San Francisco schools may shut down if teachers strike in coming days, District Superintendent Maria Su announced Friday, as negotiations with the union continue.

Yes, eating carrots can help your eyesight. The World War II propaganda that touted the veggie wasn't totally wrong, but carrots still won't give you night vision. Carrots' beta-carotene pigment can help support retina health, but the root vegetable still has its limits. Breakthroughs, discoveries, and DIY tips sent six days a week. In a British propaganda poster from World War II, an illustration in shadowy tones captures a dramatic nighttime scene: a woman and young girl peer around a black automobile, as if looking for a quick escape.

Scarcity of labeled training data remains the long pole in the tent for building performant language technology and generative AI models. Transformer models -- particularly LLMs -- are increasingly being used to mitigate the data scarcity problem via synthetic data generation. However, because the models are black boxes, the properties of the synthetic data are difficult to predict. In practice it is common for language technology engineers to 'fiddle' with the LLM temperature setting and hope that what comes out the other end improves the downstream model. Faced with this uncertainty, here we propose Data Kernel Perspective Space (DKPS) to provide the foundation for mathematical analysis yielding concrete statistical guarantees for the quality of the outputs of transformer models. We first show the mathematical derivation of DKPS and how it provides performance guarantees. Next we show how DKPS performance guarantees can elucidate performance of a downstream task, such as neural machine translation models or LLMs trained using Contrastive Preference Optimization (CPO). Limitations of the current work and future research are also discussed.

Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is inefficient yet robust and may arise from the architectural bias of residual networks and target functions incompatible with smooth dynamics. The findings suggest that improving LLM efficiency may require architectural innovations to encourage compositional use of depth.

Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably, ensuring robustness to small input perturbations and generalization to out-of-distribution data. These critical challenges underscore the need to understand the underlying fundamental principles that govern robustness and generalization. Among the theoretical tools available, Lipschitz continuity plays a pivotal role in governing the fundamental properties of neural networks related to robustness and generalization. It quantifies the worst-case sensitivity of network's outputs to small input perturbations. While its importance is widely acknowledged, prior research has predominantly focused on empirical regularization approaches based on Lipschitz constraints, leaving the underlying principles less explored. This thesis seeks to advance a principled understanding of the principles of Lipschitz continuity in neural networks within the paradigm of machine learning, examined from two complementary perspectives: an internal perspective -- focusing on the temporal evolution of Lipschitz continuity in neural networks during training (i.e., training dynamics); and an external perspective -- investigating how Lipschitz continuity modulates the behavior of neural networks with respect to features in the input data, particularly its role in governing frequency signal propagation (i.e., modulation of frequency signal propagation).

Modern systems, such as digital platforms and service systems, increasingly rely on contextual bandits for online decision-making; however, their deployment can inadvertently create unfair exposure among arms, undermining long-term platform sustainability and supplier trust. This paper studies the contextual bandit problem under a uniform $(1-δ)$-fairness constraint, and addresses its unique vulnerabilities to strategic manipulation. The fairness constraint ensures that preferential treatment is strictly justified by an arm's actual reward across all contexts and time horizons, using uniformity to prevent statistical loopholes. We develop novel algorithms that achieve (nearly) minimax-optimal regret for both linear and smooth reward functions, while maintaining strong $(1-\tilde{O}(1/T))$-fairness guarantees, and further characterize the theoretically inherent yet asymptotically marginal "price of fairness". However, we reveal that such merit-based fairness becomes uniquely susceptible to signal manipulation. We show that an adversary with a minimal $\tilde{O}(1)$ budget can not only degrade overall performance as in traditional attacks, but also selectively induce insidious fairness-specific failures while leaving conspicuous regret measures largely unaffected. To counter this, we design robust variants incorporating corruption-adaptive exploration and error-compensated thresholding. Our approach yields the first minimax-optimal regret bounds under $C$-budgeted attack while preserving $(1-\tilde{O}(1/T))$-fairness. Numerical experiments and a real-world case demonstrate that our algorithms sustain both fairness and efficiency.

Setting the learning rate for a deep learning model is a critical part of successful training, yet choosing this hyperparameter is often done empirically with trial and error. In this work, we explore a solvable model of optimal learning rate schedules for a powerlaw random feature model trained with stochastic gradient descent (SGD). We consider the optimal schedule $η_T^\star(t)$ where $t$ is the current iterate and $T$ is the total training horizon. This schedule is computed both numerically and analytically (when possible) using optimal control methods. Our analysis reveals two regimes which we term the easy phase and hard phase. In the easy phase the optimal schedule is a polynomial decay $η_T^\star(t) \simeq T^{-ξ} (1-t/T)^δ$ where $ξ$ and $δ$ depend on the properties of the features and task. In the hard phase, the optimal schedule resembles warmup-stable-decay with constant (in $T$) initial learning rate and annealing performed over a vanishing (in $T$) fraction of training steps. We investigate joint optimization of learning rate and batch size, identifying a degenerate optimality condition. Our model also predicts the compute-optimal scaling laws (where model size and training steps are chosen optimally) in both easy and hard regimes. Going beyond SGD, we consider optimal schedules for the momentum $β(t)$, where speedups in the hard phase are possible. We compare our optimal schedule to various benchmarks in our task including (1) optimal constant learning rates $η_T(t) \sim T^{-ξ}$ (2) optimal power laws $η_T(t) \sim T^{-ξ} t^{-χ}$, finding that our schedule achieves better rates than either of these. Our theory suggests that learning rate transfer across training horizon depends on the structure of the model and task. We explore these ideas in simple experimental pretraining setups.

Why Are Some Women Training for Pregnancy Like It's a Marathon? A growing legion of "zero trimester" influencers are convincing followers that healthy pregnancies are a choice--and that raw milk, watching sunsets, and pricey specialized courses can help. Three years ago, Esther Rohr and her husband decided to start thinking about pregnancy. The 26-year-old Oregon-based wedding photographer made small but intentional lifestyle changes--going to bed earlier, drinking more water and less alcohol, dialing in her fitness, loading up on protein, and taking supplements like beef organ capsules and Vitamin D3. They started charging their phones in the kitchen for better sleep and unplugging their Wi-Fi at night, because her research suggested it might affect cellular health. Concerned about their exposure to reproductive toxins, Rohr began the slow, painstaking task of swapping out all their synthetic workout clothes, nonstick pans, and scented personal care products that might contain phthalates or other endocrine-disrupting chemicals. She bought an air purifier and hopes to eventually replace their LED bulbs with incandescents, because she worries they might be affecting her circadian rhythm.

We introduce a new preference-based framework for conditional treatment effect estimation and policy learning, built on the Conditional Preference-based Treatment Effect (CPTE). CPTE requires only that outcomes be ranked under a preference rule, unlocking flexible modeling of heterogeneous effects with multivariate, ordinal, or preference-driven outcomes. This unifies applications such as conditional probability of necessity and sufficiency, conditional Win Ratio, and Generalized Pairwise Comparisons. Despite the intrinsic non-identifiability of comparison-based estimands, CPTE provides interpretable targets and delivers new identifiability conditions for previous unidentifiable estimands. We present estimation strategies via matching, quantile, and distributional regression, and further design efficient influence-function estimators to correct plug-in bias and maximize policy value. Synthetic and semi-synthetic experiments demonstrate clear performance gains and practical impact.