Many computational tasks benefit from being formulated as the composition of neural networks followed by a discrete symbolic program. The goal of neurosymbolic learning is to train the neural networks using only end-to-end input-output labels of the composite. We introduce CTSketch, a novel, scalable neurosymbolic learning algorithm. CTSketch uses two techniques to improve the scalability of neurosymbolic inference: decompose the symbolic program into sub-programs and summarize each sub-program with a sketched tensor. This strategy allows us to approximate the output distribution of the program with simple tensor operations over the input distributions and summaries. We provide theoretical insight into the maximum error of the approximation. Furthermore, we evaluate CTSketch on many benchmarks from the neurosymbolic literature, including some designed for evaluating scalability. Our results show that CTSketch pushes neurosymbolic learning to new scales that have previously been unattainable by obtaining high accuracy on tasks involving over one thousand inputs.

--Ensemble learning plays a crucial role in practical applications of online learning due to its enhanced classification performance and adaptable adjustment mechanisms. However, most weight allocation strategies in ensemble learning are heuristic, making it challenging to theoretically guarantee that the ensemble classifier outperforms its base classifiers. T o address this issue, a performance-bounded online ensemble learning method based on multi-armed bandits, named PB-OEL, is proposed in this paper . Specifically, multi-armed bandit with expert advice is incorporated into online ensemble learning, aiming to update the weights of base classifiers and make predictions. A theoretical framework is established to bound the performance of the ensemble classifier relative to base classifiers. By setting expert advice of bandits, the bound exceeds the performance of any base classifier when the length of data stream is sufficiently large. Additionally, performance bounds for scenarios with limited annotations are also derived. Numerous experiments on benchmark datasets and a dataset of real-time safety assessment tasks are conducted. The experimental results validate the theoretical bound to a certain extent and demonstrate that the proposed method outperforms existing state-of-the-art methods. Index T erms --Online ensemble learning, performance bound, multi-armed bandits, concept drift, real-time safety assessment. NLINE learning (OL) holds significant potential for handling continuous data and is widely applied across various domains, including industry, recommendation systems, finance, and control systems [1]-[5]. The objective of OL is to continuously learn and update models from new data, enabling adaptation to non-stationary environments for optimized predictions or decisions. One mainstream idea in OL relies on maintaining a set of vectors for decision, as exemplified by the perceptron algorithm [6], passive-aggressive algorithm [7], confidence weighted-based algorithm [8] and imbalanced class weighted-based algorithm [9].

A vast amount of instruction tuning data is crucial for the impressive performance of Large Multimodal Models (LMMs), but the associated computational costs and data collection demands during supervised fine-tuning make it impractical for most researchers. Federated learning (FL) has the potential to leverage all distributed data and training resources to reduce the overhead of joint training. However, most existing methods assume a fixed number of tasks, while in real-world scenarios, clients continuously encounter new knowledge and often struggle to retain old tasks due to memory constraints. In this work, we introduce the Federated Continual Instruction Tuning (FCIT) benchmark to model this real-world challenge. Our benchmark includes two realistic scenarios, encompassing four different settings and twelve carefully curated instruction tuning datasets. To address the challenges posed by FCIT, we propose dynamic knowledge organization to effectively integrate updates from different tasks during training and subspace selective activation to allocate task-specific output during inference. Extensive experimental results demonstrate that our proposed method significantly enhances model performance across varying levels of data heterogeneity and catastrophic forgetting. Our source code and dataset will be made publicly available.

This paper describes Meta's ACH system for mutation-guided LLM-based test generation. ACH generates relatively few mutants (aka simulated faults), compared to traditional mutation testing. Instead, it focuses on generating currently undetected faults that are specific to an issue of concern. From these currently uncaught faults, ACH generates tests that can catch them, thereby `killing' the mutants and consequently hardening the platform against regressions. We use privacy concerns to illustrate our approach, but ACH can harden code against {\em any} type of regression. In total, ACH was applied to 10,795 Android Kotlin classes in 7 software platforms deployed by Meta, from which it generated 9,095 mutants and 571 privacy-hardening test cases. ACH also deploys an LLM-based equivalent mutant detection agent that achieves a precision of 0.79 and a recall of 0.47 (rising to 0.95 and 0.96 with simple pre-processing). ACH was used by Messenger and WhatsApp test-a-thons where engineers accepted 73% of its tests, judging 36% to privacy relevant. We conclude that ACH hardens code against specific concerns and that, even when its tests do not directly tackle the specific concern, engineers find them useful for their other benefits.

