Flat Minima and Generalization: from Matrix Sensing to Neural Networks
Maryam Fazel, University of Washington
When do overparameterized neural networks avoid overfitting and generalize to unseen data? Empirical evidence suggests that the shape of the training loss function near the solution matters—the minima where the loss is “flatter” tend to lead to better generalization. Yet quantifying flatness and its rigorous analysis, even in simple models, has been limited. In this talk, we examine overparameterized nonconvex models such as low-rank matrix sensing, matrix completion, robust PCA, as well as a 2-layer neural network as test cases. We show that under standard statistical assumptions, "flat" minima (minima with the smallest local average curvature, measured by the trace of the Hessian matrix) provably generalize in all these cases. These algorithm-agnostic results suggest a theoretical basis for favoring methods that bias iterates towards flat solutions, and help inform the design of better training algorithms.
Hunting the Hessian
Madeleine Udell, Stanford University
Ill conditioned loss landscapes are ubiquitous in machine learning, and they slow down optimization. Preconditioning the gradient to make the loss more isotropic is a natural solution, but is challenging for extremely large problems, as direct access to the problem Hessian is prohibitively expensive. We present two fresh approaches to preconditioning using tools from randomized numerical linear algebra and online convex optimization for efficient access to Hessian information, motivated by the question: what is the most useful information we can query from the problem Hessian using linear memory and compute?
One Small Step, One Giant Leap: From Test-Time Tweaks to Global Guarantees
Mahdi Soltanolkotabi, USC
Simple first-order methods like Gradient Descent (GD) remain foundational to modern machine learning. Yet, despite their widespread use, our theoretical understanding of the GD trajectory—how and why it works—remains incomplete in both classical and contemporary settings. This talk explores new horizons in understanding the behavior and power of GD across two distinct but connected fronts.
In the first part, we examine the surprising power of a single gradient step in enhancing model reasoning. We focus on test-time training (TTT)—a gradient-based approach that adapts model parameters using individual test instances. We introduce a theoretical framework that reveals how TTT can effectively handle distribution shifts and significantly reduce the data required for in-context learning, shedding light on why such simple methods often outperform expectations.
The second part turns to a more classical optimization setting: learning shallow neural networks with GD. Despite extensive study, even fitting a one-hidden-layer model to basic target functions lacks rigorous performance guarantees. We present a comprehensive analysis of the GD trajectory in this regime, showing how it avoids suboptimal stationary points and converges efficiently to global optima. Our results offer new theoretical foundations for understanding how GD succeeds in the presence of sub-optimal stationary points.
The Wisdom of the Body Revisited
Benjamin Recht, UC Berkeley
In 1932, Walter Cannon published his seminal text, The Wisdom of the Body, introducing the notion of homeostasis. He conceived of the body as a complex system actively working to keep itself in a stable state despite adversarial engagement with an uncertain and dangerous environment. Cannon’s concept of homeostasis would not only revolutionize the way we think about medicine but also inspire cyberneticists and early artificial intelligence researchers to think about the body and brain as well-regulated machines.
In this talk, I refocus Canon's work under a contemporary lens, showing how non-neural biological networks do very smart things. I will describe concepts from feedback control that illuminate necessary architectures for homeostasis. I will show how such systems can be both resilient to most disturbances while fragile to specific adversarial vectors. Identifying these fragilities can guide positive interventions that can steer dysregulated systems back to stable behavior. Throughout, I aim to highlight the role of mathematical and qualitative theory in our understanding and optimization of systems that behave effectively in unknown futures.
Accelerating Nonconvex Optimization via Online Learning
Aryan Mokhtari, UT Austin
A fundamental problem in optimization is finding an ε-first-order stationary point of a smooth function using only gradient information. The best-known gradient query complexity for this task, assuming both the gradient and Hessian of the objective function are Lipschitz continuous, is O( ε^(−7/4) ). In this talk, I present a method with a gradient complexity of O( d^(1/4) ε^(−13/8) ), where d is the problem dimension—yielding improved complexity when d = O( ε^(−1/2) ). The proposed method builds on quasi-Newton ideas and operates by solving two online learning problems under the hood.
