In the embedding phase, NIERT uniformly embeds both observed and target points. A learnable mask vector is introduced for target points lacking value data. The NIERT interpolator's core is a Transformer encoder with a masked self-attention mechanism, uniformly encoding observed and The NIERT, a Transformer encoder-only architecture that uniformly encodes observed points and models their correlations, exhibits superior interpolation accuracy. Our proposed architecture, specifically adapted to HINT's overall framework, introduces HINT employs residuals on observed points to estimate residuals on target points. Table 1: Statistics of the interpolation tasks used for training in each dataset.Dataset d Theoretical dataset II: Perlin is another synthetic assembly of interpolation tasks, specifically designed for the numerical interpolation of two-dimensional rough functions.

HINT consists of several sequentially arranged lightweight interpolation blocks.

Orientation learning plays a pivotal role in many tasks. However, the rotation group SO(3) is a Riemannian manifold. As a result, the distortion caused by non-Euclidean geometric nature introduces difficulties to the incorporation of local constraints, especially for the simultaneous incorporation of multiple local constraints. To address this issue, we propose the Angle-Axis Space-based orientation representation method to solve several orientation learning problems, including orientation adaptation and minimization of angular acceleration. Specifically, we propose a weighted average mechanism in SO(3) based on the angle-axis representation method. Our main idea is to generate multiple trajectories by considering different local constraints at different basepoints. Then these multiple trajectories are fused to generate a smooth trajectory by our proposed weighted average mechanism, achieving the goal to incorporate multiple local constraints simultaneously. Compared with existing solution, ours can address the distortion issue and make the off-theshelf Euclidean learning algorithm be re-applicable in non-Euclidean space. Simulation and Experimental evaluations validate that our solution can not only adapt orientations towards arbitrary desired via-points and cope with angular acceleration constraints, but also incorporate multiple local constraints simultaneously to achieve extra benefits, e.g., achieving smaller acceleration costs.

We report adversarial training and standard training.

We have included multiple references for knapsack solvers in the paper (including the book above).

A core challenge in program synthesis is taming the large space of possible programs. Since program synthesis is essentially a combinatorial search, the community has sought to leverage powerful combinatorial constraint solvers. Here, constraints are used to express the program semantics, but not as a potentially potent tool to remove unwanted programs. Recent inductive logic programming approaches introduce constraints on the program's syntax to be synthesized. These syntactic constraints allow for checking and propagating a constraint without executing the program, and thus for arbitrary operators. In this work, we leverage syntactic constraints to model program spaces, defining not just solutions that are feasible, but also ones that are likely useful. To demonstrate this idea, we introduce BART, a solver that efficiently propagates and solves these constraints. We evaluate BART on program space enumeration tasks, finding that the constraints eliminate up to 99 percent of the program space, and that modeling program spaces significantly reduces enumeration time.

Real-world planning problems require constant adaptation to changing requirements and balancing of competing constraints. However, current benchmarks for evaluating LLMs' planning capabilities primarily focus on static, single-turn scenarios. We introduce Flex-TravelPlanner, a benchmark that evaluates language models' ability to reason flexibly in dynamic planning scenarios. Building on the TravelPlanner dataset~\citep{xie2024travelplanner}, we introduce two novel evaluation settings: (1) sequential constraint introduction across multiple turns, and (2) scenarios with explicitly prioritized competing constraints. Our analysis of GPT-4o and Llama 3.1 70B reveals several key findings: models' performance on single-turn tasks poorly predicts their ability to adapt plans across multiple turns; constraint introduction order significantly affects performance; and models struggle with constraint prioritization, often incorrectly favoring newly introduced lower priority preferences over existing higher-priority constraints. These findings highlight the importance of evaluating LLMs in more realistic, dynamic planning scenarios and suggest specific directions for improving model performance on complex planning tasks. The code and dataset for our framework are publicly available at https://github.com/juhyunohh/FlexTravelBench.