Breakthroughs, discoveries, and DIY tips sent every weekday. Mitsubishi's bragging rights for designing the world's fastest Rubik's cube-solving robot have officially been stolen by a team of undergrads in Indiana. Earlier this month, Purdue University announced four collaborators in its Elmore Family School of Electrical and Computer Engineering (ECE) successfully designed and built a bot that not only set the new Guinness World Record--it absolutely demolished the multinational company's previous time. Meet Purdubik's Cube: a machine capable of completing a randomly shuffled Rubik's cube in just 0.103 seconds. At 1-2 times faster than the blink of a human eye, the feat is difficult to see, much less comprehend.

In this paper we propose for the first time the hyperparameter optimization (HPO) algorithm POCAII. POCAII differs from the Hyperband and Successive Halving literature by explicitly separating the search and evaluation phases and utilizing principled approaches to exploration and exploitation principles during both phases. Such distinction results in a highly flexible scheme for managing a hyperparameter optimization budget by focusing on search (i.e., generating competing configurations) towards the start of the HPO process while increasing the evaluation effort as the HPO comes to an end. POCAII was compared to state of the art approaches SMAC, BOHB and DEHB. Our algorithm shows superior performance in low-budget hyperparameter optimization regimes. Since many practitioners do not have exhaustive resources to assign to HPO, it has wide applications to real-world problems. Moreover, the empirical evidence showed how POCAII demonstrates higher robustness and lower variance in the results. This is again very important when considering realistic scenarios with extremely expensive models to train.

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of $60.74\%$ on MiniF2F and $21.18\%$ on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

As modern software systems expand in scale and complexity, the challenges associated with their modeling and formulation grow increasingly intricate. Traditional approaches often fall short in effectively addressing these complexities, particularly in tasks such as design pattern detection for maintenance and assessment, as well as code refactoring for optimization and long-term sustainability. This growing inadequacy underscores the need for a paradigm shift in how such challenges are approached and resolved. This paper presents Analytical Software Engineering (ASE), a novel design paradigm aimed at balancing abstraction, tool accessibility, compatibility, and scalability. ASE enables effective modeling and resolution of complex software engineering problems. The paradigm is evaluated through two frameworks Behavioral-Structural Sequences (BSS) and Optimized Design Refactoring (ODR), both developed in accordance with ASE principles. BSS offers a compact, language-agnostic representation of codebases to facilitate precise design pattern detection. ODR unifies artifact and solution representations to optimize code refactoring via heuristic algorithms while eliminating iterative computational overhead. By providing a structured approach to software design challenges, ASE lays the groundwork for future research in encoding and analyzing complex software metrics.

Mixed-integer programming (MIP) provides a powerful frame work for optimization problems, with Branch-and-Cut (B&C) being the predomi nant algorithm in state-of-the-art solvers. The efficiency of B&C critically depends on heuristic policies for making sequential decisions, including node s election, cut selection, and branching variable selection. While traditional solve rs often employ heuristics with manually tuned parameters, recent approaches increas ingly leverage machine learning, especially neural networks, to learn these polic ies directly from data. A key challenge is to understand the theoretical underpinnin gs of these learned policies, particularly their generalization performance from finite data. This paper establishes rigorous sample complexity bounds for learnin g B&C policies where the scoring functions guiding each decision step (node, cut, branch) have a certain piecewise polynomial structure. This structure gener alizes the linear models that form the most commonly deployed policies in practice an d investigated recently in a foundational series of theoretical works by Balc an et al. Such piece-wise polynomial policies also cover the neural network arch itectures (e.g., using ReLU activations) that have been the focal point of contempo rary practical studies. Consequently, our theoretical framework closely refle cts the models utilized by practitioners investigating machine learning within B& C, offering a unifying perspective relevant to both established theory and modern empirical research in this area. Furthermore, our theory applies to quite general sequential decision making problems beyond B&C.

Recent work investigated the use of Reinforcement Learning (RL) for the synthesis of heuristic guidance to improve the performance of temporal planners when a domain is fixed and a set of training problems (not plans) is given. The idea is to extract a heuristic from the value function of a particular (possibly infinite-state) MDP constructed over the training problems. In this paper, we propose an evolution of this learning and planning framework that focuses on exploiting the information provided by symbolic heuristics during both the RL and planning phases. First, we formalize different reward schemata for the synthesis and use symbolic heuristics to mitigate the problems caused by the truncation of episodes needed to deal with the potentially infinite MDP . Second, we propose learning a residual of an existing symbolic heuristic, which is a "correction" of the heuristic value, instead of eagerly learning the whole heuristic from scratch. Finally, we use the learned heuristic in combination with a symbolic heuristic using a multiple-queue planning approach to balance systematic search with imperfect learned information. We experimentally compare all the approaches, highlighting their strengths and weaknesses and significantly advancing the state of the art for this planning and learning schema.

