Discrete Flow-based Models (DFMs) are powerful generative models for high-quality discrete data but typically suffer from slow sampling speeds due to their reliance on iterative decoding processes. This reliance on a multi-step process originates from the factorization approximation of DFMs, which is necessary for handling high-dimensional data. In this paper, we analyze the factorization approximation error using Conditional Total Correlation (TC), and reveal its dependence on the coupling. To address the challenge of efficient few-step generation, we propose Rectified Discrete Flow (ReDi), a novel iterative method that reduces the underlying factorization error (measured as Conditional TC) by rectifying the coupling between source and target distributions. We theoretically prove that each ReDi step guarantees a monotonic decreasing Conditional TC, ensuring its convergence. Empirically, ReDi significantly reduces Conditional TC and enables few-step generation. Moreover, we demonstrate that the rectified couplings are well-suited for training efficient one-step models on image generation. ReDi offers a simple and theoretically grounded approach for tackling the few-step challenge, providing a new perspective on efficient discrete data synthesis.

While large language models (LLMs) demonstrate impressive capabilities across numerous applications, their robustness remains a critical concern. This paper is motivated by a specific vulnerability: the order sensitivity of LLMs. This vulnerability manifests itself as the order bias observed when LLMs decide between possible options (for example, a preference for the first option) and the tendency of LLMs to provide different answers when options are reordered. The use cases for this scenario extend beyond the classical case of multiple-choice question answering to the use of LLMs for multidocument tasks and as automated evaluators in AI pipelines. We introduce Set-LLM, a novel architectural adaptation for pretrained LLMs that enables the processing of mixed set-text inputs with permutation invariance guarantees. The adaptations involve a new attention mask and new positional encodings specifically designed for sets. We provide a theoretical proof of invariance and demonstrate through experiments that Set-LLM can be trained effectively, achieving comparable or improved performance and maintaining the runtime of the original model, while altogether eliminating order sensitivity.

Many domain experts do not have the time or expertise to write formal Bayesian models. This paper takes an informal problem description as input, and combines a large language model and a probabilistic programming language to define a joint distribution over formal models, latent variables, and data. A posterior over latent variables follows by conditioning on observed data and integrating over formal models. This presents a challenging inference problem. We suggest an inference recipe that amounts to generating many formal models from the large language model, performing approximate inference on each, and then doing a weighted average. This is justified and analyzed as a combination of self-normalized importance sampling, MCMC, and importance-weighted variational inference. Experimentally, this produces sensible predictions from only data and an informal problem description, without the need to specify a formal model.

Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize the length of the flow integration trajectories. We investigate the benefits of using path gradients to fine-tune CNFs initially trained by Flow Matching, in the setting where a target energy is known. Our experiments show that this hybrid approach yields up to a threefold increase in sampling efficiency for molecular systems, all while using the same model, a similar computational budget and without the need for additional sampling. Furthermore, by measuring the length of the flow trajectories during fine-tuning, we show that path gradients largely preserve the learned structure of the flow.

This position paper argues that the use of generative artificial intelligence (GenAI) to control, direct, guide or govern any weapon, either in situ or remotely, should be prohibited by government agencies and non-governmental organizations. Such a moratorium should exist until hallucinations can be successfully modeled and predicted. Generative AI is inherently unreliable and not appropriate in environments that could result in the loss of life.

Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question: when can learning be implemented as a computer program? We address this question for universal online learning, a generalist theoretical model of online binary classification, recently characterized by Bousquet et al. (STOC 2021). In this model, there is no hypothesis fixed in advance; instead, Adversary--playing the role of Nature--can change their mind as long as local consistency with the given class of hypotheses is maintained. We require Learner to achieve a finite number of mistakes while using a strategy that can be implemented as a computer program. We show that universal online learning does not imply computable universal online learning, even if the class of hypotheses is relatively easy from a computability-theoretic perspective. We then study the agnostic variant of computable universal online learning and provide an exact characterization of classes that are learnable in this sense. We also consider a variant of proper universal online learning and show exactly when it is possible. Together, our results give a more realistic perspective on the existing theory of online binary classification and the related problem of inductive inference.

Efficient online decision-making in contextual bandits is challenging, as methods without informative priors often suffer from computational or statistical inefficiencies. In this work, we leverage pre-trained diffusion models as expressive priors to capture complex action dependencies and develop a practical algorithm that efficiently approximates posteriors under such priors, enabling both fast updates and sampling. Empirical results demonstrate the effectiveness and versatility of our approach across diverse contextual bandit settings.

We consider the problem of diversity maximization from the perspective of individual fairness: given a set $P$ of $n$ points in a metric space, we aim to extract a subset $S$ of size $k$ from $P$ so that (1) the diversity of $S$ is maximized and (2) $S$ is \emph{individually fair} in the sense that every point in $P$ has at least one of its $\frac{n}{k}$-nearest neighbors as its ``representative'' in $S$. We propose $\left(O(1), 3\right)$-bicriteria approximation algorithms for the individually fair variants of the three most common diversity maximization problems, namely, max-min diversification, max-sum diversification, and sum-min diversification. Specifically, the proposed algorithms provide a set of points where every point in the dataset finds a point within a distance at most $3$ times its distance to its $\frac{n}{k}$-nearest neighbor while achieving a diversity value at most $O(1)$ times lower than the optimal solution. Numerical experiments on real-world and synthetic datasets demonstrate that the proposed algorithms generate solutions that are individually fairer than those produced by unconstrained algorithms and incur only modest losses in diversity.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of'flows' -- one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

We provide the first sharp characterization of the optimal first-order query complexity of agnostic active learning, and propose a new general active learning algorithm which achieves it. Remarkably, the optimal query complexity admits a leading term which is $\textit{always}$ strictly smaller than the sample complexity of passive supervised learning (by a factor proportional to the best-in-class error rate). This was not previously known to be possible. For comparison, in all previous general analyses, the leading term exhibits an additional factor, such as the disagreement coefficient or related complexity measures, and therefore only provides improvements over passive learning in restricted cases. The present work completely removes such factors from the leading term, implying that $\textit{every}$ concept class benefits from active learning in the non-realizable case. Whether such benefits are possible has been the driving question underlying the past two decades of research on the theory of agnostic active learning. This work finally settles this fundamental question.