The growing complexity of deep learning models introduces challenges in scalability and adaptability. This paper explores how modular design, inspired by software engineering, can enhance deep learning systems. This paper also showed that modern deep learning techniques such as Mixture of Experts (MoE) and LoRA are advancing toward higher modularity. By promoting modular architectures, we emphasize the need to move beyond monolithic models toward more reusable, maintainable, and scalable AI systems, providing a potential research direction for future work.

Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and quantization. The spectral-norm robustness of low-rank inverse approximations remains poorly understood. We systematically study the spectral-norm error $\| \tilde{A}_p^{-1} - A_p^{-1} \|$ for an $n\times n$ symmetric matrix $A$, where $A_p^{-1}$ denotes the best rank-\(p\) approximation of $A^{-1}$, and $\tilde{A} = A + E$ is a noisy observation. Under mild assumptions on the noise, we derive sharp non-asymptotic perturbation bounds that reveal how the error scales with the eigengap, spectral decay, and noise alignment with low-curvature directions of $A$. Our analysis introduces a novel application of contour integral techniques to the \emph{non-entire} function $f(z) = 1/z$, yielding bounds that improve over naive adaptations of classical full-inverse bounds by up to a factor of $\sqrt{n}$. Empirically, our bounds closely track the true perturbation error across a variety of real-world and synthetic matrices, while estimates based on classical results tend to significantly overpredict. These findings offer practical, spectrum-aware guarantees for low-rank inverse approximations in noisy computational environments.

A central challenge in machine learning is to understand how noise or measurement errors affect low-rank approximations, particularly in the spectral norm. This question is especially important in differentially private low-rank approximation, where one aims to preserve the top-$p$ structure of a data-derived matrix while ensuring privacy. Prior work often analyzes Frobenius norm error or changes in reconstruction quality, but these metrics can over- or under-estimate true subspace distortion. The spectral norm, by contrast, captures worst-case directional error and provides the strongest utility guarantees. We establish new high-probability spectral-norm perturbation bounds for symmetric matrices that refine the classical Eckart--Young--Mirsky theorem and explicitly capture interactions between a matrix $A \in \mathbb{R}^{n \times n}$ and an arbitrary symmetric perturbation $E$. Under mild eigengap and norm conditions, our bounds yield sharp estimates for $\| (A + E)_p - A_p \|$, where $A_p$ is the best rank-$p$ approximation of $A$, with improvements of up to a factor of $\sqrt{n}$. As an application, we derive improved utility guarantees for differentially private PCA, resolving an open problem in the literature. Our analysis relies on a novel contour bootstrapping method from complex analysis and extends it to a broad class of spectral functionals, including polynomials and matrix exponentials. Empirical results on real-world datasets confirm that our bounds closely track the actual spectral error under diverse perturbation regimes.

This paper introduces Global Contextualized Representations (GCoRe) – an extension for existing transformer-based language models. GCoRe addresses limitations in capturing global context and long-range dependencies by utilizing Graph Neural Networks for graph inference on a context graph constructed from the input text. Global contextualized features, derived from the context graph, are added to the token representations from the base language model. Experiment results show that GCoRe improves the performance of the baseline model (DeBERTa v3) by 0.57% on the HotpotQA dataset and by 0.15% on the SQuAD v2 dataset. In addition, GCoRe is able to answer questions that require logical reasoning and multi-hop inference, while the baseline model fails to provide correct answers.

This paper presents a reinforcement learning approach for foreign exchange trading. Inspired by technical analysis methods, this approach makes use of technical indicators by encoding them into Gramian Angular Fields and searches for patterns that indicate price movements using convolutional neural networks (CNN). In addition to the policy that determines the action to take, an extra regression head is utilized to determine the size of market orders. This paper also experimentally shows that maximizing the return of individual trade or cumulative reward in a finite time window results to better performance.