Constrained pathfinding is a well-studied, yet challenging network optimisation problem that can be seen in a broad range of real-world applications. Pathfinding with multiple resource limits, which is known as the Resource Constrained Shortest Path Problem (RCSP), aims to plan a cost-optimum path subject to limited usage of resources. Given the recent advances in constrained and multi-criteria search with A*, this paper introduces a new resource constrained search framework on the basis of A* to tackle RCSP in large networks, even in the presence of negative cost and negative resources. We empirically evaluate our new algorithm on a set of large instances and show up to two orders of magnitude faster performance compared to state-of-the-art RCSP algorithms in the literature.

Cognition swiftly breaks high-dimensional sensory streams into familiar parts and uncovers their relations. Why do structures emerge, and how do they enable learning, generalization, and prediction? What computational principles underlie this core aspect of perception and intelligence? A sensory stream, simplified, is a one-dimensional sequence. In learning such sequences, we naturally segment them into parts -- a process known as chunking. In the first project, I investigated factors influencing chunking in a serial reaction time task and showed that humans adapt to underlying chunks while balancing speed and accuracy. Building on this, I developed models that learn chunks and parse sequences chunk by chunk. Normatively, I proposed chunking as a rational strategy for discovering recurring patterns and nested hierarchies, enabling efficient sequence factorization. Learned chunks serve as reusable primitives for transfer, composition, and mental simulation -- letting the model compose the new from the known. I demonstrated this model's ability to learn hierarchies in single and multi-dimensional sequences and highlighted its utility for unsupervised pattern discovery. The second part moves from concrete to abstract sequences. I taxonomized abstract motifs and examined their role in sequence memory. Behavioral evidence suggests that humans exploit pattern redundancies for compression and transfer. I proposed a non-parametric hierarchical variable model that learns both chunks and abstract variables, uncovering invariant symbolic patterns. I showed its similarity to human learning and compared it to large language models. Taken together, this thesis suggests that chunking and abstraction as simple computational principles enable structured knowledge acquisition in hierarchically organized sequences, from simple to complex, concrete to abstract.

Expressing confidence is challenging for embodied agents navigating dynamic multimodal environments, where uncertainty arises from both perception and decision-making processes. We present the first work investigating embodied confidence elicitation in open-ended multimodal environments. We introduce Elicitation Policies, which structure confidence assessment across inductive, deductive, and abductive reasoning, along with Execution Policies, which enhance confidence calibration through scenario reinterpretation, action sampling, and hypothetical reasoning. Evaluating agents in calibration and failure prediction tasks within the Minecraft environment, we show that structured reasoning approaches, such as Chain-of-Thoughts, improve confidence calibration. However, our findings also reveal persistent challenges in distinguishing uncertainty, particularly under abductive settings, underscoring the need for more sophisticated embodied confidence elicitation methods.

While large multimodal models (LMMs) have demonstrated strong performance across various Visual Question Answering (VQA) tasks, certain challenges require complex multi-step reasoning to reach accurate answers. One particularly challenging task is autonomous driving, which demands thorough cognitive processing before decisions can be made. In this domain, a sequential and interpretive understanding of visual cues is essential for effective perception, prediction, and planning. Nevertheless, common VQA benchmarks often focus on the accuracy of the final answer while overlooking the reasoning process that enables the generation of accurate responses. Moreover, existing methods lack a comprehensive framework for evaluating step-by-step reasoning in realistic driving scenarios. To address this gap, we propose DriveLMM-o1, a new dataset and benchmark specifically designed to advance step-wise visual reasoning for autonomous driving. Our benchmark features over 18k VQA examples in the training set and more than 4k in the test set, covering diverse questions on perception, prediction, and planning, each enriched with step-by-step reasoning to ensure logical inference in autonomous driving scenarios. We further introduce a large multimodal model that is fine-tuned on our reasoning dataset, demonstrating robust performance in complex driving scenarios. In addition, we benchmark various open-source and closed-source methods on our proposed dataset, systematically comparing their reasoning capabilities for autonomous driving tasks. Our model achieves a +7.49% gain in final answer accuracy, along with a 3.62% improvement in reasoning score over the previous best open-source model. Our framework, dataset, and model are available at https://github.com/ayesha-ishaq/DriveLMM-o1.

We introduce LUMOS, a language-conditioned multi-task imitation learning framework for robotics. LUMOS learns skills by practicing them over many long-horizon rollouts in the latent space of a learned world model and transfers these skills zero-shot to a real robot. By learning on-policy in the latent space of the learned world model, our algorithm mitigates policy-induced distribution shift which most offline imitation learning methods suffer from. LUMOS learns from unstructured play data with fewer than 1% hindsight language annotations but is steerable with language commands at test time. We achieve this coherent long-horizon performance by combining latent planning with both image- and language-based hindsight goal relabeling during training, and by optimizing an intrinsic reward defined in the latent space of the world model over multiple time steps, effectively reducing covariate shift. In experiments on the difficult long-horizon CALVIN benchmark, LUMOS outperforms prior learning-based methods with comparable approaches on chained multi-task evaluations. To the best of our knowledge, we are the first to learn a language-conditioned continuous visuomotor control for a real-world robot within an offline world model. Videos, dataset and code are available at http://lumos.cs.uni-freiburg.de.

