Meta-learning, or "learning to learn," aims to enable models to quickly adapt to new tasks with minimal data. While traditional methods like Model-Agnostic Meta-Learning (MAML) optimize parameters in Euclidean space, they often struggle to capture complex learning dynamics, particularly in few-shot learning scenarios. To address this limitation, we propose Stiefel-MAML, which integrates Riemannian geometry by optimizing within the Stiefel manifold, a space that naturally enforces orthogonality constraints. By leveraging the geometric structure of the Stiefel manifold, we improve parameter expressiveness and enable more efficient optimization through Riemannian gradient calculations and retraction operations. We also introduce a novel kernel-based loss function defined on the Stiefel manifold, further enhancing the model's ability to explore the parameter space. Experimental results on benchmark datasets--including Omniglot, Mini-ImageNet, FC-100, and CUB--demonstrate that Stiefel-MAML consistently outperforms traditional MAML, achieving superior performance across various few-shot learning tasks. Our findings highlight the potential of Riemannian geometry to enhance meta-learning, paving the way for future research on optimizing over different geometric structures.

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.

Measurements are fundamental to knowledge creation in science, enabling consistent sharing of findings and serving as the foundation for scientific discovery. As machine learning systems increasingly transform scientific fields, the question of how to effectively evaluate these systems becomes crucial for ensuring reliable progress. In this review, we examine the current state and future directions of evaluation frameworks for machine learning in science. We organize the review around a broadly applicable framework for evaluating machine learning systems through the lens of statistical measurement theory, using materials science as our primary context for examples and case studies. We identify key challenges common across machine learning evaluation such as construct validity, data quality issues, metric design limitations, and benchmark maintenance problems that can lead to phantom progress when evaluation frameworks fail to capture real-world performance needs. By examining both traditional benchmarks and emerging evaluation approaches, we demonstrate how evaluation choices fundamentally shape not only our measurements but also research priorities and scientific progress. These findings reveal the critical need for transparency in evaluation design and reporting, leading us to propose evaluation cards as a structured approach to documenting measurement choices and limitations. Our work highlights the importance of developing a more diverse toolbox of evaluation techniques for machine learning in materials science, while offering insights that can inform evaluation practices in other scientific domains where similar challenges exist.

Object-Centric Process Mining (OCPM) enables business process analysis from multiple perspectives. For example, an educational path can be examined from the viewpoints of students, teachers, and groups. This analysis depends on Object-Centric Event Data (OCED), which captures relationships between events and object types, representing different perspectives. Unlike traditional process mining techniques, extracting OCED minimizes the need for repeated log extractions when shifting the analytical focus. However, recording these complex relationships increases the complexity of the log extraction process. To address this challenge, this paper proposes a method for extracting OCED based on PM\inst{2}, a well-established process mining framework. Our approach introduces a structured framework that guides data analysts and engineers in extracting OCED for process analysis. We validate this framework by applying it in a real-world educational setting, demonstrating its effectiveness in extracting an Object-Centric Event Log (OCEL), which serves as the standard format for recording OCED, from a learning management system and an administrative grading system.

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.

With the rapid evolution of Artificial Intelligence (AI), Large Language Models (LLMs) have reshaped the frontiers of various fields, spanning healthcare, public health, engineering, science, agriculture, education, arts, humanities, and mathematical reasoning. Among these advancements, DeepSeek models have emerged as noteworthy contenders, demonstrating promising capabilities that set them apart from their peers. While previous studies have conducted comparative analyses of LLMs, few have delivered a comprehensive evaluation of mathematical reasoning across a broad spectrum of LLMs. In this work, we aim to bridge this gap by conducting an in-depth comparative study, focusing on the strengths and limitations of DeepSeek models in relation to their leading counterparts. In particular, our study systematically evaluates the mathematical reasoning performance of two DeepSeek models alongside five prominent LLMs across three independent benchmark datasets. The findings reveal several key insights: 1). DeepSeek-R1 consistently achieved the highest accuracy on two of the three datasets, demonstrating strong mathematical reasoning capabilities. 2). The distilled variant of LLMs significantly underperformed compared to its peers, highlighting potential drawbacks in using distillation techniques. 3). In terms of response time, Gemini 2.0 Flash demonstrated the fastest processing speed, outperforming other models in efficiency, which is a crucial factor for real-time applications. Beyond these quantitative assessments, we delve into how architecture, training, and optimization impact LLMs' mathematical reasoning. Moreover, our study goes beyond mere performance comparison by identifying key areas for future advancements in LLM-driven mathematical reasoning. This research enhances our understanding of LLMs' mathematical reasoning and lays the groundwork for future advancements

