Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the area of neurosymbolic Artificial Intelligence (AI). In this chapter, a simple energy-based neurosymbolic AI system is described that can represent and reason formally about any propositional logic formula. This creates a powerful combination of learning from data and knowledge and logical reasoning. We start by positioning neurosymbolic AI in the context of the current AI landscape that is unsurprisingly dominated by Large Language Models (LLMs). We identify important challenges of data efficiency, fairness and safety of LLMs that might be addressed by neurosymbolic reasoning systems with formal reasoning capabilities. We then discuss the representation of logic by the specific energy-based system, including illustrative examples and empirical evaluation of the correspondence between logical reasoning and energy minimization using Restricted Boltzmann Machines (RBM). Learning from data and knowledge is also evaluated empirically and compared with a symbolic, neural and a neurosymbolic system. Results reported in this chapter in an accessible way are expected to reignite the research on the use of neural networks as massively-parallel models for logical reasoning and promote the principled integration of reasoning and learning in deep networks. We conclude the chapter with a discussion of the importance of positioning neurosymbolic AI within a broader framework of formal reasoning and accountability in AI, discussing the challenges for neurosynbolic AI to tackle the various known problems of reliability of deep learning.

We propose RaDeR, a set of reasoning-based dense retrieval models trained with data derived from mathematical problem solving using large language models (LLMs). Our method leverages retrieval-augmented reasoning trajectories of an LLM and self-reflective relevance evaluation, enabling the creation of both diverse and hard-negative samples for reasoning-intensive relevance. RaDeR retrievers, trained for mathematical reasoning, effectively generalize to diverse reasoning tasks in the BRIGHT and RAR-b benchmarks, consistently outperforming strong baselines in overall performance. Notably, RaDeR achieves significantly higher performance than baselines on the Math and Coding splits. In addition, RaDeR presents the first dense retriever that outperforms BM25 when queries are Chain-of-Thought reasoning steps, underscoring the critical role of reasoning-based retrieval to augment reasoning language models. Furthermore, RaDeR achieves comparable or superior performance while using only 2.5% of the training data used by the concurrent work REASONIR, highlighting the quality of our synthesized training data.

Recent large reasoning models (LRMs) have demonstrated strong reasoning capabilities through reinforcement learning (RL). These improvements have primarily been observed within the short-context reasoning tasks. In contrast, extending LRMs to effectively process and reason on long-context inputs via RL remains a critical unsolved challenge. To bridge this gap, we first formalize the paradigm of long-context reasoning RL, and identify key challenges in suboptimal training efficiency and unstable optimization process. To address these issues, we propose QwenLong-L1, a framework that adapts short-context LRMs to long-context scenarios via progressive context scaling. Specifically, we utilize a warm-up supervised fine-tuning (SFT) stage to establish a robust initial policy, followed by a curriculum-guided phased RL technique to stabilize the policy evolution, and enhanced with a difficulty-aware retrospective sampling strategy to incentivize the policy exploration. Experiments on seven long-context document question-answering benchmarks demonstrate that QwenLong-L1-32B outperforms flagship LRMs like OpenAI-o3-mini and Qwen3-235B-A22B, achieving performance on par with Claude-3.7-Sonnet-Thinking, demonstrating leading performance among state-of-the-art LRMs. This work advances the development of practical long-context LRMs capable of robust reasoning across information-intensive environments.

Large reasoning models (LRMs) already possess a latent capacity for long chain-of-thought reasoning. Prior work has shown that outcome-based reinforcement learning (RL) can incidentally elicit advanced reasoning behaviors such as self-correction, backtracking, and verification phenomena often referred to as the model's "aha moment". However, the timing and consistency of these emergent behaviors remain unpredictable and uncontrollable, limiting the scalability and reliability of LRMs' reasoning capabilities. To address these limitations, we move beyond reliance on prompts and coincidental "aha moments". Instead, we explicitly align models with three meta-abilities: deduction, induction, and abduction, using automatically generated, self-verifiable tasks. Our three stage-pipeline individual alignment, parameter-space merging, and domain-specific reinforcement learning, boosting performance by over 10\% relative to instruction-tuned baselines. Furthermore, domain-specific RL from the aligned checkpoint yields an additional gain in performance ceiling for both 7B and 32B models across math, coding, and science benchmarks, demonstrating that explicit meta-ability alignment offers a scalable and dependable foundation for reasoning. Code is available at: https://github.com/zhiyuanhubj/Meta-Ability-Alignment

