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We introduce a constrained optimization framework for training transformers that behave like optimization descent algorithms. Specifically, we enforce layerwise descent constraints on the objective function and replace standard empirical…

Diffusion models have recently gained prominence in offline reinforcement learning due to their ability to effectively learn high-performing, generalizable policies from static datasets. Diffusion-based planners facilitate long-horizon…

Controlling the behavior of language models (LMs) without re-training is a major open problem in natural language generation. While recent works have demonstrated successes on controlling simple sentence attributes (e.g., sentiment), there…

Recent work has framed constrained text generation with autoregressive language models as a probabilistic inference problem. Among these, Zhao et al. (2024) introduced a promising approach based on twisted Sequential Monte Carlo, which…

Many realistic decision-making problems in networked scenarios, such as formation control and collaborative task offloading, often involve complicatedly entangled local decisions, which, however, have not been sufficiently investigated yet.…

Diffusion-based language models (dLLMs) have emerged as a promising alternative to autoregressive language models, offering the potential for parallel token generation and bidirectional context modeling. However, harnessing this flexibility…

In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…

Variational autoencoders have been widely applied for natural language generation, however, there are two long-standing problems: information under-representation and posterior collapse. The former arises from the fact that only the last…

We are considering in this paper the task of label-efficient fine-tuning of segmentation models: We assume that a large labeled dataset is available and allows to train an accurate segmentation model in one domain, and that we have to adapt…

Derivative based optimization methods are efficient at solving optimal control problems near local optima. However, their ability to converge halts when derivative information vanishes. The inference approach to optimal control does not…

Diffusion denoising models have become a popular approach for image generation, but they often suffer from slow convergence during training. In this paper, we identify that this slow convergence is partly due to the complexity of the…

In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…

Recent advances in diffusion generative models have yielded remarkable progress. While the quality of generated content continues to improve, these models have grown considerably in size and complexity. This increasing computational burden…

Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such…

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a…

We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…

We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…

Recent endeavors in Multimodal Large Language Models (MLLMs) aim to unify visual comprehension and generation by combining LLM and diffusion models, the state-of-the-art in each task, respectively. Existing approaches rely on spatial visual…

Adapting large-scale foundation flow and diffusion generative models to optimize task-specific objectives while preserving prior information is crucial for real-world applications such as molecular design, protein docking, and creative…

We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…