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Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.

Co-evolutionary algorithms have a wide range of applications, such as in hardware design, evolution of strategies for board games, and patching software bugs. However, these algorithms are poorly understood and applications are often limited by pathological behaviour, such as loss of gradient, relative over-generalisation, and mediocre objective stasis. It is an open challenge to develop a theory that can predict when co-evolutionary algorithms find solutions efficiently and reliable. This paper provides a first step in developing runtime analysis for population-based competitive co-evolutionary algorithms. We provide a mathematical framework for describing and reasoning about the performance of co-evolutionary processes. An example application of the framework shows a scenario where a simple co-evolutionary algorithm obtains a solution in polynomial expected time. Finally, we describe settings where the co-evolutionary algorithm needs exponential time with overwhelmingly high probability to obtain a solution.

The logic of information flows (LIF) has recently been proposed as a general framework in the field of knowledge representation. In this framework, tasks of procedural nature can still be modeled in a declarative, logic-based fashion. In this paper, we focus on the task of query processing under limited access patterns, a well-studied problem in the database literature. We show that LIF is well-suited for modeling this task. Toward this goal, we introduce a variant of LIF called "forward" LIF (FLIF), in a first-order setting. FLIF takes a novel graph-navigational approach; it is an XPath-like language that nevertheless turns out to be equivalent to the "executable" fragment of first-order logic defined by Nash and Lud\"ascher. One can also classify the variables in FLIF expressions as inputs and outputs. Expressions where inputs and outputs are disjoint, referred to as io-disjoint FLIF expressions, allow a particularly transparent translation into algebraic query plans that respect the access limitations. Finally, we show that general FLIF expressions can always be put into io-disjoint form.

Reconstructing and simulating elastic objects from visual observations is crucial for applications in computer vision and robotics. Existing methods, such as 3D Gaussians, provide modeling for 3D appearance and geometry but lack the ability to simulate physical properties or optimize parameters for heterogeneous objects. We propose Spring-Gaus, a novel framework that integrates 3D Gaussians with physics-based simulation for reconstructing and simulating elastic objects from multi-view videos. Our method utilizes a 3D Spring-Mass model, enabling the optimization of physical parameters at the individual point level while decoupling the learning of physics and appearance. This approach achieves great sample efficiency, enhances generalization, and reduces sensitivity to the distribution of simulation particles. We evaluate Spring-Gaus on both synthetic and real-world datasets, demonstrating accurate reconstruction and simulation of elastic objects. This includes future prediction and simulation under varying initial states and environmental parameters. Project page: //zlicheng.com/spring_gaus.

We build on recent research on polynomial randomized approximation (PRAX) algorithms for the hard problems of NFA universality and NFA equivalence. Loosely speaking, PRAX algorithms use sampling of infinite domains within any desired accuracy $\delta$. In the spirit of experimental mathematics, we extend the concept of PRAX algorithms to be applicable to the emptiness and universality problems in any domain whose instances admit a tractable distribution as defined in this paper. A technical result here is that a linear (w.r.t. $1/\delta$) number of samples is sufficient, as opposed to the quadratic number of samples in previous papers. We show how the improved and generalized PRAX algorithms apply to universality and emptiness problems in various domains: ordinary automata, tautology testing of propositions, 2D automata, and to solution sets of certain Diophantine equations.

Machine-learning algorithms can facilitate low-cost, user-guided visual diagnostic platforms for addressing disparities in access to sexual health services. We developed a clinical image dataset using original and augmented images for five penile diseases: herpes eruption, syphilitic chancres, penile candidiasis, penile cancer, and genital warts. We used a U-net architecture model for semantic pixel segmentation into background or subject image, the Inception-ResNet version 2 neural architecture to classify each pixel as diseased or non-diseased, and a salience map using GradCAM++. We trained the model on a random 91% sample of the image database using 150 epochs per image, and evaluated the model on the remaining 9% of images, assessing recall (or sensitivity), precision, specificity, and F1-score (accuracy). Of the 239 images in the validation dataset, 45 (18.8%) were of genital warts, 43 (18.0%) were of HSV infection, 29 (12.1%) were of penile cancer, 40 (16.7%) were of penile candidiasis, 37 (15.5%) were of syphilitic chancres, and 45 (18.8%) were of non-diseased penises. The overall accuracy of the model for correctly classifying the diseased image was 0.944. Between July 1st and October 1st 2023, there were 2,640 unique users of the mobile platform. Among a random sample of submissions (n=437), 271 (62.0%) were from the United States, 64 (14.6%) from Singapore, 41 (9.4%) from Candia, 40 (9.2%) from the United Kingdom, and 21 (4.8%) from Vietnam. The majority (n=277 [63.4%]) were between 18 and 30 years old. We report on the development of a machine-learning model for classifying five penile diseases, which demonstrated excellent performance on a validation dataset. That model is currently in use globally and has the potential to improve access to diagnostic services for penile diseases.

We introduce discretizations of infinite-dimensional optimization problems with total variation regularization and integrality constraints on the optimization variables. We advance the discretization of the dual formulation of the total variation term with Raviart--Thomas functions which is known from literature for certain convex problems. Since we have an integrality constraint, the previous analysis from Caillaud and Chambolle [10] does not hold anymore. Even weaker $\Gamma$-convergence results do not hold anymore because the recovery sequences generally need to attain non-integer values to recover the total variation of the limit function. We solve this issue by introducing a discretization of the input functions on an embedded, finer mesh. A superlinear coupling of the mesh sizes implies an averaging on the coarser mesh of the Raviart--Thomas ansatz, which enables to recover the total variation of integer-valued limit functions with integer-valued discretized input functions. Moreover, we are able to estimate the discretized total variation of the recovery sequence by the total variation of its limit and an error depending on the mesh size ratio. For the discretized optimization problems, we additionally add a constraint that vanishes in the limit and enforces compactness of the sequence of minimizers, which yields their convergence to a minimizer of the original problem. This constraint contains a degree of freedom whose admissible range is determined. Its choice may have a strong impact on the solutions in practice as we demonstrate with an example from imaging.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.