In-context learning and Occam's razor

The goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for 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.

Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction

Generative modeling of discrete data underlies important applications spanning text-based agents like ChatGPT to the design of the very building blocks of life in protein sequences. However, application domains need to exert control over the generated data by steering the generative process - typically via RLHF - to satisfy a specified property, reward, or affinity metric. In this paper, we study the problem of steering Masked Diffusion Models (MDMs), a recent class of discrete diffusion models that offer a compelling alternative to traditional autoregressive models. We introduce Discrete Denoising Posterior Prediction (DDPP), a novel framework that casts the task of steering pre-trained MDMs as a problem of probabilistic inference by learning to sample from a target Bayesian posterior. Our DDPP framework leads to a family of three novel objectives that are all simulation-free, and thus scalable while applying to general non-differentiable reward functions. Empirically, we instantiate DDPP by steering MDMs to perform class-conditional pixel-level image modeling, RLHF-based alignment of MDMs using text-based rewards, and finetuning protein language models to generate more diverse secondary structures and shorter proteins. We substantiate our designs via wet-lab validation, where we observe transient expression of reward-optimized protein sequences.

Recurrent Interpolants for Probabilistic Time Series Prediction

Sequential models such as recurrent neural networks or transformer-based models became \textit{de facto} tools for multivariate time series forecasting in a probabilistic fashion, with applications to a wide range of datasets, such as finance, biology, medicine, etc. Despite their adeptness in capturing dependencies, assessing prediction uncertainty, and efficiency in training, challenges emerge in modeling high-dimensional complex distributions and cross-feature dependencies. To tackle these issues, recent works delve into generative modeling by employing diffusion or flow-based models. Notably, the integration of stochastic differential equations or probability flow successfully extends these methods to probabilistic time series imputation and forecasting. However, scalability issues necessitate a computational-friendly framework for large-scale generative model-based predictions. This work proposes a novel approach by blending the computational efficiency of recurrent neural networks with the high-quality probabilistic modeling of the diffusion model, which addresses challenges and advances generative models' application in time series forecasting. Our method relies on the foundation of stochastic interpolants and the extension to a broader conditional generation framework with additional control features, offering insights for future developments in this dynamic field.

Amortizing intractable inference in diffusion models for vision, language, and control

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning.

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 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.

On diffusion models for amortized inference: Benchmarking and improving stochastic control and sampling

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.

Leveraging Synthetic Targets for Machine Translation

In this work, we provide a recipe for training machine translation models in a limited resource setting by leveraging synthetic target data generated using a large pre-trained model. We show that consistently across different benchmarks in bilingual, multilingual, and speech translation setups, training models on synthetic targets outperforms training on the actual ground-truth data. This performance gap grows bigger with increasing limits on the amount of available resources in the form of the size of the dataset and the number of parameters in the model. We also provide preliminary analysis into whether this boost in performance is linked to ease of optimization or more deterministic nature of the predictions, and whether this paradigm leads to better out-of-distribution performance across different testing domains.

MixupE: Understanding and Improving Mixup from Directional Derivative Perspective

Mixup is a popular data augmentation technique for training deep neural networks where additional samples are generated by linearly interpolating pairs of inputs and their labels. This technique is known to improve the generalization performance in many learning paradigms and applications. In this work, we first analyze Mixup and show that it implicitly regularizes infinitely many directional derivatives of all orders. We then propose a new method to improve Mixup based on the novel insight. To demonstrate the effectiveness of the proposed method, we conduct experiments across various domains such as images, tabular data, speech, and graphs. Our results show that the proposed method improves Mixup across various datasets using a variety of architectures, for instance, exhibiting an improvement over Mixup by 0.8% in ImageNet top-1 accuracy.

From Points to Functions: Infinite-dimensional Representations in Diffusion Models

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples from the target distribution in a single step. Thus, in diffusion models every sample is naturally connected to a random trajectory which is a solution to a learned stochastic differential equation (SDE). Generative models are only concerned with the final state of this trajectory that delivers samples from the desired distribution. Abstreiter et. al showed that these stochastic trajectories can be seen as continuous filters that wash out information along the way. Consequently, it is reasonable to ask if there is an intermediate time step at which the preserved information is optimal for a given downstream task. In this work, we show that a combination of information content from different time steps gives a strictly better representation for the downstream task. We introduce an attention and recurrence based modules that ``learn to mix'' information content of various time-steps such that the resultant representation leads to superior performance in downstream tasks.