Multi-task regression aims at jointly solving multiple regression problems, called tasks. Compared to solving each task separately, better performances can be achieved as long as the tasks are sufficiently related. Full-conformal prediction is a framework that formulates a data-dependent prediction-region containing the unknown output-vector at any prescribed confidence level. However, explicit computation of this prediction-region is intractable in general since it requires training infinitely many predictors. The present work focuses on multi-task regression in a Reproducing Kernel Hilbert Space (RKHS) of vector-valued functions. This computational issue is addressed by designing an approximating predictionregion containing the full-conformal one. This construction is carried out in two scenarios: piq when the inter-task covariance-matrix is known, and piiq when this matrix is estimated. In terms of volume, the tightness of this approximation is assessed theoretically by means of an upper-bound in the first scenario. It is also empirically proved to improve upon the split-conformal prediction on synthetic data in both scenarios.

What Happened to Your Face? How the human countenance became something to study, edit, optimize, and scan. The physiognomists promised that your character could be read from your features. Certain forms of facial-recognition technology have revived that old fantasy in digital form. Several months ago, my partner and I bought an apartment in South London. Our previous home was a rental in which, for reasons best known to the landlord, there were mirrors everywhere. The bathroom had two; there was one outside on the terrace; in the bedroom, mirrored panels stretched across a twenty-foot-long wall. On moving day, we realized that we had a problem: the new apartment was mirror-free, and because we'd been so spoiled we weren't bringing one of our own. We spent a few days filling our drafty rooms, decanting books, building furniture, and dressing every morning without seeing ourselves in profile. It was a couple of weeks before we bought a simple mirror, wooden and round, to hang above the bathroom sink. By then, I joked, we didn't recognize ourselves.

Multi-agent systems (MAS) are central to applications such as swarm robotics and traffic routing, where agents must coordinate in a decentralized manner to achieve a common objective. Stochastic Shortest Path (SSP) problems provide a natural framework for modeling decentralized control in such settings. While the problem of learning in SSP has been extensively studied in single-agent settings, the decentralized multi-agent variant remains largely unexplored. In this work, we take a step towards addressing that gap. We study decentralized multi-agent SSPs (Dec-MASSPs) under linear function approximation, where the transition dynamics and costs are represented using linear models. Applying novel symmetry-based arguments, we identify the structure of optimal policies. Our main contribution is the first regret lower bound for this setting based on the construction of hard-tolearn instances for any number of agents, n. Our regret lower bound of Ω( K), over K episodes, highlights the inherent learning difficulty in Dec-MASSPs. These insights clarify the learning complexity of decentralized control and can further guide the design of efficient learning algorithms in multi-agent systems.

We introduce LoRAShop, the first framework for multi-concept image editing with LoRA models. LoRAShop builds on a key observation about the feature interaction patterns inside Flux-style diffusion transformers: concept-specific transformer features activate spatially coherent regions early in the denoising process. We harness this observation to derive a disentangled latent mask for each concept in a prior forward pass and blend the corresponding LoRA weights only within regions bounding the concepts to be personalized.

Diffusion LLMs have emerged as a promising alternative to conventional autoregressive LLMs, offering substantial potential for improving runtime efficiency. However, existing diffusion models fail to provably enforce user-specified formal constraints, such as regular expressions, which makes them unreliable for tasks that require structured outputs, such as fixed-schema JSON generation. Unlike autoregressive models, which generate tokens sequentially, diffusion LLMs predict a block of tokens in parallel. This parallelism makes traditional constrained decoding algorithms, designed to enforce constraints with sequential token prediction, ineffective at preserving the true output distribution. To address this limitation, we propose DINGO, a dynamic programming-based constrained decoding strategy that is both efficient and provably distribution-preserving. DINGO enables sampling of output strings with the highest probability under the model's predicted distribution while strictly adhering to any user-specified regular expression. On standard symbolic math and JSON generation benchmarks, DINGO achieves up to a 68%points of improvement over unconstrained inference. The code is available at DINGO.

What property of the data distribution determines the excess risk of principal component analysis? In this paper, we provide a precise answer to this question. We establish a central limit theorem for the error of the principal subspace estimated by PCA, and derive the asymptotic distribution of its excess risk under the reconstruction loss. We obtain a non-asymptotic upper bound on the excess risk of PCA that recovers, in the large sample limit, our asymptotic characterization. Underlying our contributions is the following result: we prove that the negative block Rayleigh quotient, defined on the Grassmannian, is generalized self-concordant along geodesics emanating from its minimizer of maximum rotation less than π/4.

Time normalization is the task of converting natural language temporal expressions into machine-readable representations.

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We propose VASA-3D, an audio-driven, single-shot 3D head avatar generator. This research tackles two major challenges: capturing the subtle expression details present in real human faces, and reconstructing an intricate 3D head avatar from a single portrait image. To accurately model expression details, VASA-3D leverages the motion latent of VASA-1 [1], a method that yields exceptional realism and vividness in 2D talking heads. A critical element of our work is translating this motion latent to 3D, which is accomplished by devising a 3D head model that is conditioned on the motion latent. Customization of this model to a single image is achieved through an optimization framework that employs numerous video frames of the reference head synthesized from the input image. The optimization takes various training losses robust to artifacts and limited pose coverage in the generated training data. Our experiment shows that VASA-3D produces realistic 3D talking heads that cannot be achieved by prior art, and it supports the online generation of 512 512 free-viewpoint videos at up to 75 FPS, facilitating more immersive engagements with lifelike 3D avatars.

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