are available at \url{deepchrome.org}

The past decade has seen a revolution in genomic technologies that enabled a flood of genome-wide profiling of chromatin marks. Recent literature tried to understand gene regulation by predicting gene expression from large-scale chromatin measurements. Two fundamental challenges exist for such learning tasks: (1) genome-wide chromatin signals are spatially structured, high-dimensional and highly modular; and (2) the core aim is to understand what are the relevant factors and how they work together. Previous studies either failed to model complex dependencies among input signals or relied on separate feature analysis to explain the decisions. This paper presents an attention-based deep learning approach; AttentiveChrome, that uses a unified architecture to model and to interpret dependencies among chromatin factors for controlling gene regulation. AttentiveChrome uses a hierarchy of multiple Long Short-Term Memory (LSTM) modules to encode the input signals and to model how various chromatin marks cooperate automatically. AttentiveChrome trains two levels of attention jointly with the target prediction, enabling it to attend differentially to relevant marks and to locate important positions per mark. We evaluate the model across 56 different cell types (tasks) in human. Not only is the proposed architecture more accurate, but its attention scores also provide a better interpretation than state-of-the-art feature visualization methods such as saliency map.

One of the fundamental tasks in understanding genomics is the problem of predicting Transcription Factor Binding Sites (TFBSs). With more than hundreds of Transcription Factors (TFs) as labels, genomic-sequence based TFBS prediction is a challenging multi-label classification task. There are two major biological mechanisms for TF binding: (1) sequence-specific binding patterns on genomes known as "motifs" and (2) interactions among TFs known as co-binding effects. In this paper, we propose a novel deep architecture, the Prototype Matching Network (PMN) to mimic the TF binding mechanisms. Our PMN model automatically extracts prototypes ("motif"-like features) for each TF through a novel prototype-matching loss. Borrowing ideas from few-shot matching models, we use the notion of support set of prototypes and an LSTM to learn how TFs interact and bind to genomic sequences. On a reference TFBS dataset with $2.1$ $million$ genomic sequences, PMN significantly outperforms baselines and validates our design choices empirically. To our knowledge, this is the first deep learning architecture that introduces prototype learning and considers TF-TF interactions for large-scale TFBS prediction. Not only is the proposed architecture accurate, but it also models the underlying biology.