The Binary Iterative Hard Thresholding Algorithm
Arya Mazumdar, TILOS & UC San Diego
We will discuss our work on the convergence of iterative hard threshold algorithms for sparse signal recovery problems. For classification problems with nonseparable data this algorithm can be thought of minimizing the so-called ReLU loss. It seems to be very effective (statistically optimal, simple iterative method) for a large class of models of nonseparable data—sparse generalized linear models. It is also robust to adversarial perturbation. Based on joint work with Namiko Matsumoto.
Reverse diffusion Monte Carlo
Yian Ma, TILOS & UC San Diego
I will introduce a novel Monte Carlo sampling approach that uses the reverse diffusion process. In particular, the intermediary updates—the score functions—can be explicitly estimated to arbitrary accuracy, leading to an unbiased Bayesian inference algorithm. I will then discuss how to use this idea to improve sampling in the diffusion models via reverse transition kernels.
Linear Bregman Divergence Control
Babak Hassibi, Caltech
In the past couple of decades, the use of "non-quadratic" convex cost functions has revolutionized signal processing, machine learning, and statistics, allowing one to customize solutions to have desired structures and properties. However, the situation is not the same in control where the use of quadratic costs still dominates, ostensibly because determining the "value function", i.e., the optimal expected cost-to-go, which is critical to the construction of the optimal controller, becomes computationally intractable as soon as one considers general convex costs. As a result, practitioners often resort to heuristics and approximations, such as model predictive control that only looks a few steps into the future. In the quadratic case, the value function is easily determined by appealing to certainty-equivalence and solving Riccati equations. In this talk, we consider a special class of convex cost functions constructed from Bregman divergence and show how, with appropriate choices, they can be used to fully extend the framework developed for the quadratic case. The resulting optimal controllers are infinite horizon, come with stability guarantees, and have state-feedback, or estimated state-feedback, laws. They exhibit a much wider range of behavior than their quadratic counterparts since the feedback laws are nonlinear. We demonstrate the applicability of the approach to several cases of interest, including safety control, sparse control, and bang-bang control.
Unleashing the Power of Variance Reduction for Training Large Models
Quanquan Gu, Caltech
Training deep neural networks—and more recently, large language models demands efficient and scalable optimizers. Adaptive gradient algorithms like Adam, AdamW, and their variants have been central to this task. Despite the development of numerous variance reduction algorithms in the past decade aimed at accelerating stochastic optimization in both convex and nonconvex settings, variance reduction has not found widespread success in training deep neural networks or large language models. Consequently, it has remained a less favored approach in modern AI. In this talk, I will introduce a unified optimization framework, MARS (Make vAriance Reduction Shine), which reconciles preconditioned gradient methods with variance reduction via a scaled stochastic recursive momentum technique. Within this framework, I will introduce three instances of MARS that leverage preconditioned gradient updates based on AdamW, Lion, and Shampoo, respectively. In addition, I will draw a connection between our algorithms and existing optimizers. Experimental results on training GPT-2 models indicate that MARS consistently outperforms AdamW by a large margin.
Optimization and Reasoning
Sicun (Sean) Gao, TILOS & UC San Diego
For a while, the remarkable progress in ML/AI has led many to dismiss the old-fashioned concerns of NP-hardness, with the belief that sufficiently large nonlinear functions can be trained to encode solutions to everything of practical relevance. Yet, as these functions are increasingly deployed as black-box models with agency, their usability is once again constrained by our ability to answer fundamental questions that demand deeper understanding across the entire training and inference pipeline. These questions inevitably correspond to solving NP-hard problems that remain well beyond the reach of existing algorithms. The formal reasoning community has spent decades developing a rich arsenal of tools for tackling similar problems, but mostly for discrete symbolic computing systems. Extending the same rigor and algorithmic power to the continuous domain is a grand challenge that has to be confronted. We need to unify optimization and reasoning towards new generations of capable algorithms that bring together numerical/analytic, combinatorial/algebraic, and statistical/probabilistic approaches. Addressing these challenges can establish new computational foundations for all real-world engineering disciplines too.