Current robotic planning methods often rely on predicting multi-frame images with full pixel details. While this fine-grained approach can serve as a generic world model, it introduces two significant challenges for downstream policy learning: substantial computational costs that hinder real-time deployment, and accumulated inaccuracies that can mislead action extraction. Planning with coarse-grained subgoals partially alleviates efficiency issues. However, their forward planning schemes can still result in off-task predictions due to accumulation errors, leading to misalignment with long-term goals. This raises a critical question: Can robotic planning be both efficient and accurate enough for real-time control in long-horizon, multi-stage tasks? To address this, we propose a Latent Space Backward Planning scheme (LBP), which begins by grounding the task into final latent goals, followed by recursively predicting intermediate subgoals closer to the current state. The grounded final goal enables backward subgoal planning to always remain aware of task completion, facilitating on-task prediction along the entire planning horizon. The subgoal-conditioned policy incorporates a learnable token to summarize the subgoal sequences and determines how each subgoal guides action extraction. Through extensive simulation and real-robot long-horizon experiments, we show that LBP outperforms existing fine-grained and forward planning methods, achieving SOTA performance. Project Page: https://lbp-authors.github.io

We introduce S1-Bench, a novel benchmark designed to evaluate the performance of Large Reasoning Models (LRMs) on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their heavy reliance on system 2 thinking may limit their system 1 thinking capabilities. However, there is a lack of an appropriate benchmark for evaluating LRM's system 1 thinking capabilities. To fill this gap, S1-Bench introduces a suite of simple, diverse, and natural questions across multiple domains and languages, specifically designed to assess LRMs' performance on questions more suitable for system 1 . We conduct extensive evaluations across 28 LRMs, revealing their inefficiency, inadequate accuracy, and limited robustness when handling simple questions. Additionally, we observe a gap between their difficulty perception and generation length. Overall, this work paves the way toward dual-system compatibility in the development of LRMs.

The trajectories of 6G and AI are set for a creative collision. However, current visions for 6G remain largely incremental evolutions of 5G, while progress in AI is hampered by brittle, data-hungry models that lack robust reasoning capabilities. This paper argues for a foundational paradigm shift, moving beyond the purely technical level of communication toward systems capable of semantic understanding and effective, goal-oriented interaction. We propose a unified research vision rooted in the principles of System-2 cognition, built upon three pillars: Abstraction, enabling agents to learn meaningful world models from raw sensorimotor data; Compositionality, providing the algebraic tools to combine learned concepts and subsystems; and Emergent Communication, allowing intelligent agents to create their own adaptive and grounded languages. By integrating these principles, we lay the groundwork for truly intelligent systems that can reason, adapt, and collaborate, unifying advances in wireless communications, machine learning, and robotics under a single coherent framework.

Large language models (LLMs) have shown remarkable reasoning capabilities, yet aligning such abilities to small language models (SLMs) remains a challenge due to distributional mismatches and limited model capacity. Existing reasoning datasets, typically designed for powerful LLMs, often lead to degraded performance when directly applied to weaker models. In this work, we introduce Dynamic Adaptation of Reasoning Trajectories (DART), a novel data adaptation framework that bridges the capability gap between expert reasoning trajectories and diverse SLMs. Instead of uniformly imitating expert steps, DART employs a selective imitation strategy guided by step-wise adaptability estimation via solution simulation. When expert steps surpass the student's capacity -- signaled by an Imitation Gap -- the student autonomously explores alternative reasoning paths, constrained by outcome consistency. We validate DART across multiple reasoning benchmarks and model scales, demonstrating that it significantly improves generalization and data efficiency over static fine-tuning. Our method enhances supervision quality by aligning training signals with the student's reasoning capabilities, offering a scalable solution for reasoning alignment in resource-constrained models.

Complex visual reasoning and question answering (VQA) is a challenging task that requires compositional multi-step processing and higher-level reasoning capabilities beyond the immediate recognition and localization of objects and events. Here, we introduce a fully neural Iterative and Parallel Reasoning Mechanism (IPRM) that combines two distinct forms of computation -- iterative and parallel -- to better address complex VQA scenarios. Specifically, IPRM's "iterative" computation facilitates compositional step-by-step reasoning for scenarios wherein individual operations need to be computed, stored, and recalled dynamically (e.g. when computing the query "determine the color of pen to the left of the child in red t-shirt sitting at the white table"). Meanwhile, its "parallel'' computation allows for the simultaneous exploration of different reasoning paths and benefits more robust and efficient execution of operations that are mutually independent (e.g. when counting individual colors for the query: "determine the maximum occurring color amongst all t-shirts'"). We design IPRM as a lightweight and fully-differentiable neural module that can be conveniently applied to both transformer and non-transformer vision-language backbones. It notably outperforms prior task-specific methods and transformer-based attention modules across various image and video VQA benchmarks testing distinct complex reasoning capabilities such as compositional spatiotemporal reasoning (AGQA), situational reasoning (STAR), multi-hop reasoning generalization (CLEVR-Humans) and causal event linking (CLEVRER-Humans).

Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields.