We thank the reviewers for their useful comments. The reference for the complexity of joint alignment of N time-series via DTW is [4]. Re Eq. (3): indeed, we define θ As suggested, we will drop the LHS. Eq. (4) is correct: as written there, T The complexity of each gradient component is similar and the components are parallelized over. DTAN has 3 HPs: 1 for Ω, and 2 for the prior.

Despite the success of CNNs, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a "fabric" that embeds an exponentially large number of architectures. The fabric consists of a 3D trellis that connects response maps at different layers, scales, and channels with a sparse homogeneous local connectivity pattern.

We study the problem of private online learning, focusing on online prediction from experts (OPE) and online convex optimization (OCO). We propose a new transformation that translates lazy, low-switching online learning algorithms into private algorithms. We apply our transformation to differentially private OPE and OCO using existing lazy algorithms for these problems.

Multimodal large language models (MLLMs) have shown impressive success across modalities such as image, video, and audio in a variety of understanding and generation tasks. However, current MLLMs are surprisingly poor at understanding webpage screenshots and generating their corresponding HTML code. To address this problem, we propose Web2Code, a benchmark consisting of a new large-scale webpage-to-code dataset for instruction tuning and an evaluation framework for the webpage understanding and HTML code translation abilities of MLLMs. For dataset construction, we leverage pretrained LLMs to enhance existing webpageto-code datasets as well as generate a diverse pool of new webpages rendered into images. Specifically, the inputs are webpage images and instructions, while the responses are the webpage's HTML code. We further include diverse natural language QA pairs about the webpage content in the responses to enable a more comprehensive understanding of the web content. To evaluate model performance in these tasks, we develop an evaluation framework for testing MLLMs' abilities in webpage understanding and web-to-code generation. Extensive experiments show that our proposed dataset is beneficial not only to our proposed tasks but also in the general visual domain. We hope our work will contribute to the development of general MLLMs suitable for web-based content generation and task automation.

Calcium imaging is an important technique for monitoring the activity of thousands of neurons simultaneously. As calcium imaging datasets grow in size, automated detection of individual neurons is becoming important. Here we apply a supervised learning approach to this problem and show that convolutional networks can achieve near-human accuracy and superhuman speed. Accuracy is superior to the popular PCA/ICA method based on precision and recall relative to ground truth annotation by a human expert. These results suggest that convolutional networks are an efficient and flexible tool for the analysis of large-scale calcium imaging data.

The term (1 γ) is like a normalizer.

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given dataset. In doing so, they define a Bayesian model without explicitly positing a prior distribution over latent global parameters; they instead adopt priors over the relational structure of the given dataset, a task that is much simpler. We show how we can learn such models from data, demonstrate that they are scalable to large datasets through mini-batch optimization and describe how we can make predictions for new points via their posterior predictive distribution. We experimentally evaluate FNPs on the tasks of toy regression and image classification and show that, when compared to baselines that employ global latent parameters, they offer both competitive predictions as well as more robust uncertainty estimates.

Combinatorial optimization problems are widespread but inherently challenging due to their discrete nature. The primary limitation of existing methods is that they can only access a small fraction of the solution space at each iteration, resulting in limited efficiency for searching the global optimal. To overcome this challenge, diverging from conventional efforts of expanding the solver's search scope, we focus on enabling information to actively propagate to the solver through heat diffusion.

Diffusion models have demonstrated competitive performance in missing data imputation (MDI) task. However, directly applying diffusion models to MDI produces suboptimal performance due to two primary defects. First, the sample diversity promoted by diffusion models hinders the accurate inference of missing values. Second, data masking reduces observable indices for model training, obstructing imputation performance. To address these challenges, we introduce Negative Entropy-regularized Wasserstein gradient flow for Imputation (NewImp), enhancing diffusion models for MDI from a gradient flow perspective. To handle the first defect, we incorporate a negative entropy regularization term into the cost functional to suppress diversity and improve accuracy. To handle the second defect, we demonstrate that the imputation procedure of NewImp, induced by the conditional distribution-related cost functional, can equivalently be replaced by that induced by the joint distribution, thereby naturally eliminating the need for data masking.

The Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT solvers relies on extensive empirical testing on a set of real-world benchmark formulas. However, the availability of such real-world SAT formulas is limited. While these benchmark formulas can be augmented with synthetically generated ones, existing approaches for doing so are heavily hand-crafted and fail to simultaneously capture a wide range of characteristics exhibited by real-world SAT instances. In this work, we present G2SAT, the first deep generative framework that learns to generate SAT formulas from a given set of input formulas. Our key insight is that SAT formulas can be transformed into latent bipartite graph representations which we model using a specialized deep generative neural network. We show that G2SAT can generate SAT formulas that closely resemble given real-world SAT instances, as measured by both graph metrics and SAT solver behavior. Further, we show that our synthetic SAT formulas could be used to improve SAT solver performance on real-world benchmarks, which opens up new opportunities for the continued development of SAT solvers and a deeper understanding of their performance.