We therefore explore training amortized models with noisy labels, and we find that this is inexpensive and surprisingly effective.

\noindent Hyper-parameter selection is a central practical problem in modern machine learning, governing regularization strength, model capacity, and robustness choices. Cross-validation is often computationally prohibitive at scale, while fully Bayesian hyper-parameter learning can be difficult due to the cost of posterior sampling. We develop a generative perspective on hyper-parameter tuning that combines two ideas: (i) optimization-based approximations to Bayesian posteriors via randomized, weighted objectives (weighted Bayesian bootstrap), and (ii) amortization of repeated optimization across many hyper-parameter settings by learning a transport map from hyper-parameters (including random weights) to the corresponding optimizer. This yields a ``generator look-up table'' for estimators, enabling rapid evaluation over grids or continuous ranges of hyper-parameters and supporting both predictive tuning objectives and approximate Bayesian uncertainty quantification. We connect this viewpoint to weighted $M$-estimation, envelope/auxiliary-variable representations that reduce non-quadratic losses to weighted least squares, and recent generative samplers for weighted $M$-estimators.

We study how the word usage of U.S. Congressional speeches varies across states and party affiliation, how words are used differently across sections of the ArXiv, and how the co-purchase patterns of groceries can vary across seasons.

Contrastive Language-Image Pretraining (CLIP) has demonstrated strong zero-shot performance across diverse downstream text-image tasks. Existing CLIP methods typically optimize a contrastive objective using negative samples drawn from each minibatch. To achieve robust representation learning, these methods require extremely large batch sizes and escalate computational demands to hundreds or even thousands of GPUs. Prior approaches to mitigate this issue often compromise downstream performance, prolong training duration, or face scalability challenges with very large datasets. To overcome these limitations, we propose AmorLIP, an efficient CLIP pretraining framework that amortizes expensive computations involved in contrastive learning through lightweight neural networks, which substantially improves training efficiency and performance. Leveraging insights from a spectral factorization of energy-based models, we introduce novel amortization objectives along with practical techniques to improve training stability. Extensive experiments across 38 downstream tasks demonstrate the superior zero-shot classification and retrieval capabilities of AmorLIP, consistently outperforming standard CLIP baselines with substantial relative improvements of up to 12.24%.

Modern learning systems increasingly rely on amortized learning - the idea of reusing computation or inductive biases shared across tasks to enable rapid generalization to novel problems. This principle spans a range of approaches, including meta-learning, in-context learning, prompt tuning, learned optimizers and more. While motivated by similar goals, these approaches differ in how they encode and leverage task-specific information, often provided as in-context examples. In this work, we propose a unified framework which describes how such methods differ primarily in the aspects of learning they amortize - such as initializations, learned updates, or predictive mappings - and how they incorporate task data at inference. We introduce a taxonomy that categorizes amortized models into parametric, implicit, and explicit regimes, based on whether task adaptation is externalized, internalized, or jointly modeled. Building on this view, we identify a key limitation in current approaches: most methods struggle to scale to large datasets because their capacity to process task data at inference (e.g., context length) is often limited. To address this, we propose iterative amortized inference, a class of models that refine solutions step-by-step over mini-batches, drawing inspiration from stochastic optimization. Our formulation bridges optimization-based meta-learning with forward-pass amortization in models like LLMs, offering a scalable and extensible foundation for general-purpose task adaptation.

We therefore explore training amortized models with noisy labels, and we find that this is inexpensive and surprisingly effective.