Sarthak Mittal

Next-Token Prediction Should be Ambiguity-Sensitive: A Meta-Learning Perspective

The rapid adaptation ability of auto-regressive foundation models is often attributed to the diversity of their pre-training data. This is b… (see more)ecause, from a Bayesian standpoint, minimizing prediction error in such settings requires integrating over all plausible latent hypotheses consistent with observations. While this behavior is desirable in principle, it often proves too ambitious in practice: under high ambiguity, the number of plausible latent alternatives makes Bayes-optimal prediction computationally intractable. Cognitive science has long recognized this limitation, suggesting that under such conditions, heuristics or information-seeking strategies are preferable to exhaustive inference. Translating this insight to next-token prediction, we hypothesize that low- and high-ambiguity predictions pose different computational demands, making ambiguity-agnostic next-token prediction a detrimental inductive bias. To test this, we introduce MetaHMM, a synthetic sequence meta-learning benchmark with rich compositional structure and a tractable Bayesian oracle. We show that Transformers indeed struggle with high-ambiguity predictions across model sizes. Motivated by cognitive theories, we propose a method to convert pre-trained models into Monte Carlo predictors that decouple task inference from token prediction. Preliminary results show substantial gains in ambiguous contexts through improved capacity allocation and test-time scalable inference, though challenges remain.

2025-06-19

ArXiv (preprint)

Next-Token Prediction Should be Ambiguity-Sensitive : A Meta-Learing Perspective

2025-06-11

ICML.cc/2025/Workshop/ES-FoMo-III (published)

Does learning the right latent variables necessarily improve in-context learning?

Large autoregressive models like Transformers can solve tasks through in-context learning (ICL) without learning new weights, suggesting ave… (see more)nues 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.

2025-05-01

ICML.cc/2025/Conference (poster)

In-context learning and Occam's razor

Mahan Fathi

A central goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees fo… (see more)r generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best: a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning: an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved. We make our code available at https://github.com/3rdCore/PrequentialCode.

2025-05-01

ICML.cc/2025/Conference (poster)

Laurence Perreault-Levasseur

Solving Bayesian inverse problems with diffusion priors and off-policy RL

Luca Scimeca

Siddarth Venkatraman

Moksh J. Jain

Minsu Kim

Yoshua Bengio

Glen Berseth

Nikolay Malkin

This paper presents a practical application of Relative Trajectory Balance (RTB), a recently introduced off-policy reinforcement learning (R… (see more)L) objective that can asymptotically solve Bayesian inverse problems optimally. We extend the original work by using RTB to train conditional diffusion model posteriors from pretrained unconditional priors for challenging linear and non-linear inverse problems in vision, and science. We use the objective alongside techniques such as off-policy backtracking exploration to improve training. Importantly, our results show that existing training-free diffusion posterior methods struggle to perform effective posterior inference in latent space due to inherent biases.

2025-03-06

ICLR.cc/2025/Workshop/DeLTa (poster)

In-Context Parametric Inference: Point or Distribution Estimators?

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random vari… (see more)ables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods assume fixed but unknown hypotheses, relying on estimators like maximum likelihood. While extensive research has compared these approaches, the frequentist paradigm of obtaining point estimates has become predominant in deep learning, as Bayesian inference is challenging due to the computational complexity and the approximation gap of posterior estimation methods. However, a good understanding of trade-offs between the two approaches is lacking in the regime of amortized estimators, where in-context learners are trained to estimate either point values via maximum likelihood or maximum a posteriori estimation, or full posteriors using normalizing flows, score-based diffusion samplers, or diagonal Gaussian approximations, conditioned on observations. To help resolve this, we conduct a rigorous comparative analysis spanning diverse problem settings, from linear models to shallow neural networks, with a robust evaluation framework assessing both in-distribution and out-of-distribution generalization on tractable tasks. Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems, and we further discuss why this might be the case.

2025-02-17

ArXiv (preprint)

In-Context Parametric Inference: Point or Distribution Estimators?

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random vari… (see more)ables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods assume fixed but unknown hypotheses, relying on estimators like maximum likelihood. While extensive research has compared these approaches, the frequentist paradigm of obtaining point estimates has become predominant in deep learning, as Bayesian inference is challenging due to the computational complexity and the approximation gap of posterior estimation methods. However, a good understanding of trade-offs between the two approaches is lacking in the regime of amortized estimators, where in-context learners are trained to estimate either point values via maximum likelihood or maximum a posteriori estimation, or full posteriors using normalizing flows, score-based diffusion samplers, or diagonal Gaussian approximations, conditioned on observations. To help resolve this, we conduct a rigorous comparative analysis spanning diverse problem settings, from linear models to shallow neural networks, with a robust evaluation framework assessing both in-distribution and out-of-distribution generalization on tractable tasks. Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems, and we further discuss why this might be the case.

2025-02-17

ArXiv (preprint)

Amortized In-Context Bayesian Posterior Estimation

Sarthak Mittal

N. L. Bracher

Guillaume Lajoie

Priyank Jaini

Marcus Brubaker

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Cur… (see more)rent solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

2025-02-10

ArXiv (preprint)

Amortized In-Context Bayesian Posterior Estimation

Sarthak Mittal

N. L. Bracher

Guillaume Lajoie

Priyank Jaini

Marcus Brubaker

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Cur… (see more)rent solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

2025-02-10

ArXiv (preprint)

Amortized In-Context Bayesian Posterior Estimation

Sarthak Mittal

N. L. Bracher

Guillaume Lajoie

Priyank Jaini

Marcus Brubaker

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Cur… (see more)rent solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

2025-02-10

ArXiv (preprint)