Here, we integrate these two approaches by trading off utility, informativeness, and complexity in EC.

Reconciling symbolic and distributed representations is a crucial challenge that can potentially resolve the limitations of current deep learning. Remarkable advances in this direction have been achieved recently via generative object-centric representation models. While learning a recognition model that infers object-centric symbolic representations like bounding boxes from raw images in an unsupervised way, no such model can provide another important ability of a generative model, i.e., generating (sampling) according to the structure of learned world density. In this paper, we propose Generative Neurosymbolic Machines, a generative model that combines the benefits of distributed and symbolic representations to support both structured representations of symbolic components and density-based generation. These two crucial properties are achieved by a two-layer latent hierarchy with the global distributed latent for flexible density modeling and the structured symbolic latent map. To increase the model flexibility in this hierarchical structure, we also propose the StructDRAW prior. In experiments, we show that the proposed model significantly outperforms the previous structured representation models as well as the state-of-the-art non-structured generative models in terms of both structure accuracy and image generation quality.

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing tasks. However, temporal reasoning, particularly under complex temporal constraints, remains a major challenge. To this end, existing approaches have explored symbolic methods, which encode temporal structure explicitly, and reflective mechanisms, which revise reasoning errors through multi-step inference. Nonetheless, symbolic approaches often underutilize the reasoning capabilities of LLMs, while reflective methods typically lack structured temporal representations, which can result in inconsistent or hallucinated reasoning. As a result, even when the correct temporal context is available, LLMs may still misinterpret or misapply time-related information, leading to incomplete or inaccurate answers. To address these limitations, in this work, we propose Neuro-Symbolic Temporal Reasoning (NeSTR), a novel framework that integrates structured symbolic representations with hybrid reflective reasoning to enhance the temporal sensitivity of LLM inference. NeSTR preserves explicit temporal relations through symbolic encoding, enforces logical consistency via verification, and corrects flawed inferences using abductive reflection. Extensive experiments on diverse temporal question answering benchmarks demonstrate that NeSTR achieves superior zero-shot performance and consistently improves temporal reasoning without any fine-tuning, showcasing the advantage of neuro-symbolic integration in enhancing temporal understanding in large language models.

Abstract-- Deploying autonomous robots that can learn new skills from demonstrations is an important challenge of modern robotics. Existing solutions often apply end-to-end imitation learning with Vision-Language Action (VLA) models or symbolic approaches with Action Model Learning (AML). On the one hand, current VLA models are limited by the lack of high-level symbolic planning, which hinders their abilities in long-horizon tasks. In this paper we present a new neuro-symbolic approach, GraSP-VLA, a framework that uses a Continuous Scene Graph representation to generate a symbolic representation of human demonstrations. This representation is used to generate new planning domains during inference and serves as an orchestrator for low-level VLA policies, scaling up the number of actions that can be reproduced in a row. Our results show that GraSP-VLA is effective for modeling symbolic representations on the task of automatic planning domain generation from observations. In addition, results on real-world experiments show the potential of our Continuous Scene Graph representation to orchestrate low-level VLA policies in long-horizon tasks. Inferring the preconditions and outcomes of actions from observations is a long-lasting challenge in robotics. These representations can then be used to compose long-horizon tasks using pre-trained low-level behaviors. In AML, we define an action as a set of initial states (i.e.

Labeling or classifying time series is a persistent challenge in the physical sciences, where expert annotations are scarce, costly, and often inconsistent. Yet robust labeling is essential to enable machine learning models for understanding, prediction, and forecasting. We present the \textit{Clustering and Indexation Pipeline with Human Evaluation for Recognition} (CIPHER), a framework designed to accelerate large-scale labeling of complex time series in physics. CIPHER integrates \textit{indexable Symbolic Aggregate approXimation} (iSAX) for interpretable compression and indexing, density-based clustering (HDBSCAN) to group recurring phenomena, and a human-in-the-loop step for efficient expert validation. Representative samples are labeled by domain scientists, and these annotations are propagated across clusters to yield systematic, scalable classifications. We evaluate CIPHER on the task of classifying solar wind phenomena in OMNI data, a central challenge in space weather research, showing that the framework recovers meaningful phenomena such as coronal mass ejections and stream interaction regions. Beyond this case study, CIPHER highlights a general strategy for combining symbolic representations, unsupervised learning, and expert knowledge to address label scarcity in time series across the physical sciences. The code and configuration files used in this study are publicly available to support reproducibility.

Reinforcement learning (RL) has experienced a second wind in the past decade. While incredibly successful in images and videos, these systems still operate within the realm of propositional tasks ignoring the inherent structure that exists in the problem. Consequently, relational extensions (RRL) have been developed for such structured problems that allow for effective generalization to arbitrary number of objects. However, they inherently make strong assumptions about the problem structure. We introduce a novel framework that combines RRL with object-centric representation to handle both structured and unstructured data. We enhance learning by allowing the system to actively query the human expert for guidance by explicitly modeling the uncertainty over the policy. Our empirical evaluation demonstrates the effectiveness and efficiency of our proposed approach.

Recent advances in large language models (LLMs) have created new opportunities for symbolic music generation. However, existing formats such as MIDI, ABC, and MusicXML are either overly complex or structurally inconsistent, limiting their suitability for token-based learning architectures. To address these challenges, we propose HNote, a novel hexadecimal-based notation system extended from YNote, which encodes both pitch and duration within a fixed 32-unit measure framework. This design ensures alignment, reduces ambiguity, and is directly compatible with LLM architectures. We converted 12,300 Jiangnan-style songs generated from traditional folk pieces from YNote into HNote, and fine-tuned LLaMA-3.1(8B) using parameter-efficient LoRA. Experimental results show that HNote achieves a syntactic correctness rate of 82.5%, and BLEU and ROUGE evaluations demonstrate strong symbolic and structural similarity, producing stylistically coherent compositions. This study establishes HNote as an effective framework for integrating LLMs with cultural music modeling.