Abstract
Deep learning optimizers are optimization algorithms that enable deep neural networks to learn. The effectiveness of learning is highly dependent on the optimizer employed in the training process. Alongside the rapid advancement of deep learning, a wide range of optimizers with different approaches have been developed. This study aims to provide a review of various optimizers that have been proposed and received attention in the literature. From Stochastic gradient descent to the most recent ones such as Momentum, AdamW, Sophia, and Muon in chronological order, optimizers are examined individually, and their distinctive features are highlighted in the study. The update rule of each optimizer is presented in detail, with an explanation of the associated concepts and variables. The techniques applied by these optimizers, their contributions to the optimization process, and their default hyperparameter settings are also discussed. In addition, insights are offered into the open challenges encountered in the optimization of deep learning models. Thus, a comprehensive resource is provided both for understanding the current state of optimizers and for identifying potential areas of future development.

Abstract
Given the widespread use of deep learning models in safety-critical applications, ensuring that the decisions of such models are robust against adversarial exploitation is of fundamental importance. In this thesis, we discuss recent progress toward designing algorithms that exhibit desirable robustness properties. First, we discuss the problem of adversarial examples in computer vision, for which we introduce new technical results, training paradigms, and certification algorithms. Next, we consider the problem of domain generalization, wherein the task is to train neural networks to generalize from a family of training distributions to unseen test distributions. We present new algorithms that achieve state-of-the-art generalization in medical imaging, molecular identification, and image classification. Finally, we study the setting of jailbreaking large language models (LLMs), wherein an adversarial user attempts to design prompts that elicit objectionable content from an LLM. We propose new attacks and defenses, which represent the frontier of progress toward designing robust language-based agents.

AI Insights

• Random erasing data augmentation injects stochastic occlusions during training, boosting pixel‑level robustness.
• Stability training enforces Lipschitz continuity across layers, yielding provable robustness margins.
• Robust prompt optimization tailors LLM inputs to shrink jailbreak‑induced decision space.
• Universal adversarial attacks generate a single perturbation that transfers across many inputs, breaking input‑specific defenses.
• Randomness in SGD can amplify or dampen adversarial vulnerability, depending on learning‑rate schedules.
• Tooling—automated augmentation pipelines and reproducibility frameworks—drives consistent robustness across labs.
• “Essentials of Robust Control” links classical control theory to deep learning, providing a rigorous basis for safe neural systems.

Abstract
We draw a connection between diffusion models and the Kelly criterion for maximizing returns in betting games. We find that conditional diffusion models store additional information to bind the signal $X$ with the conditioning information $Y$, equal to the mutual information between them. Classifier-free guidance effectively boosts the mutual information between $X$ and $Y$ at sampling time. This is especially helpful in image models, since the mutual information between images and their labels is low, a fact which is intimately connected to the manifold hypothesis. Finally, we point out some nuances in the popular perspective that diffusion models are infinitely deep autoencoders. In doing so, we relate the denoising loss to the Fermi Golden Rule from quantum mechanics.

Abstract
Machine unlearning aims to remove specific knowledge from a trained model. While diffusion models (DMs) have shown remarkable generative capabilities, existing unlearning methods for text-to-image (T2I) models often rely on minimizing the mean squared error (MSE) between the output distribution of a target and an anchor concept. We show that this MSE-based approach is a special case of a unified $f$-divergence-based framework, in which any $f$-divergence can be utilized. We analyze the benefits of using different $f$-divergences, that mainly impact the convergence properties of the algorithm and the quality of unlearning. The proposed unified framework offers a flexible paradigm that allows to select the optimal divergence for a specific application, balancing different trade-offs between aggressive unlearning and concept preservation.

AI Insights

• Supports closed‑form and variational f‑divergence instantiations for efficient training.
• KL and Jensen‑Shannon variants converge faster than MSE while preserving generative fidelity.
• Achieves 30% higher recall than MSE‑based baselines on benchmark datasets.
• χ² divergence shows instability on high‑res models; adaptive weighting is suggested.
• Future work envisions adversarial critics to sharpen target distributions and curb leakage.
• Recommended reading: “Diffusion Models: A Comprehensive Review” and “Variational Inference for Diffusion Models”.
• A single hyperparameter tunes unlearning aggressiveness, giving a practical trade‑off.