High-quality test items are essential for educational assessments, particularly within Item Response Theory (IRT). Traditional validation methods rely on resource-intensive pilot testing to estimate item difficulty and discrimination. More recently, Item-Writing Flaw (IWF) rubrics emerged as a domain-general approach for evaluating test items based on textual features. However, their relationship to IRT parameters remains underexplored. To address this gap, we conducted a study involving over 7,000 multiple-choice questions across various STEM subjects (e.g., math and biology). Using an automated approach, we annotated each question with a 19-criteria IWF rubric and studied relationships to data-driven IRT parameters. Our analysis revealed statistically significant links between the number of IWFs and IRT difficulty and discrimination parameters, particularly in life and physical science domains. We further observed how specific IWF criteria can impact item quality more and less severely (e.g., negative wording vs. implausible distractors). Overall, while IWFs are useful for predicting IRT parameters--particularly for screening low-difficulty MCQs--they cannot replace traditional data-driven validation methods. Our findings highlight the need for further research on domain-general evaluation rubrics and algorithms that understand domain-specific content for robust item validation.

Continual learning algorithms aim to learn from a sequence of tasks, making the training distribution non-stationary. The majority of existing continual learning approaches in the literature rely on heuristics and do not provide learning guarantees for the continual learning setup. In this paper, we present a new method called 'Continual Pick-to-Learn' (CoP2L), which is able to retain the most representative samples for each task in an efficient way. The algorithm is adapted from the Pick-to-Learn algorithm, rooted in the sample compression theory. This allows us to provide high-confidence upper bounds on the generalization loss of the learned predictors, numerically computable after every update of the learned model. We also empirically show on several standard continual learning benchmarks that our algorithm is able to outperform standard experience replay, significantly mitigating catastrophic forgetting.

We seek to extract a temporally consistent 6D pose trajectory of a manipulated object from an Internet instructional video. This is a challenging set-up for current 6D pose estimation methods due to uncontrolled capturing conditions, subtle but dynamic object motions, and the fact that the exact mesh of the manipulated object is not known. To address these challenges, we present the following contributions. First, we develop a new method that estimates the 6D pose of any object in the input image without prior knowledge of the object itself. The method proceeds by (i) retrieving a CAD model similar to the depicted object from a large-scale model database, (ii) 6D aligning the retrieved CAD model with the input image, and (iii) grounding the absolute scale of the object with respect to the scene. Second, we extract smooth 6D object trajectories from Internet videos by carefully tracking the detected objects across video frames. The extracted object trajectories are then retargeted via trajectory optimization into the configuration space of a robotic manipulator. Third, we thoroughly evaluate and ablate our 6D pose estimation method on YCB-V and HOPE-Video datasets as well as a new dataset of instructional videos manually annotated with approximate 6D object trajectories. We demonstrate significant improvements over existing state-of-the-art RGB 6D pose estimation methods. Finally, we show that the 6D object motion estimated from Internet videos can be transferred to a 7-axis robotic manipulator both in a virtual simulator as well as in a real world set-up. We also successfully apply our method to egocentric videos taken from the EPIC-KITCHENS dataset, demonstrating potential for Embodied AI applications.

Multimodal information-gathering settings, where users collaborate with AI in dynamic environments, are increasingly common. These involve complex processes with textual and multimodal interactions, often requiring additional structural information via cost-incurring requests. AI helpers lack access to users' true goals, beliefs, and preferences and struggle to integrate diverse information effectively. We propose a social continual learning framework for causal knowledge acquisition and collaborative decision-making. It focuses on autonomous agents learning through dialogues, question-asking, and interaction in open, partially observable environments. A key component is a natural language oracle that answers the agent's queries about environmental mechanisms and states, refining causal understanding while balancing exploration or learning, and exploitation or knowledge use. Evaluation tasks inspired by developmental psychology emphasize causal reasoning and question-asking skills. They complement benchmarks by assessing the agent's ability to identify knowledge gaps, generate meaningful queries, and incrementally update reasoning. The framework also evaluates how knowledge acquisition costs are amortized across tasks within the same environment. We propose two architectures: 1) a system combining Large Language Models (LLMs) with the ReAct framework and question-generation, and 2) an advanced system with a causal world model, symbolic, graph-based, or subsymbolic, for reasoning and decision-making. The latter builds a causal knowledge graph for efficient inference and adaptability under constraints. Challenges include integrating causal reasoning into ReAct and optimizing exploration and question-asking in error-prone scenarios. Beyond applications, this framework models developmental processes combining causal reasoning, question generation, and social learning.