Olfactory perception plays a critical role in both human and organismal interactions, yet understanding of its underlying mechanisms and influencing factors remain insufficient. Molecular structures influence odor perception through intricate biochemical interactions, and accurately quantifying structure-odor relationships presents significant challenges. The Quantitative Structure-Odor Relationship (QSOR) task, which involves predicting the associations between molecular structures and their corresponding odors, seeks to address these challenges. To this end, we propose a method for QSOR, utilizing Graph Attention Networks to model molecular structures and capture both local and global features. Unlike conventional QSOR approaches reliant on predefined descriptors, our method leverages diverse molecular feature extraction techniques to automatically learn comprehensive representations. This integration enhances the model's capacity to handle complex molecular information, improves prediction accuracy. Our approach demonstrates clear advantages in QSOR prediction tasks, offering valuable insights into the application of deep learning in cheminformatics.

In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first establish a mapping of such models to sequence multi-index models, a generalization of the widely studied multi-index model to sequential covariates, for which we establish a number of general results. In the context of Bayesian-optimal learning, in the limit of large dimension $D$ and commensurably large number of samples $N$, we derive a sharp asymptotic characterization of the optimal performance as well as the performance of the best-known polynomial-time algorithm for this setting --namely approximate message-passing--, and characterize sharp thresholds on the minimal sample complexity required for better-than-random prediction performance. Our analysis uncovers, in particular, how the different layers are learned sequentially. Finally, we discuss how this sequential learning can also be observed in a realistic setup.

Graph representation learning has emerged as a cornerstone for tasks like node classification and link prediction, yet prevailing self-supervised learning (SSL) methods face challenges such as computational inefficiency, reliance on contrastive objectives, and representation collapse. Existing approaches often depend on feature reconstruction, negative sampling, or complex decoders, which introduce training overhead and hinder generalization. Further, current techniques which address such limitations fail to account for the contribution of node embeddings to a certain prediction in the absence of labeled nodes. To address these limitations, we propose a novel joint embedding predictive framework for graph SSL that eliminates contrastive objectives and negative sampling while preserving semantic and structural information. Additionally, we introduce a semantic-aware objective term that incorporates pseudo-labels derived from Gaussian Mixture Models (GMMs), enhancing node discriminability by evaluating latent feature contributions. Extensive experiments demonstrate that our framework outperforms state-of-the-art graph SSL methods across benchmarks, achieving superior performance without contrastive loss or complex decoders. Key innovations include (1) a non-contrastive, view-invariant joint embedding predictive architecture, (2) Leveraging single context and multiple targets relationship between subgraphs, and (3) GMM-based pseudo-label scoring to capture semantic contributions. This work advances graph SSL by offering a computationally efficient, collapse-resistant paradigm that bridges spatial and semantic graph features for downstream tasks. The code for our paper can be found at https://github.com/Deceptrax123/JPEB-GSSL

Accurate decoding of neural spike trains and relating them to motor output is a challenging task due to the inherent sparsity and length in neural spikes and the complexity of brain circuits. This master project investigates experimental methods for decoding zebra finch motor outputs (in both discrete syllables and continuous spectrograms), from invasive neural recordings obtained from Neuropixels. There are three major achievements: (1) XGBoost with SHAP analysis trained on spike rates revealed neuronal interaction patterns crucial for syllable classification. (2) Novel method (tokenizing neural data with GPT2) and architecture (Mamba2) demonstrated potential for decoding of syllables using spikes. (3) A combined contrastive learning-VAE framework successfully generated spectrograms from binned neural data. This work establishes a promising foundation for neural decoding of complex motor outputs and offers several novel methodological approaches for processing sparse neural data.

Recent work has shown that purely quadratic functions can replace MLPs in transformers with no significant loss in performance, while enabling new methods of interpretability based on linear algebra. In this work, we theoretically derive closed-form least-squares optimal approximations of feedforward networks (multilayer perceptrons and gated linear units) using polynomial functions of arbitrary degree. When the $R^2$ is high, this allows us to interpret MLPs and GLUs by visualizing the eigendecomposition of the coefficients of their linear and quadratic approximants. We also show that these approximants can be used to create SVD-based adversarial examples. By tracing the $R^2$ of linear and quadratic approximants across training time, we find new evidence that networks start out simple, and get progressively more complex. Even at the end of training, however, our quadratic approximants explain over 95% of the variance in network outputs.

Due to the ever growing amounts of data leveraged for machine learning and scientific computing, it is increasingly important to develop algorithms that sample only a small portion of the data at a time. In the case of linear least-squares, the randomized block Kaczmarz method (RBK) is an appealing example of such an algorithm, but its convergence is only understood under sampling distributions that require potentially prohibitively expensive preprocessing steps. To address this limitation, we analyze RBK when the data is sampled uniformly, showing that its iterates converge in a Monte Carlo sense to a $\textit{weighted}$ least-squares solution. Unfortunately, for general problems the condition number of the weight matrix and the variance of the iterates can become arbitrarily large. We resolve these issues by incorporating regularization into the RBK iterations. Numerical experiments, including examples arising from natural gradient optimization, suggest that the regularized algorithm, ReBlocK, outperforms minibatch stochastic gradient descent for realistic problems that exhibit fast singular value decay.