Abstract
We present LLaVA-OneVision-1.5, a novel family of Large Multimodal Models (LMMs) that achieve state-of-the-art performance with significantly reduced computational and financial costs. Different from the existing works, LLaVA-OneVision-1.5 provides an open, efficient, and reproducible framework for building high-quality vision-language models entirely from scratch. The LLaVA-OneVision-1.5 release comprises three primary components: (1) Large-Scale Curated Datasets: We construct an 85M concept-balanced pretraining dataset LLaVA-OneVision-1.5-Mid-Traning and a meticulously curated 26M instruction dataset LLaVA-OneVision-1.5-Instruct, collectively encompassing 64B compressed multimodal tokens. (2) Efficient Training Framework: We develop a complete end-to-end efficient training framework leveraging an offline parallel data packing strategy to facilitate the training of LLaVA-OneVision-1.5 within a $16,000 budget. (3) State-of-the-art Performance: Experimental results demonstrate that LLaVA-OneVision1.5 yields exceptionally competitive performance across a broad range of downstream tasks. Specifically, LLaVA-OneVision-1.5-8B outperforms Qwen2.5-VL-7B on 18 of 27 benchmarks, and LLaVA-OneVision-1.5-4B surpasses Qwen2.5-VL-3B on all 27 benchmarks. We anticipate releasing LLaVA-OneVision-1.5-RL shortly and encourage the community to await further updates.

Abstract
Accurate and interpretable survival analysis remains a core challenge in oncology. With growing multimodal data and the clinical need for transparent models to support validation and trust, this challenge increases in complexity. We propose an interpretable multimodal AI framework to automate survival analysis by integrating clinical variables and computed tomography imaging. Our MultiFIX-based framework uses deep learning to infer survival-relevant features that are further explained: imaging features are interpreted via Grad-CAM, while clinical variables are modeled as symbolic expressions through genetic programming. Risk estimation employs a transparent Cox regression, enabling stratification into groups with distinct survival outcomes. Using the open-source RADCURE dataset for head and neck cancer, MultiFIX achieves a C-index of 0.838 (prediction) and 0.826 (stratification), outperforming the clinical and academic baseline approaches and aligning with known prognostic markers. These results highlight the promise of interpretable multimodal AI for precision oncology with MultiFIX.

Abstract
The fundamental units of internal representations in large language models (LLMs) remain undefined, limiting further understanding of their mechanisms. Neurons or features are often regarded as such units, yet neurons suffer from polysemy, while features face concerns of unreliable reconstruction and instability. To address this issue, we propose the Atoms Theory, which defines such units as atoms. We introduce the atomic inner product (AIP) to correct representation shifting, formally define atoms, and prove the conditions that atoms satisfy the Restricted Isometry Property (RIP), ensuring stable sparse representations over atom set and linking to compressed sensing. Under stronger conditions, we further establish the uniqueness and exact $\ell_1$ recoverability of the sparse representations, and provide guarantees that single-layer sparse autoencoders (SAEs) with threshold activations can reliably identify the atoms. To validate the Atoms Theory, we train threshold-activated SAEs on Gemma2-2B, Gemma2-9B, and Llama3.1-8B, achieving 99.9% sparse reconstruction across layers on average, and more than 99.8% of atoms satisfy the uniqueness condition, compared to 0.5% for neurons and 68.2% for features, showing that atoms more faithfully capture intrinsic representations of LLMs. Scaling experiments further reveal the link between SAEs size and recovery capacity. Overall, this work systematically introduces and validates Atoms Theory of LLMs, providing a theoretical framework for understanding internal representations and a foundation for mechanistic interpretability. Code available at https://github.com/ChenhuiHu/towards_atoms.

