We study square loss in a realizable time-series framework with martingale difference noise.

Deep learning models for medical image segmentation suffer significant performance drops due to distribution shifts, but the causal mechanisms behind these drops remain poorly understood. We extend causal attribution frameworks to high-dimensional segmentation tasks, quantifying how acquisition protocols and annotation variability independently contribute to performance degradation. We model the data-generating process through a causal graph and employ Shapley values to fairly attribute performance changes to individual mechanisms. Our framework addresses unique challenges in medical imaging: high-dimensional outputs, limited samples, and complex mechanism interactions. Validation on multiple sclerosis (MS) lesion segmentation across 4 centers and 7 annotators reveals context-dependent failure modes: annotation protocol shifts dominate when crossing annotators (7.4% $\pm$ 8.9% DSC attribution), while acquisition shifts dominate when crossing imaging centers (6.5% $\pm$ 9.1%). This mechanism-specific quantification enables practitioners to prioritize targeted interventions based on deployment context.

Modern data processing workflows frequently encounter ragged data: collections with variable-length elements that arise naturally in domains like natural language processing, scientific measurements, and autonomous AI agents. Existing workflow engines lack native support for tracking the shapes and dependencies inherent to ragged data, forcing users to manage complex indexing and dependency bookkeeping manually. We present Operon, a Rust-based workflow engine that addresses these challenges through a novel formalism of named dimensions with explicit dependency relations. Operon provides a domain-specific language where users declare pipelines with dimension annotations that are statically verified for correctness, while the runtime system dynamically schedules tasks as data shapes are incrementally discovered during execution. We formalize the mathematical foundation for reasoning about partial shapes and prove that Operon's incremental construction algorithm guarantees deterministic and confluent execution in parallel settings. The system's explicit modeling of partially-known states enables robust persistence and recovery mechanisms, while its per-task multi-queue architecture achieves efficient parallelism across heterogeneous task types. Empirical evaluation demonstrates that Operon outperforms an existing workflow engine with 14.94x baseline overhead reduction while maintaining near-linear end-to-end output rates as workloads scale, making it particularly suitable for large-scale data generation pipelines in machine learning applications.

We study square loss in a realizable time-series framework with martingale difference noise.

Discovering pure causes or driver variables in deterministic LTI systems is of vital importance in the data-driven reconstruction of causal networks. A recent work by Kathari and Tangirala, proposed in 2022, formulated the causal discovery method as a constraint identification problem. The constraints are identified using a dynamic iterative PCA (DIPCA)-based approach for dynamical systems corrupted with Gaussian measurement errors. The DIPCA-based method works efficiently for dynamical systems devoid of any algebraic relations. However, several dynamical systems operate under feedback control and/or are coupled with conservation laws, leading to differential-algebraic (DAE) or mixed causal systems. In this work, a method, namely the partition of variables (PoV), for causal discovery in LTI-DAE systems is proposed. This method is superior to the method that was presented by Kathari and Tangirala (2022), as PoV also works for pure dynamical systems, which are devoid of algebraic equations. The proposed method identifies the causal drivers up to a minimal subset. PoV deploys DIPCA to first determine the number of algebraic relations ($n_a$), the number of dynamical relations ($n_d$) and the constraint matrix. Subsequently, the subsets are identified through an admissible partitioning of the constraint matrix by finding the condition number of it. Case studies are presented to demonstrate the effectiveness of the proposed method.

Decision trees are a fundamental tool in machine learning for representing, classifying, and generalizing data. It is desirable to construct ``small'' decision trees, by minimizing either the \textit{size} ($s$) or the \textit{depth} $(d)$ of the \textit{decision tree} (\textsc{DT}). Recently, the parameterized complexity of \textsc{Decision Tree Learning} has attracted a lot of attention. We consider a generalization of \textsc{Decision Tree Learning} where given a \textit{classification instance} $E$ and an integer $t$, the task is to find a ``small'' \textsc{DT} that disagrees with $E$ in at most $t$ examples. We consider two problems: \textsc{DTSO} and \textsc{DTDO}, where the goal is to construct a \textsc{DT} minimizing $s$ and $d$, respectively. We first establish that both \textsc{DTSO} and \textsc{DTDO} are W[1]-hard when parameterized by $s+δ_{max}$ and $d+δ_{max}$, respectively, where $δ_{max}$ is the maximum number of features in which two differently labeled examples can differ. We complement this result by showing that these problems become \textsc{FPT} if we include the parameter $t$. We also consider the kernelization complexity of these problems and establish several positive and negative results for both \textsc{DTSO} and \textsc{DTDO}.

Drift vehicle control offers valuable insights to support safe autonomous driving in extreme conditions, which hinges on tracking a particular path while maintaining the vehicle states near the drift equilibrium points (DEP). However, conventional tracking methods are not adaptable for drift vehicles due to their opposite steering angle and yaw rate. In this paper, we propose an adaptive path tracking (APT) control method to dynamically adjust drift states to follow the reference path, improving the commonly utilized predictive path tracking methods with released computation burden. Furthermore, existing control strategies necessitate a precise system model to calculate the DEP, which can be more intractable due to the highly nonlinear drift dynamics and sensitive vehicle parameters. To tackle this problem, an adaptive learning-based model predictive control (ALMPC) strategy is proposed based on the APT method, where an upper-level Bayesian optimization is employed to learn the DEP and APT control law to instruct a lower-level MPC drift controller. This hierarchical system architecture can also resolve the inherent control conflict between path tracking and drifting by separating these objectives into different layers. The ALMPC strategy is verified on the Matlab-Carsim platform, and simulation results demonstrate its effectiveness in controlling the drift vehicle to follow a clothoid-based reference path even with the misidentified road friction parameter.

While large language models (LLMs) have shown promising capabilities as zero-shot planners for embodied agents, their inability to learn from experience and build persistent mental models limits their robustness in complex open-world environments like Minecraft. We introduce MINDSTORES, an experience-augmented planning framework that enables embodied agents to build and leverage mental models through natural interaction with their environment. Drawing inspiration from how humans construct and refine cognitive mental models, our approach extends existing zero-shot LLM planning by maintaining a database of past experiences that informs future planning iterations. The key innovation is representing accumulated experiences as natural language embeddings of (state, task, plan, outcome) tuples, which can then be efficiently retrieved and reasoned over by an LLM planner to generate insights and guide plan refinement for novel states and tasks. Through extensive experiments in the MineDojo environment, a simulation environment for agents in Minecraft that provides low-level controls for Minecraft, we find that MINDSTORES learns and applies its knowledge significantly better than existing memory-based LLM planners while maintaining the flexibility and generalization benefits of zero-shot approaches, representing an important step toward more capable embodied AI systems that can learn continuously through natural experience.