The Architecture of Intelligence
John Doyle, Caltech
The vast diversity of organisms and machines that show even minimal “intelligence” from bacteria to humans to the latest LLMs, nevertheless share a universal architecture involving layers, levels, and laws, or ULA for short. We will discuss the most important features of ULAs, which are Diversity-enable Sweet Spots (DeSS), efficiency-speed-accuracy constraints, tradeoffs, and conservation laws, and “constraints that deconstrain.” Depending on interest, motivating case studies can come from biology, neuroscience, medicine, and technology, with language offering a timely, familiar, fun, and controversial subject. Much of the relevant math is relatively new and will be sketched with links to publications. Most of it can be viewed as applications of optimization to control, networks, and “intelligence.”
Tutorial on AI Alignment (part 2 of 2): Methodologies for AI Alignment
Ahmad Beirami, Google DeepMind
Hamed Hassani, University of Pennsylvania
The second part of the tutorial focuses on AI alignment techniques and is structured as three segments: In the first segment, we examine black-box techniques aimed at aligning models towards various goals (e.g., safety), such as controlled decoding and the best-of-N algorithm. In the second segment, we will also consider efficiency, where we examine information-theoretic techniques designed to improve inference latency, such as model compression or speculative decoding. If time permits, in the final segment, we discuss inference-aware alignment, which is a framework to align models to work better with inference-time compute algorithms.
Tutorial on AI Alignment (part 1 of 2): Safety Vulnerabilities of Current Frontier Models
Ahmad Beirami, Google DeepMind
Hamed Hassani, University of Pennsylvania
In recent years, large language models have been used to solve a multitude of natural language tasks. In the first part of the tutorial, we start by giving a brief overview of the history of language modeling and the fundamental techniques that led to the development of the modern language models behind Claude, Gemini, GPT, and Llama. We then dive into the safety failure modes of the current frontier models. Specifically, we will explain that, despite efforts to align large language models (LLMs) with human intentions, popular LLMs are susceptible to jailbreaking attacks, wherein an adversary fools a targeted LLM into generating objectionable content. We review the current state of the jailbreaking literature, including new questions about robust generalization, discussions of open-box and black-box attacks on LLMs, defenses against jailbreaking attacks, and a new leaderboard to evaluate the robust generalization of production LLMs.
The focus of the first session will be mostly on safety vulnerabilities of the frontier LLMs. In the second session, we will focus on the current methodologies that aim to mitigate these vulnerabilities and more generally align language models with human standards.
IEEE Seasonal School: Manufacturability, Testing, Reliability, and Security
00:00:00 - Introduction
01:51:00 - "Machine Learning for DFM", Bei Yu, Associate Professor, Chinese University of Hong Kong
59:54:00 - "ML for Testing and Yield", Li-C. Wang, Professor, UC Santa Barbara
01:59:00 - "ML for Cross-Layer Reliability and Security", Muhammad Shafique, Professor of Computer Engineering, NYU Abu Dhabi
IEEE Seasonal School: Standard Platforms for ML in EDA and IC Design
00:00:00 - Introduction
00:02:45 - "Exchanging EDA data for AI/ML using Standard API", Kerim Kalafala, Senior Technical Staff Member, IBM (co-chair, AI/ML for EDA Special Interest Group, Si2), Richard Taggart, Senior Software Engineering Manager, IBM and Akhilesh Kumar, Principal R&D Engineer, Ansys
01:29:30 - "IEEE CEDA DATC RDF and METRICS2.1: Toward a Standard Platform for ML-Enabled EDA and IC Design", Jinwook Jung, Research Staff Member, IBM Research
IEEE Seasonal School: Applications / Future Frontiers
00:00:00 - Introduction
01:23:00 - "Automating Analog Layout: Why This Time is Different", Sachin Sapatnekar, Professor, University of Minnesota
57:20:00 - "Machine Learning-Powered Tools and Methodologies for 3D Integration", Sung Kyu Lim, Professor, Georgia Institute of Technology
01:58:18 - "ML for Verification", Shobha Vasudevan, Researcher at Google and Adjunct Professor at UIUC