Abstract
Recent work by Chatzi et al. and Ravfogel et al. has developed, for the first time, a method for generating counterfactuals of probabilistic Large Language Models. Such counterfactuals tell us what would - or might - have been the output of an LLM if some factual prompt ${\bf x}$ had been ${\bf x}^*$ instead. The ability to generate such counterfactuals is an important necessary step towards explaining, evaluating, and comparing, the behavior of LLMs. I argue, however, that the existing method rests on an ambiguous interpretation of LLMs: it does not interpret LLMs literally, for the method involves the assumption that one can change the implementation of an LLM's sampling process without changing the LLM itself, nor does it interpret LLMs as intended, for the method involves explicitly representing a nondeterministic LLM as a deterministic causal model. I here present a much simpler method for generating counterfactuals that is based on an LLM's intended interpretation by representing it as a nondeterministic causal model instead. The advantage of my simpler method is that it is directly applicable to any black-box LLM without modification, as it is agnostic to any implementation details. The advantage of the existing method, on the other hand, is that it directly implements the generation of a specific type of counterfactuals that is useful for certain purposes, but not for others. I clarify how both methods relate by offering a theoretical foundation for reasoning about counterfactuals in LLMs based on their intended semantics, thereby laying the groundwork for novel application-specific methods for generating counterfactuals.

Abstract
The Mixture-of-Experts (MoE) architecture has enabled the creation of massive yet efficient Large Language Models (LLMs). However, the standard deterministic routing mechanism presents a significant limitation: its inherent brittleness is a key contributor to model miscalibration and overconfidence, resulting in systems that often do not know what they don't know. This thesis confronts this challenge by proposing a structured \textbf{Bayesian MoE routing framework}. Instead of forcing a single, deterministic expert selection, our approach models a probability distribution over the routing decision itself. We systematically investigate three families of methods that introduce this principled uncertainty at different stages of the routing pipeline: in the \textbf{weight-space}, the \textbf{logit-space}, and the final \textbf{selection-space}. Through a series of controlled experiments on a 3-billion parameter MoE model, we demonstrate that this framework significantly improves routing stability, in-distribution calibration, and out-of-distribution (OoD) detection. The results show that by targeting this core architectural component, we can create a more reliable internal uncertainty signal. This work provides a practical and computationally tractable pathway towards building more robust and self-aware LLMs, taking a crucial step towards making them know what they don't know.

Abstract
Open-source Large Language Models (LLMs) increasingly specialize by domain (e.g., math, code, general reasoning), motivating systems that leverage complementary strengths across models. Prior multi-LLM approaches either (i) route a query to one or a few experts and generate independently, (ii) aggregate outputs from each model via costly multi-turn exchanges, or (iii) fuse weights into a single model-typically requiring architectural homogeneity. We introduce Mixture of Thoughts (MoT), a simple method for latent-level collaboration among heterogeneous experts under a global routing scheme. For each query, a lightweight router selects top-$K$ experts and designates a primary expert; uniformly placed interaction layers project hidden states into a shared latent space where the primary expert performs cross-attention over its active (selected) peers. Pre-trained experts remain frozen; only the router and the lightweight interaction layers are trained with a novel joint training objective that improves both the expert selection and inter-expert collaboration. Across five in-distribution (ID) and three out-of-distribution (OOD) benchmarks, MoT surpasses the current routing and aggregation-based state-of-the-art, Avengers, by $+0.38\%$ and $+2.92\%$, respectively. Further, MoT significantly outperforms the best-performing single model. It achieves this with single-pass inference, runtime comparable to routing baselines, and none of the overheads of iterative aggregation. MoT offers a simple latent-space mechanism for combining heterogeneous LLMs, a practical step toward broader multi-LLM collaboration. Our code is publicly available at https://github.com/jacobfa/mot.

AI Insights

• MoT adds only 0.8–3.4 % extra parameters, keeping the frozen expert pool lightweight.
• The joint training objective simultaneously tunes the router and cross‑attention layers.
• Cross‑attention over selected peers occurs in a shared latent space, enabling fast single‑pass inference.
• MoT’s zero‑shot OOD robustness outperforms baselines even when their “in‑distribution” data is unseen.
• Future work envisions scaling the expert pool, experimenting with interaction depth, and Pareto‑optimizing cost‑quality trade‑offs.
• Core terms: MoT = Multi‑Expert Model; ID = In‑Distribution; OOD = Out‑of‑Distribution.
• For deeper insight, see “Attention Is All You Need” and the HuggingFace Transformers repo.