The rise of single-cell sequencing technologies has revolutionized the exploration of drug resistance, revealing the crucial role of cellular heterogeneity in advancing precision medicine. By building computational models from existing single-cell drug response data, we can rapidly annotate cellular responses to drugs in subsequent trials. To this end, we developed scGSDR, a model that integrates two computational pipelines grounded in the knowledge of cellular states and gene signaling pathways, both essential for understanding biological gene semantics. scGSDR enhances predictive performance by incorporating gene semantics and employs an interpretability module to identify key pathways contributing to drug resistance phenotypes. Our extensive validation, which included 16 experiments covering 11 drugs, demonstrates scGSDR's superior predictive accuracy, when trained with either bulk-seq or scRNA-seq data, achieving high AUROC, AUPR, and F1 Scores. The model's application has extended from single-drug predictions to scenarios involving drug combinations. Leveraging pathways of known drug target genes, we found that scGSDR's cell-pathway attention scores are biologically interpretable, which helped us identify other potential drug-related genes. Literature review of top-ranking genes in our predictions such as BCL2, CCND1, the AKT family, and PIK3CA for PLX4720; and ICAM1, VCAM1, NFKB1, NFKBIA, and RAC1 for Paclitaxel confirmed their relevance. In conclusion, scGSDR, by incorporating gene semantics, enhances predictive modeling of cellular responses to diverse drugs, proving invaluable for scenarios involving both single drug and combination therapies and effectively identifying key resistance-related pathways, thus advancing precision medicine and targeted therapy development.

In neuroscience, identifying distinct patterns linked to neurological disorders, such as Alzheimer's and Autism, is critical for early diagnosis and effective intervention. Graph Neural Networks (GNNs) have shown promising in analyzing brain networks, but there are two major challenges in using GNNs: (1) distribution shifts in multi-site brain network data, leading to poor Out-of-Distribution (OOD) generalization, and (2) limited interpretability in identifying key brain regions critical to neurological disorders. To bridge these gaps, we introduce BrainOOD, a novel framework tailored for brain networks that enhances GNNs' OOD generalization and interpretability. BrainOOD framework consists of a feature selector and a structure extractor, which incorporates various auxiliary losses including an improved Graph Information Bottleneck (GIB) objective to recover causal subgraphs. By aligning structure selection across brain networks and filtering noisy features, BrainOOD offers reliable interpretations of critical brain regions. Our approach outperforms 16 existing methods and improves generalization to OOD subjects by up to 8.5%. Case studies highlight the scientific validity of the patterns extracted, which aligns with the findings in known neuroscience literature. We also propose the first OOD brain network benchmark, which provides a foundation for future research in this field. In neuroscience, a major goal is to identify distinct patterns linked to neurological disorders, such as Alzheimer's and Autism, by examining brain data of both healthy individuals and patients with these disorders (Poldrack et al., 2009). Among the neuroimaging techniques, resting-state functional magnetic resonance imaging (fMRI) is widely used to capture the functional connectivity between different brain regions (Worsley et al., 2002). These connections provide insights into how different brain regions co-activate or show correlated activities, offering a framework to study neurological systems through graphbased methods (Kawahara et al., 2017; Lanciano et al., 2020; Wang et al., 2023; Xu et al., 2024c). The most prevalent brain network analysis model is based on Graph Neural Networks (GNNs), which have recently shown promising results (Li et al., 2019; 2021; Xu et al., 2024a).

Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs and FNOs, there is currently no optimization convergence guarantee for learning such networks using gradient descent (GD). In this paper, we address this open problem by presenting a unified framework for optimization based on GD and applying it to establish convergence guarantees for both DONs and FNOs. In particular, we show that the losses associated with both of these neural operators satisfy two conditions -- restricted strong convexity (RSC) and smoothness -- that guarantee a decrease on their loss values due to GD. Remarkably, these two conditions are satisfied for each neural operator due to different reasons associated with the architectural differences of the respective models. One takeaway that emerges from the theory is that wider networks should lead to better optimization convergence for both DONs and FNOs. We present empirical results on canonical operator learning problems to support our theoretical results.

Conformal prediction is an emerging technique for uncertainty quantification that constructs prediction sets guaranteed to contain the true label with a predefined probability. Recent work develops online conformal prediction methods that adaptively construct prediction sets to accommodate distribution shifts. However, existing algorithms typically assume perfect label accuracy which rarely holds in practice. In this work, we investigate the robustness of online conformal prediction under uniform label noise with a known noise rate, in both constant and dynamic learning rate schedules. We show that label noise causes a persistent gap between the actual mis-coverage rate and the desired rate $\alpha$, leading to either overestimated or underestimated coverage guarantees. To address this issue, we propose Noise Robust Online Conformal Prediction (dubbed NR-OCP) by updating the threshold with a novel robust pinball loss, which provides an unbiased estimate of clean pinball loss without requiring ground-truth labels. Our theoretical analysis shows that NR-OCP eliminates the coverage gap in both constant and dynamic learning rate schedules, achieving a convergence rate of $\mathcal{O}(T^{-1/2})$ for both empirical and expected coverage errors under uniform label noise. Extensive experiments demonstrate the effectiveness of our method by achieving both precise coverage and improved efficiency.