Existing vision-language models (VLMs) often suffer from visual hallucination, where the generated responses contain inaccuracies that are not grounded in the visual input. Efforts to address this issue without model finetuning primarily mitigate hallucination by reducing biases contrastively or amplifying the weights of visual embedding during decoding. However, these approaches improve visual perception at the cost of impairing the language reasoning capability. In this work, we propose the Perception Magnifier (PM), a novel visual decoding method that iteratively isolates relevant visual tokens based on attention and magnifies the corresponding regions, spurring the model to concentrate on fine-grained visual details during decoding. Specifically, by magnifying critical regions while preserving the structural and contextual information at each decoding step, PM allows the VLM to enhance its scrutiny of the visual input, hence producing more accurate and faithful responses. Extensive experimental results demonstrate that PM not only achieves superior hallucination mitigation but also enhances language generation while preserving strong reasoning capabilities. Code is available at https://github.com/ShunqiM/PM .

This paper introduces the System 0/1/2/3 framework as an extension of dual-process theory, employing a quad-process model of cognition. Expanding upon System 1 (fast, intuitive thinking) and System 2 (slow, deliberative thinking), we incorporate System 0, which represents pre-cognitive embodied processes, and System 3, which encompasses collective intelligence and symbol emergence. We contextualize this model within Bergson's philosophy by adopting multi-scale time theory to unify the diverse temporal dynamics of cognition. System 0 emphasizes morphological computation and passive dynamics, illustrating how physical embodiment enables adaptive behavior without explicit neural processing. Systems 1 and 2 are explained from a constructive perspective, incorporating neurodynamical and AI viewpoints. In System 3, we introduce collective predictive coding to explain how societal-level adaptation and symbol emergence operate over extended timescales. This comprehensive framework ranges from rapid embodied reactions to slow-evolving collective intelligence, offering a unified perspective on cognition across multiple timescales, levels of abstraction, and forms of human intelligence. The System 0/1/2/3 model provides a novel theoretical foundation for understanding the interplay between adaptive and cognitive processes, thereby opening new avenues for research in cognitive science, AI, robotics, and collective intelligence.

Reasoning ability is crucial for solving challenging tasks. With the advancement of foundation models, such as the emergence of large language models (LLMs), a wide range of reasoning strategies has been proposed, including test-time enhancements, such as Chain-ofThought, and post-training optimizations, as used in DeepSeek-R1. While these reasoning strategies have demonstrated effectiveness across various challenging language or vision tasks, their applicability and impact on time-series forecasting (TSF), particularly the challenging zero-shot TSF, remain largely unexplored. In particular, it is unclear whether zero-shot TSF benefits from reasoning and, if so, what types of reasoning strategies are most effective. To bridge this gap, we propose ReC4TS, the first benchmark that systematically evaluates the effectiveness of popular reasoning strategies when applied to zero-shot TSF tasks. ReC4TS conducts comprehensive evaluations across datasets spanning eight domains, covering both unimodal and multimodal with short-term and longterm forecasting tasks. More importantly, ReC4TS provides key insights: (1) Self-consistency emerges as the most effective test-time reasoning strategy; (2) Group-relative policy optimization emerges as a more suitable approach for incentivizing reasoning ability during post-training; (3) Multimodal TSF benefits more from reasoning strategies compared to unimodal TSF. Beyond these insights, ReC4TS establishes two pioneering starting blocks to support future zero-shot TSF reasoning research: (1) A novel dataset, TimeThinking, containing forecasting samples annotated with reasoning trajectories from multiple advanced LLMs, and (2) A new and simple test-time scaling-law validated on foundational TSF models enabled by self-consistency reasoning strategy. All data and code are publicly accessible at: https://github.com/AdityaLab/OpenTimeR

In this note, we examine the aggregation of preferences achieved by the Group Policy Optimisation (GRPO) algorithm, a reinforcement learning method used to train advanced artificial intelligence models such as DeepSeek-R1-Zero and DeepSeekMath. The GRPO algorithm trains a policy using a reward preference model, which is computed by sampling a set of outputs for a given context, observing the corresponding rewards, and applying shift-and-scale normalisation to these reward values. Additionally, it incorporates a penalty function to discourage deviations from a reference policy. We present a framework that enables us to characterise the stationary policies of the GRPO algorithm. This analysis reveals that the aggregation of preferences differs fundamentally from standard logarithmic pooling, which is implemented by other approaches such as RLHF. The precise form of preference aggregation arises from the way the reward preference model is defined and from the penalty function, which we show to essentially correspond to the reverse Kullback-Leibler (KL) divergence between the aggregation policy and the reference policy. Interestingly, we demonstrate that for groups of size two, the reward preference model corresponds to pairwise comparison preferences, similar to those in other alignment methods based on pairwise comparison feedback. We provide explicit characterisations of the aggregate preference for binary questions, for groups of size two, and in the limit of large group size. This provides insights into the dependence of the aggregate preference on parameters such as the regularisation constant and the confidence margin of question answers. Finally, we discuss the aggregation of preferences obtained by modifying the GRPO algorithm to use direct KL divergence as the penalty or to use rewards without scale normalisation.

The most promising recent methods for AI reasoning require applying variants of reinforcement learning (RL) either on rolled out trajectories from the model, even for the step-wise rewards, or large quantities of human annotated trajectory data. The reliance on the rolled-out trajectory renders the compute cost and time prohibitively high. In particular, the correctness of a reasoning trajectory can typically only be judged at its completion, leading to sparse rewards in RL or requiring expensive synthetic data generation in expert iteration-like methods. In this work, we focus on the Automatic Theorem Proving (ATP) task and propose a novel verifier-in-the-loop design, which unlike existing approaches that leverage feedback on the entire reasoning trajectory, employs an automated verifier to give intermediate feedback at each step of the reasoning process. Using Lean as the verifier, we empirically show that the step-by-step local verification produces a global improvement in the model's reasoning accuracy and efficiency.