Meta-Learning Adaptable Foundation Models

The power of foundation models (FMs) lies in their capacity to learn highly expressive representations that can be adapted to a broad spectrum of tasks. However, these pretrained models require multiple stages of fine-tuning to become effective for downstream applications. Conventionally, the model is first retrained on the aggregate of a diverse set of tasks of interest and then adapted to specific low-resource downstream tasks by utilizing a parameter-efficient fine-tuning (PEFT) scheme. While this two-phase procedure seems reasonable, the independence of the retraining and fine-tuning phases causes a major issue, as there is no guarantee the retrained model will achieve good performance post-fine-tuning. To explicitly address this issue, we introduce a meta-learning framework infused with PEFT in this intermediate retraining stage to learn a model that can be easily adapted to unseen tasks. For our theoretical results, we focus on linear models using low-rank adaptations. In this setting, we demonstrate the suboptimality of standard retraining for finding an adaptable set of parameters. Further, we prove that our method recovers the optimally adaptable parameters. We then apply these theoretical insights to retraining the RoBERTa model to predict the continuation of conversations between different personas within the ConvAI2 dataset. Empirically, we observe significant performance benefits using our proposed meta-learning scheme during retraining relative to the conventional approach.

Constrained Posterior Sampling: Time Series Generation with Hard Constraints

Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by physics or nature. Consider, for example, generating electricity demand patterns with constraints on peak demand times. This can be used to stress-test the functioning of power grids during adverse weather conditions. Existing approaches for generating constrained time series are either not scalable or degrade sample quality. To address these challenges, we introduce Constrained Posterior Sampling (CPS), a diffusion-based sampling algorithm that aims to project the posterior mean estimate into the constraint set after each denoising update. Notably, CPS scales to a large number of constraints (~100) without requiring additional training. We provide theoretical justifications highlighting the impact of our projection step on sampling. Empirically, CPS outperforms state-of-the-art methods in sample quality and similarity to real time series by around 10% and 42%, respectively, on real-world stocks, traffic, and air quality datasets.

Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

RB-Modulation: Training-Free Personalization of Diffusion Models using Stochastic Optimal Control

We propose Reference-Based Modulation (RB-Modulation), a new plug-and-play solution for training-free personalization of diffusion models. Existing training-free approaches exhibit difficulties in (a) style extraction from reference images in the absence of additional style or content text descriptions, (b) unwanted content leakage from reference style images, and (c) effective composition of style and content. RB-Modulation is built on a novel stochastic optimal controller where a style descriptor encodes the desired attributes through a terminal cost. The resulting drift not only overcomes the difficulties above, but also ensures high fidelity to the reference style and adheres to the given text prompt. We also introduce a cross-attention-based feature aggregation scheme that allows RB-Modulation to decouple content and style from the reference image. With theoretical justification and empirical evidence, our framework demonstrates precise extraction and control of content and style in a training-free manner. Further, our method allows a seamless composition of content and style, which marks a departure from the dependency on external adapters or ControlNets.

In-Context Learning with Transformers: Softmax Attention Adapts to Function Lipschitzness

A striking property of transformers is their ability to perform in-context learning (ICL), a machine learning framework in which the learner is presented with a novel context during inference implicitly through some data, and tasked with making a prediction in that context. As such that learner must adapt to the context without additional training. We explore the role of softmax attention in an ICL setting where each context encodes a regression task. We show that an attention unit learns a window that it uses to implement a nearest-neighbors predictor adapted to the landscape of the pretraining tasks. Specifically, we show that this window widens with decreasing Lipschitzness and increasing label noise in the pretraining tasks. We also show that on low-rank, linear problems, the attention unit learns to project onto the appropriate subspace before inference. Further, we show that this adaptivity relies crucially on the softmax activation and thus cannot be replicated by the linear activation often studied in prior theoretical analyses.

Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models. Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting bias. Existing second-order approximations are impractical due to prohibitive computational costs, making standard reverse diffusion processes intractable for posterior sampling. This paper introduces Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler that offers efficiency comparable to first-order Tweedie with a tractable reverse process using second-order approximation. Our theoretical results reveal that the second-order approximation is lower bounded by our surrogate loss that only requires $O(1)$ compute using the trace of the Hessian, and by the lower bound we derive a new drift term to make the reverse process tractable. Our method surpasses SoTA solvers PSLD and P2L, achieving 4X and 8X reduction in neural function evaluations, respectively, while notably enhancing sampling quality on FFHQ, ImageNet, and COCO benchmarks. In addition, we show STSL extends to text-guided image editing and addresses residual distortions present from corrupted images in leading text-guided image editing methods. To our best knowledge, this is the first work to offer an efficient second-order approximation in solving inverse problems using latent diffusion and editing real-world images with corruptions.

Provable Multi-Task Representation Learning by Two-Layer ReLU Neural Networks

Feature learning, i.e. extracting meaningful representations of data, is quintessential to the practical success of neural networks trained with gradient descent, yet it is notoriously difficult to explain how and why it occurs. Recent theoretical studies have shown that shallow neural networks optimized on a single task with gradient-based methods can learn meaningful features, extending our understanding beyond the neural tangent kernel or random feature regime in which negligible feature learning occurs. But in practice, neural networks are increasingly often trained on {\em many} tasks simultaneously with differing loss functions, and these prior analyses do not generalize to such settings. In the multi-task learning setting, a variety of studies have shown effective feature learning by simple linear models. However, multi-task learning via {\em nonlinear} models, arguably the most common learning paradigm in practice, remains largely mysterious. In this work, we present the first results proving feature learning occurs in a multi-task setting with a nonlinear model. We show that when the tasks are binary classification problems with labels depending on only $r$ directions within the ambient $d\gg r$-dimensional input space, executing a simple gradient-based multitask learning algorithm on a two-layer ReLU neural network learns the ground-truth $r$ directions. In particular, any downstream task on the $r$ ground-truth coordinates can be solved by learning a linear classifier with sample and neuron complexity independent of the ambient dimension $d$, while a random feature model requires exponential complexity in $d$ for such a guarantee.

Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Collaborative Multi-Agent Heterogeneous Multi-Armed Bandits

The study of collaborative multi-agent bandits has attracted significant attention recently. In light of this, we initiate the study of a new collaborative setting, consisting of $N$ agents such that each agent is learning one of $M$ stochastic multi-armed bandits to minimize their group cumulative regret. We develop decentralized algorithms which facilitate collaboration between the agents under two scenarios. We characterize the performance of these algorithms by deriving the per agent cumulative regret and group regret upper bounds. We also prove lower bounds for the group regret in this setting, which demonstrates the near-optimal behavior of the proposed algorithms.

InfoNCE Loss Provably Learns Cluster-Preserving Representations

The goal of contrasting learning is to learn a representation that preserves underlying clusters by keeping samples with similar content, e.g. the ``dogness'' of a dog, close to each other in the space generated by the representation. A common and successful approach for tackling this unsupervised learning problem is minimizing the InfoNCE loss associated with the training samples, where each sample is associated with their augmentations (positive samples such as rotation, crop) and a batch of negative samples (unrelated samples). To the best of our knowledge, it was unanswered if the representation learned by minimizing the InfoNCE loss preserves the underlying data clusters, as it only promotes learning a representation that is faithful to augmentations, i.e., an image and its augmentations have the same representation. Our main result is to show that the representation learned by InfoNCE with a finite number of negative samples is also consistent with respect to clusters in the data, under the condition that the augmentation sets within clusters may be non-overlapping but are close and intertwined, relative to the complexity of the learning function class.