Reinforcement Learning (RL) has achieved impressive results on complex tasks but struggles in multi-task settings with different embodiments. World models offer scalability by learning a simulation of the environment, yet they often rely on inefficient gradient-free optimization methods. We introduce Policy learning with large World Models (PWM), a novel model-based RL algorithm that learns continuous control policies from large multi-task world models. By pre-training the world model on offline data and using it for first-order gradient policy learning, PWM effectively solves tasks with up to 152 action dimensions and outperforms methods using ground-truth dynamics. Additionally, PWM scales to an 80-task setting, achieving up to 27% higher rewards than existing baselines without the need for expensive online planning. Visualizations and code available at https://www.imgeorgiev.com/pwm

We present a system for Complex Event Recognition (CER) based on automata. While multiple such systems have been described in the literature, they typically suffer from a lack of clear and denotational semantics, a limitation which often leads to confusion with respect to their expressive power. In order to address this issue, our system is based on an automaton model which is a combination of symbolic and register automata. We extend previous work on these types of automata, in order to construct a formalism with clear semantics and a corresponding automaton model whose properties can be formally investigated. We call such automata Symbolic Register Transducers (SRT). We show that SRT are closed under various operators, but are not in general closed under complement and they are not determinizable. However, they are closed under these operations when a window operator, quintessential in Complex Event Recognition, is used. We show how SRT can be used in CER in order to detect patterns upon streams of events, using our framework that provides declarative and compositional semantics, and that allows for a systematic treatment of such automata. For SRT to work in pattern detection, we allow them to mark events from the input stream as belonging to a complex event or not, hence the name "transducers". We also present an implementation of SRT which can perform CER. We compare our SRT-based CER engine against other state-of-the-art CER systems and show that it is both more expressive and more efficient.

Prognosis and Health Management (PHM), critical for ensuring task completion by complex systems and preventing unexpected failures, is widely adopted in aerospace, manufacturing, maritime, rail, energy, etc. However, PHM's development is constrained by bottlenecks like generalization, interpretation and verification abilities. Presently, generative artificial intelligence (AI), represented by Large Model, heralds a technological revolution with the potential to fundamentally reshape traditional technological fields and human production methods. Its capabilities, including strong generalization, reasoning, and generative attributes, present opportunities to address PHM's bottlenecks. To this end, based on a systematic analysis of the current challenges and bottlenecks in PHM, as well as the research status and advantages of Large Model, we propose a novel concept and three progressive paradigms of Prognosis and Health Management Large Model (PHM-LM) through the integration of the Large Model with PHM. Subsequently, we provide feasible technical approaches for PHM-LM to bolster PHM's core capabilities within the framework of the three paradigms. Moreover, to address core issues confronting PHM, we discuss a series of technical challenges of PHM-LM throughout the entire process of construction and application. This comprehensive effort offers a holistic PHM-LM technical framework, and provides avenues for new PHM technologies, methodologies, tools, platforms and applications, which also potentially innovates design, research & development, verification and application mode of PHM. And furthermore, a new generation of PHM with AI will also capably be realized, i.e., from custom to generalized, from discriminative to generative, and from theoretical conditions to practical applications.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Neuro-symbolic systems (NeSy), which claim to combine the best of both learning and reasoning capabilities of artificial intelligence, are missing a core property of reasoning systems: Declarativeness. The lack of declarativeness is caused by the functional nature of neural predicates inherited from neural networks. We propose and implement a general framework for fully declarative neural predicates, which hence extends to fully declarative NeSy frameworks. We first show that the declarative extension preserves the learning and reasoning capabilities while being able to answer arbitrary queries while only being trained on a single query type.

Language models can solve complex reasoning tasks better by learning to generate rationales for their predictions. Often these models know how to solve a task but their auto-regressive decoding nature leads to incorrect results if they start incorrectly. We observe that smaller models in particular when corrected, can solve a task that they would have otherwise struggled with. We demonstrate this phenomenon by using a larger model to guide smaller models, which leads to significantly improved performance (up to +24 points on the GSM8K dataset by 7B models). To assist smaller models in initiating the starting step, we propose QuestCoT, where a smaller model first asks itself how to start, before proceeding with a chain of reasoning. On various multistep mathematical reasoning datasets over multiple smaller models, we show that getting the right start can lead to significant performance gains across all models (gains of up to +6 points on GSM8K, +9 on SVAMP, +5 on ASDiv, and +7 on MultiArith).

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in white-box and black-box prompt learning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown in both reasoning and image generation tasks, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in \url{https://github.com/research4pan/Plum}.

Instruction subsets are heuristics that can reduce the size of the inductive programming search space by tens of orders of magnitude. Comprising many overlapping subsets of different sizes, they serve as predictions of the instructions required to code a solution for any problem. Currently, this approach employs a single, large family of subsets meaning that some problems can search thousands of subsets before a solution is found. In this paper we introduce the use of test case type signatures as hyper-heuristics to select one of many, smaller families of instruction subsets. The type signature for any set of test cases maps directly to a single family and smaller families mean that fewer subsets need to be considered for most problems. Having many families also permits subsets to be reordered to better reflect their relative occurrence in human code - again reducing the search space size for many problems. Overall the new approach can further reduce the size of the inductive programming search space by between 1 and 3 orders of magnitude, depending on the type signature. Larger and more consistent reductions are possible through the use of more sophisticated type systems. The potential use of additional test case features as hyper-heuristics and some other possible future work is also briefly discussed.

Tabular reasoning involves interpreting unstructured queries against structured tables, requiring a synthesis of textual understanding and symbolic reasoning. Existing methods rely on either of the approaches and are constrained by their respective limitations. Textual reasoning excels in semantic interpretation unlike symbolic reasoning (SQL logic), but falls short in mathematical reasoning where SQL excels. In this paper, we introduce a novel algorithm H-STAR, comprising table extraction and adaptive reasoning, integrating both symbolic and semantic (text-based) approaches. To enhance evidence extraction, H-STAR employs a multi-view approach, incorporating step-by-step row and column retrieval. It also adapts reasoning strategies based on question types, utilizing symbolic reasoning for quantitative and logical tasks, and semantic reasoning for direct lookup and complex lexical queries. Our extensive experiments demonstrate that H-STAR significantly outperforms state-of-the-art methods across three tabular question-answering (QA) and fact-verification datasets, underscoring its effectiveness and efficiency.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.