Our method leverages text-to-audio alignment and music-structural alignment rewards during inference to encourage the generated music to be consistent with the input caption. Specifically, we introduce two objectives scores: a text-audio consistency score that measures rhythmic alignment between the generated music and the original text caption, and a harmonic-consistency score that penalizes generated music containing notes inconsistent with the key. By optimizing these alignment-based objectives during the generation process, our model produces symbolic music that is more closely tied to the input captions, thereby improving the overall quality and coherence of the generated compositions. Our approach can extend any existing autoregressive model without requiring further training or fine-tuning. We evaluate our work on top of Text2midi - an existing text-to-midi generation model, demonstrating significant improvements in both objective and subjective evaluation metrics.

We study the densest subgraph problem and its variants through the lens of learning-augmented algorithms. For this problem, the greedy algorithm by Charikar (APPROX 2000) provides a linear-time $ 1/2 $-approximation, while computing the exact solution typically requires solving a linear program or performing maximum flow computations.We show that given a partial solution, i.e., one produced by a machine learning classifier that captures at least a $ (1 - ε) $-fraction of nodes in the optimal subgraph, it is possible to design an extremely simple linear-time algorithm that achieves a provable $ (1 - ε) $-approximation. Our approach also naturally extends to the directed densest subgraph problem and several NP-hard variants.An experiment on the Twitch Ego Nets dataset shows that our learning-augmented algorithm outperforms Charikar's greedy algorithm and a baseline that directly returns the predicted densest subgraph without additional algorithmic processing.

--Recently, large language models (LLMs) have demonstrated impressive performance in Knowledge Graph Question Answering (KGQA) tasks, which aim to find answers based on knowledge graphs (KGs) for natural language questions. Existing LLMs-based KGQA methods typically follow the Graph Retrieval-Augmented Generation (GraphRAG) paradigm, which first retrieves reasoning paths from the large KGs, and then generates the answers based on them. However, these methods emphasize the exploration of new optimal reasoning paths in KGs while ignoring the exploitation of historical reasoning paths, which may lead to sub-optimal reasoning paths. Additionally, the complex semantics contained in questions may lead to the retrieval of inaccurate reasoning paths. T o address these issues, this paper proposes a novel and training-free framework for KGQA tasks called Reward-guided Tree Search on Graph (RTSoG). RTSoG decomposes an original question into a series of simpler and well-defined sub-questions to handle the complex semantics. Then, a Self-Critic Monte Carlo Tree Search (SC-MCTS) guided by a reward model is introduced to iteratively retrieve weighted reasoning paths as contextual knowledge. Finally, it stacks the weighted reasoning paths according to their weights to generate the final answers. Extensive experiments on four datasets demonstrate the effectiveness of RTSoG. Notably, it achieves 8.7% and 7.0% performance improvement over the state-of-the-art method on the GrailQA and the WebQSP respectively. Knowledge Graph Question Answering (KGQA) has drawn much attention in recent years.

Real-world networks often involve both keywords and locations, along with travel time variations between locations due to traffic conditions. However, most existing cohesive subgraph-based community search studies utilize a single attribute, either keywords or locations, to identify communities. They do not simultaneously consider both keywords and locations, which results in low semantic or spatial cohesiveness of the detected communities, and they fail to account for variations in travel time. Additionally, these studies traverse the entire network to build efficient indexes, but the detected community only involves nodes around the query node, leading to the traversal of nodes that are not relevant to the community. Therefore, we propose the problem of discovering semantic-spatial aware k-core, which refers to a k-core with high semantic and time-dependent spatial cohesiveness containing the query node. To address this problem, we propose an exact and a greedy algorithm, both of which gradually expand outward from the query node. They are local methods that only access the local part of the attributed network near the query node rather than the entire network. Moreover, we design a method to calculate the semantic similarity between two keywords using large language models. This method alleviates the disadvantages of keyword-matching methods used in existing community search studies, such as mismatches caused by differently expressed synonyms and the presence of irrelevant words. Experimental results show that the greedy algorithm outperforms baselines in terms of structural, semantic, and time-dependent spatial cohesiveness.