In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases into training in a hope to reduce statistical complexity. Alternatively, we propose stochastically shared embeddings (SSE), a data-driven approach to regularizing embedding layers, which stochastically transitions between embeddings during stochastic gradient descent (SGD). Because SSE integrates seamlessly with existing SGD algorithms, it can be used with only minor modifications when training large scale neural networks. We develop two versions of SSE: SSE-Graph using knowledge graphs of embeddings; SSE-SE using no prior information.

The workhorse of machine learning is stochastic gradient descent.To access stochastic gradients, it is common to consider iteratively input/output pairs of a training dataset.Interestingly, it appears that one does not need full supervision to access stochastic gradients, which is the main motivation of this paper.After formalizing the "active labeling" problem, which focuses on active learning with partial supervision, we provide a streaming technique that provably minimizes the ratio of generalization error over the number of samples.We illustrate our technique in depth for robust regression.

Previous work has proposed many new loss functions and regularizers that improve test accuracy on image classification tasks. However, it is not clear whether these loss functions learn better representations for downstream tasks. This paper studies how the choice of training objective affects the transferability of the hidden representations of convolutional neural networks trained on ImageNet. We show that many objectives lead to statistically significant improvements in ImageNet accuracy over vanilla softmax cross-entropy, but the resulting fixed feature extractors transfer substantially worse to downstream tasks, and the choice of loss has little effect when networks are fully fine-tuned on the new tasks. Using centered kernel alignment to measure similarity between hidden representations of networks, we find that differences among loss functions are apparent only in the last few layers of the network. We delve deeper into representations of the penultimate layer, finding that different objectives and hyperparameter combinations lead to dramatically different levels of class separation. Representations with higher class separation obtain higher accuracy on the original task, but their features are less useful for downstream tasks. Our results suggest there exists a trade-off between learning invariant features for the original task and features relevant for transfer tasks.

We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the estimation problem can be thought of as solving a zero-sum game between a modeler who is optimizing over the hypothesis space of the target model and an adversary who identifies violating moments over a test function space. We analyze the statistical estimation rate of the resulting estimator for arbitrary hypothesis spaces, with respect to an appropriate analogue of the mean squared error metric, for ill-posed inverse problems. We show that when the minimax criterion is regularized with a second moment penalty on the test function and the test function space is sufficiently rich, then the estimation rate scales with the critical radius of the hypothesis and test function spaces, a quantity which typically gives tight fast rates. Our main result follows from a novel localized Rademacher analysis of statistical learning problems defined via minimax objectives.

Electrifying space and water heating is a critical priority for the energy transition. The necessary widespread adoption of heat pumps will have significant impacts on the power grid. Studies report heating electrification may increase winter peak electricity demand by up to 70%, with some colder regions experiencing a more than fourfold increase in peak demand. The process of upgrading the grid has a critical spatial dimension, as heating demand, electricity demand, and the capacity of existing grid infrastructure vary significantly across regions. Grid planning also involves a critical temporal dimension: short-term weather patterns and long-term climate change introduce complexities and uncertainties that can be di fficult to quantify. However, most existing demand forecasts are provided and validated only at aggregated spatial scales, lack temporal detail, and provide single-valued predictions. Without accurate, probabilistic, and spatially and temporally resolved demand forecasts, planners risk misallocating scarce resources. We present a novel framework for high-resolution forecasting of residential heating and electricity demand using probabilistic deep learning models. We focus specifically on providing hourly building-level electricity and heating demand forecasts for the residential sector. Leveraging multimodal building-level information - including data on building footprint areas, heights, nearby building density, nearby building size, land use patterns, and high-resolution weather data - and probabilistic modeling, our methods provide granular insights into demand heterogeneity. V alida-tion at the building level underscores a step change improvement in performance relative to NREL's ResStock model, which has emerged as a research community standard for residential heating and electricity demand characterization. In building-level heating and electricity estimation backtests, our probabilistic models respectively achieve RMSE scores 18.3% and 35.1% lower than those based on ResStock. Introduction Electrifying space and water heating is a critical priority for the energy transition [1, 2]. Residential and commercial buildings make up 13% of all U.S. emissions [3], with fossil-fueled space heating representing the single greatest constituent of this share [4]. The necessary widespread adoption of heat pumps will have significant impacts on the power grid.

Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives -- using principles from classical search. We propose a general framework that orchestrates local and global search to efficiently navigate the generative space. It employs a theoretically grounded local search via annealed Langevin MCMC and performs compute-efficient global exploration using breadth-first and depth-first tree search. We evaluate our approach on a range of challenging domains, including planning, offline reinforcement learning, and image generation. Across all tasks, we observe significant gains in both performance and efficiency. These results show that classical search provides a principled and practical foundation for inference-time scaling in diffusion models. Project page at diffusion-inference-scaling.github.io.

This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of a stepsize by a feedback function motivated from a convergence measure and uses the feedback to adjust the stepsize through an online learning algorithm. Consequently, instantiations of OSGM achieve convergence rates that are asymptotically no worse than the optimal stepsize. OSGM yields desirable convergence guarantees on smooth convex problems, including 1) trajectory-dependent global convergence on smooth convex objectives; 2) an improved complexity result on smooth strongly convex problems, and 3) local superlinear convergence. Notably, OSGM constitutes a new family of first-order methods with non-asymptotic superlinear convergence, joining the celebrated quasi-Newton methods. Finally, OSGM explains the empirical success of the popular hypergradient-descent heuristic in optimization for machine learning.

Recent advances in language modeling have underscored the role of preference feedback in enhancing model performance. This paper investigates the conditions under which preference feedback improves parameter estimation in classes of continuous parametric distributions. In our framework, the learner observes pairs of samples from an unknown distribution along with their relative preferences depending on the same unknown parameter. We show that preference-based M-estimators achieve a better asymptotic variance than sample-only M-estimators, further improved by deterministic preferences. Leveraging the hard constraints revealed by deterministic preferences, we propose an estimator achieving an estimation error scaling of $\mathcal{O}(1/n)$ -- a significant improvement over the $Θ(1/\sqrt{n})$ rate attainable with samples alone. Next, we establish a lower bound that matches this accelerated rate; up to dimension and problem-dependent constants. While the assumptions underpinning our analysis are restrictive, they are satisfied by notable cases such as Gaussian or Laplace distributions for preferences based on the log-probability reward.