It is desirable to restrict the number of components (i.e., encourage sparsity) for

Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we challenge this implicit assumption and argue that reliability should be regarded as a first-class property of learned representations themselves. We propose a principled framework for reliable representation learning that explicitly models representation-level uncertainty and leverages structural constraints as inductive biases to regularize the space of feasible representations. Our approach introduces uncertainty-aware regularization directly in the representation space, encouraging representations that are not only predictive but also stable, well-calibrated, and robust to noise and structural perturbations. Structural constraints, such as sparsity, relational structure, or feature-group dependencies, are incorporated to define meaningful geometry and reduce spurious variability in learned representations, without assuming fully correct or noise-free structure. Importantly, the proposed framework is independent of specific model architectures and can be integrated with a wide range of representation learning methods.

Generalized Additive Models (GAMs) are a family of flexible and interpretable models with old roots in statistics. GAMs are often used with pairwise interactions to improve model accuracy while still retaining flexibility and interpretability but lead to computational challenges as we are dealing with order of $p^2$ terms. It is desirable to restrict the number of components (i.e., encourage sparsity) for easier interpretability, and better computational and statistical properties. Earlier approaches, considering sparse pairwise interactions, have limited scalability, especially when imposing additional structural interpretability constraints. We propose a flexible GRAND-SLAMIN framework that can learn GAMs with interactions under sparsity and additional structural constraints in a differentiable end-to-end fashion. We customize first-order gradient-based optimization to perform sparse backpropagation to exploit sparsity in additive effects for any differentiable loss function in a GPU-compatible manner. Additionally, we establish novel non-asymptotic prediction bounds for our estimators with tree-based shape functions. Numerical experiments on real-world datasets show that our toolkit performs favorably in terms of performance, variable selection and scalability when compared with popular toolkits to fit GAMs with interactions. Our work expands the landscape of interpretable modeling while maintaining prediction accuracy competitive with non-interpretable black-box models.

Large Language Model (LLM) agents have shown remarkable capabilities in reasoning and problem-solving when augmented with retrieval mechanisms [1, 2]. However, a critical challenge persists: ensuring that retrieved information maintains logical and structural consistency with the agent's current reasoning context. Traditional retrieval methods, such as vector similarity search, retrieve information based solely on semantic similarity, without considering structural relationships within knowledge bases. This limitation becomes particularly problematic in multi-hop reasoning scenarios, where an agent must traverse a knowledge graph to answer complex queries. When an agent is reasoning about a specific concept (the "anchor"), retrieving information from structurally disconnected parts of the knowledge graph can introduce inconsistencies and contradictions into the reasoning process. For example, if an agent is reasoning about "cloud computing architecture" starting from a specific node, retrieving information about unrelated topics that happen to be semantically similar can lead to incoherent reasoning chains due to lack of structural consistency. We propose Path-Constrained Retrieval (PCR), a retrieval method that enforces structural constraints by restricting the search space to nodes reachable from an anchor node in a knowledge graph.

This paper delves into designing stabilizing feedback control gains for continuous linear systems with unknown state matrix, in which the control is subject to a general structural constraint. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. We first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the Linear Quadratic Regulator (LQR) gain computation in the continuous-time setting. Subsequently, we transform this LQR formulation into a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. Theoretical guarantees are provided for stability and convergence of the structured RL (SRL) algorithm. The introduced RL framework is general and can be applied to any control structure. A special control structure enabled by this RL framework is distributed learning control which is necessary for many large-scale cyber-physical systems. As such, we validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

This paper proposes a composable fine-tuning method that integrates graph structural priors with modular adapters to address the high computational cost and structural instability faced by large-scale pre-trained models in multi-task adaptation. The method introduces a relation matrix to model dependencies among tasks, explicitly encoding correlations between nodes and paths into graph structural priors, which provide unified structural constraints for adapter weight allocation and path selection. Modular adapters are embedded into different layers through low-rank mapping and a pluggable mechanism, enabling efficient cross-task composition and reuse under prior guidance. This mechanism not only improves parameter efficiency and training stability but also alleviates path conflicts and redundant computation in multi-task scenarios. Furthermore, experiments on hyperparameter sensitivity, environmental sensitivity, and data sensitivity are conducted to systematically analyze key factors such as routing temperature, gating thresholds, and relation matrix regularization strength, verifying the consistency and superior performance of the method under structural constraints. The results demonstrate that the proposed framework significantly enhances task prediction accuracy, adapter weight allocation precision, and overall computational efficiency while maintaining model lightweight design, highlighting the synergistic advantages of graph priors and modular mechanisms in composable fine-tuning.

Matrix completion problems have been widely studied under special low dimensional structures such as low rank or structure induced by decomposable norms. In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by any norm regularization. We consider two estimators for the general problem of structured matrix completion, and provide unified upper bounds on the sample complexity and the estimation error. Our analysis relies on generic chaining, and we establish two intermediate results of independent interest: (a) in characterizing the size or complexity of low dimensional subsets in high dimensional ambient space, a certain partial complexity measure encountered in the analysis of matrix completion problems is characterized in terms of a well understood complexity measure of Gaussian widths, and (b) it is shown that a form of restricted strong convexity holds for matrix completion problems under general norm regularization. Further, we provide several non-trivial examples of structures included in our framework, notably including the recently proposed spectral k -support norm.

Controllable generation is a fundamental task in NLP with many applications, providing a basis for function calling to agentic communication. However, even state-of-the-art autoregressive Large Language Models (LLMs) today exhibit unreliability when required to generate structured output. Inspired by the current new diffusion-based large language models (dLLM), we realize that the architectural difference, especially the global information-sharing mechanism for language modeling, may be the key to unlock next-level controllable generation. Experiments demonstrate that our method substantially unlocks the dLLM's potential in controllable generation in terms of structure adherence, content fidelity, and faithfulness. These results establish new perspectives and practical pathways for deploying language models in controllable generation tasks. Controllable generation is a fundamental task in the era of LLMs. It provides the foundation for stable tool use, agentic communication, and interaction with existing application programming interfaces (APIs). Existing works demonstrate that structured output still poses significant challenges even for state-of-the-art autoregressive LLMs.

This study presents a system integration approach for planning schedules, sequences, tasks, and motions for reconfigurable robots to automatically disassemble constrained structures in a non-destructive manner. Such systems must adapt their configuration and coordination to the target structure, but the large and complex search space makes them prone to local optima. To address this, we integrate multiple robot arms equipped with different types of tools, together with a rotary stage, into a reconfigurable setup. This flexible system is based on a hierarchical optimization method that generates plans meeting multiple preferred conditions under mandatory requirements within a realistic timeframe. The approach employs two many-objective genetic algorithms for sequence and task planning with motion evaluations, followed by constraint programming for scheduling. Because sequence planning has a much larger search space, we introduce a chromosome initialization method tailored to constrained structures to mitigate the risk of local optima. Simulation results demonstrate that the proposed method effectively solves complex problems in reconfigurable robotic disassembly.