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging benchmark aimed at evaluating the general cognitive reasoning abilities of MLLMs. PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across 10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning. We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies, including Chain-of-Thought and Step-Back. The best scores achieved on PolyMATH are ~41%, ~36%, and ~27%, obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively - highlighting the logical and visual complexity of these questions. A further fine-grained error analysis reveals that these models struggle to understand spatial relations and perform drawn-out, high-level reasoning. This is further strengthened by our ablation study estimating MLLM performance when given textual descriptions in place of diagrams. As evidenced by ~4% improvement over textual descriptions as opposed to actual images, we discover that models do not truly comprehend visual diagrams and the spatial information therein, and are thus prone to logical errors. Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline, highlighting the difficulty of the benchmark. The results on PolyMATH highlight the room for improvement in multi-modal reasoning and provide unique insights to guide the development of future MLLMs.

The rapid advancement of Large Language Models (LLMs) in the realm of mathematical reasoning necessitates comprehensive evaluations to gauge progress and inspire future directions. Existing assessments predominantly focus on problem-solving from the examinee perspective, overlooking a dual perspective of examiner regarding error identification and correction. From the examiner perspective, we define four evaluation tasks for error identification and correction along with a new dataset with annotated error types and steps. We also design diverse prompts to thoroughly evaluate eleven representative LLMs. Our principal findings indicate that GPT-4 outperforms all models, while open-source model LLaMA-2-7B demonstrates comparable abilities to closed-source models GPT-3.5 and Gemini Pro. Notably, calculation error proves the most challenging error type. Moreover, prompting LLMs with the error types can improve the average correction accuracy by 47.9\%. These results reveal potential directions for developing the mathematical reasoning abilities of LLMs. Our code and dataset is available on https://github.com/LittleCirc1e/EIC.

Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive problem-solving skills in many tasks and domains, but their ability in mathematical reasoning in visual contexts has not been systematically studied. To bridge this gap, we present MathVista, a benchmark designed to combine challenges from diverse mathematical and visual tasks. It consists of 6,141 examples, derived from 28 existing multimodal datasets involving mathematics and 3 newly created datasets (i.e., IQTest, FunctionQA, and PaperQA). Completing these tasks requires fine-grained, deep visual understanding and compositional reasoning, which all state-of-the-art foundation models find challenging. With MathVista, we have conducted a comprehensive, quantitative evaluation of 12 prominent foundation models. The best-performing GPT-4V model achieves an overall accuracy of 49.9%, substantially outperforming Bard, the second-best performer, by 15.1%. Our in-depth analysis reveals that the superiority of GPT-4V is mainly attributed to its enhanced visual perception and mathematical reasoning. However, GPT-4V still falls short of human performance by 10.4%, as it often struggles to understand complex figures and perform rigorous reasoning. This significant gap underscores the critical role that MathVista will play in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. We further explore the new ability of self-verification, the application of self-consistency, and the interactive chatbot capabilities of GPT-4V, highlighting its promising potential for future research. The project is available at https://mathvista.github.io/.

Neurosymbolic AI aims to integrate deep learning with symbolic AI. This integration has many promises, such as decreasing the amount of data required to train a neural network, improving the explainability and interpretability of answers given by models and verifying the correctness of trained systems. We study neurosymbolic learning, where we have both data and background knowledge expressed using symbolic languages. How do we connect the symbolic and neural components to communicate this knowledge? One option is fuzzy reasoning, which studies degrees of truth. For example, being tall is not a binary concept. Instead, probabilistic reasoning studies the probability that something is true or will happen. Our first research question studies how different forms of fuzzy reasoning combine with learning. We find surprising results like a connection to the Raven paradox stating we confirm "ravens are black" when we observe a green apple. In this study, we did not use the background knowledge when we deployed our models after training. In our second research question, we studied how to use background knowledge in deployed models. We developed a new neural network layer based on fuzzy reasoning. Probabilistic reasoning is a natural fit for neural networks, which we usually train to be probabilistic. However, they are expensive to compute and do not scale well to large tasks. In our third research question, we study how to connect probabilistic reasoning with neural networks by sampling to estimate averages, while in the final research question, we study scaling probabilistic neurosymbolic learning to much larger problems than before. Our insight is to train a neural network with synthetic data to predict the result of probabilistic reasoning.

Fox News Flash top headlines are here. Check out what's clicking on Foxnews.com. A Star Wars-obsessed man who was encouraged by a chatbot "girlfriend" to slay Queen Elizabeth II was sentenced Thursday to nine years in prison for taking his plot to Windsor Castle, where he scaled the walls and was caught with a loaded crossbow on Christmas Day 2021. "I'm here to kill the queen," Jaswant Singh Chail, wearing a metal mask inspired by the dark force in the Star Wars movies, declared when he was encountered by a guard on the grounds of the castle in the early morning, according to the court. He then dropped the weapon and surrendered, and repeated his intent.