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.

Is implicit deep learning relevant for general pattern recognition tasks?

There are two types of deep generative models: explicit and implicit.

The concept of "implicitness" has recently been applied to various contexts of machine learning research.

We address an important problem in ecology called Species Distribution Modeling (SDM), whose goal is to predict whether a species exists at a certain position on Earth. In particular, we tackle a challenging version of this task, where we learn from presence-only data in a community-sourced dataset, model a large number of species simultaneously, and do not use any additional environmental information. Previous work has used neural implicit representations to construct models that achieve promising results. However, implicit representations often generate predictions of limited spatial precision. We attribute this limitation to their inherently global formulation and inability to effectively capture local feature variations. This issue is especially pronounced with presence-only data and a large number of species. To address this, we propose a hybrid embedding scheme that combines both implicit and explicit embeddings. Specifically, the explicit embedding is implemented with a multiresolution hashgrid, enabling our models to better capture local information. Experiments demonstrate that our results exceed other works by a large margin on various standard benchmarks, and that the hybrid representation is better than both purely implicit and explicit ones. Qualitative visualizations and comprehensive ablation studies reveal that our hybrid representation successfully addresses the two main challenges. Our code is open-sourced at https://github.com/Shiran-Yuan/HSR-SDM.

Large autoregressive models like Transformers can solve tasks through in-context learning (ICL) without learning new weights, suggesting avenues for efficiently solving new tasks. For many tasks, e.g., linear regression, the data factorizes: examples are independent given a task latent that generates the data, e.g., linear coefficients. While an optimal predictor leverages this factorization by inferring task latents, it is unclear if Transformers implicitly do so or if they instead exploit heuristics and statistical shortcuts enabled by attention layers. Both scenarios have inspired active ongoing work. In this paper, we systematically investigate the effect of explicitly inferring task latents. We minimally modify the Transformer architecture with a bottleneck designed to prevent shortcuts in favor of more structured solutions, and then compare performance against standard Transformers across various ICL tasks. Contrary to intuition and some recent works, we find little discernible difference between the two; biasing towards task-relevant latent variables does not lead to better out-of-distribution performance, in general. Curiously, we find that while the bottleneck effectively learns to extract latent task variables from context, downstream processing struggles to utilize them for robust prediction. Our study highlights the intrinsic limitations of Transformers in achieving structured ICL solutions that generalize, and shows that while inferring the right latents aids interpretability, it is not sufficient to alleviate this problem.

Decentralized partially observable Markov decision processes (Dec-POMDPs) formalize the problem of designing individual controllers for a group of collaborative agents under stochastic dynamics and partial observability. Seeking a global optimum is difficult (NEXP complete), but seeking a Nash equilibrium -- each agent policy being a best response to the other agents -- is more accessible, and allowed addressing infinite-horizon problems with solutions in the form of finite state controllers. In this paper, we show that this approach can be adapted to cases where only a generative model (a simulator) of the Dec-POMDP is available. This requires relying on a simulation-based POMDP solver to construct an agent's FSC node by node. A related process is used to heuristically derive initial FSCs. Experiment with benchmarks shows that MC-JESP is competitive with exisiting Dec-POMDP solvers, even better than many offline methods using explicit models.

With noisy intermediate-scale quantum computers showing great promise for near-term applications, a number of machine learning algorithms based on parametrized quantum circuits have been suggested as possible means to achieve learning advantages. Yet, our understanding of how these quantum machine learning models compare, both to existing classical models and to each other, remains limited. A big step in this direction has been made by relating them to so-called kernel methods from classical machine learning. By building on this connection, previous works have shown that a systematic reformulation of many quantum machine learning models as kernel models was guaranteed to improve their training performance. In this work, we first extend the applicability of this result to a more general family of parametrized quantum circuit models called data re-uploading circuits. Secondly, we show, through simple constructions and numerical simulations, that models defined and trained variationally can exhibit a critically better generalization performance than their kernel formulations, which is the true figure of merit of machine learning tasks. Our results constitute another step towards a more comprehensive theory of quantum machine learning models next to kernel formulations.