Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach hasnot yet led to comparable fidelity. There are several key obstacles: (i) the datalikelihood term is usually intractable; (ii) learned generative models cannot be directly conditioned on the distorted observations, leading to conflicting objectives between data likelihood and prior; and (iii) the reconstructions can deviate from theobserved data.

Top-kdecoding is a widely used method for sampling from LLMs: at each token, only the largest k next-token-probabilities are kept, and the next token is sampled after renormalizing them to sum to unity. Top-kand other sampling methods are motivated by the intuition that true next-token distributions are sparse, and the noisy LLM probabilities need to be truncated. However, to our knowledge, a precise theoretical motivation for the use of top-k decoding is missing. In this work, we develop a theoretical framework that both explains and generalizes top-k decoding. We view decoding at a fixed token as the recovery of a sparse probability distribution. We introduce Bregman decoders obtained by minimizing a separable Bregman divergence (for both the primal and dual cases) with a sparsity-inducing ℓ0-regularization; in particular, these decoders are adaptive in the sense that the sparsity parameter k is chosen depending on the underlying token distribution. Despite the combinatorial nature of the sparse Bregman objective, we show how to optimize it efficiently for a large class of divergences. We prove that (i) the optimal decoding strategies are greedy, and further that (ii) the objective is discretely convex in k, such that the optimal k can be identified in logarithmic time. We note that standard top-k decoding arises as a special case for the KL divergence, and construct new decoding strategies with substantially different behaviors (e.g., non-linearly up-weighting larger probabilities after renormalization).

Estimating the Kullback-Leibler (KL) divergence between language models has many applications, e.g., reinforcement learning from human feedback (RLHF), interpretability, and knowledge distillation. However, computing the exact KL divergence between two arbitrary language models is intractable. Thus, practitioners often resort to sampling-based estimators. While it is easy to fashion a simple Monte Carlo (MC) estimator that provides an unbiased estimate of the KL divergence between language models, this estimator notoriously suffers from high variance and can even result in a negative estimate of the KL divergence, a non-negative quantity. In this paper, we introduce a Rao-Blackwellized estimator that is unbiased and provably has variance less than or equal to that of the standard Monte Carlo estimator. In an empirical study on sentiment-controlled fine-tuning, we show that our estimator provides more stable KL estimates and reduces variance substantially. Additionally, we derive an analogous Rao-Blackwellized estimator of the gradient of the KL divergence, which leads to more stable training and produces models that more frequently appear on the Pareto frontier of reward vs. KL compared to the ones trained with the MC estimator of the gradient.

In this work, we first empirically demonstrate the instability and suboptimal performance of existing popular MU methods when deployed in different scenarios. To address this issue, we propose Dual Optimizer (DualOptim), which incorporates adaptive learning rate and decoupled momentum factors. Empirical and theoretical evidence demonstrates that DualOptim contributes to effective and stable unlearning. Through extensive experiments, we show that DualOptim can significantly boost MU efficacy and stability across diverse tasks, including image classification, image generation, and large language models, making it a versatile approach to empower existing MU algorithms.

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit neural emulator that enhances long-term prediction accuracy by conditioning on a hierarchy of lower-dimensional future state representations. Inspired by the stability properties of numerical implicit time-stepping methods, we developed an approach that leverages predictions several steps ahead in time at increasing compression rates for next-timestep refinements. By actively adjusting the temporal downsampling ratios, our design enables the model to capture dynamics across multiple granularities and enforce long-range temporal coherence. Experiments on turbulent fluid dynamics show that our method achieves high short-term accuracy and produces long-term stable forecasts, significantly outperforming non-hierarchical autoregressive baselines while adding minimal computational overhead. The codebase is available at this link1.

Multimodal deep learning systems are deployed in dynamic scenarios due to the robustness afforded by multiple sensing modalities. Nevertheless, they struggle with varying compute resource availability (due to multi-tenancy, device heterogeneity, etc.) and fluctuating quality of inputs (from sensor feed corruption, environmental noise, etc.). Statically provisioned multimodal systems cannot adapt when compute resources change over time, while existing dynamic networks struggle with strict compute budgets.

Pre-trained models based on deep neural networks hold strong potential for crossdomain adaptability. However, this potential is often impeded in online machine learning (OML) settings, where the breakdown of the independent and identically distributed (i.i.d.) assumption leads to unstable adaptation. While recent advances in test-time adaptation (TTA) have addressed aspects of this challenge under unsupervised learning, most existing methods focus exclusively on unsupervised objectives and overlook the risks posed by non-i.i.d.

Understanding the internal mechanisms of large language models (LLMs) remains a challenging and complex endeavor. Even fundamental questions, such as how fine-tuning affects model behavior, often require extensive empirical evaluation. In this paper, we introduce a novel perspective based on the geometric properties of contextual latent embeddings to study the effects of training and fine-tuning. To that end, we measure the local dimensions of a contextual language model's latent space and analyze their shifts during training and fine-tuning. We show that the local dimensions provide insights into the model's training dynamics and generalization ability. Specifically, the mean of the local dimensions predicts when the model's training capabilities are exhausted, as exemplified in a dialogue state tracking task, overfitting, as demonstrated in an emotion recognition task, and grokking, as illustrated with an arithmetic task. Furthermore, our experiments suggest a practical heuristic: reductions in the mean local dimension tend to accompany and predict subsequent performance gains. Through this exploration, we aim to provide practitioners with a deeper understanding of the implications of fine-tuning on embedding spaces, facilitating informed decisions when configuring models for specific applications. The results of this work contribute to the ongoing discourse on the interpretability, adaptability, and generalizability of LLMs by bridging the gap between intrinsic model mechanisms and geometric properties in embeddings.

The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we design a new form of random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

We study the problem of selecting limited features to observe such that models trained on them can perform well simultaneously across multiple subpopulations. This problem has applications in settings where collecting each feature is costly, e.g.