We propose Differentiable Temporal Logic (DTL), a model-agnostic framework that introduces temporal constraints to deep networks. DTL treats the outputs of a network as a truth assignment of a temporal logic formula, and computes a temporal logic loss reflecting the consistency between the output and the constraints. We propose a comprehensive set of constraints, which are implicit in data annotations, and incorporate them with deep networks via DTL. We evaluate the effectiveness of DTL on the temporal action segmentation task and observe improved performance and reduced logical errors in the output of different task models. Furthermore, we provide an extensive analysis to visualize the desirable effects of DTL. Figure 1: A video of activity "coffee preparation". The colored bars, from the top to the bottom, show the ground truth (GT), the predictions from a baseline [ 15 ], and the predictions from the baseline trained with DTL, respectively.

Work done while at Harvard University.

We thank all reviewers for their insightful comments. "repulsive/diverse functions" also makes it more likely to violate a constraint; for example, Figure S1 below shows that (instead of 50). We acknowledge points about similarity to [18] made by R4. Equation (1) in Definition 4.2 should read:

On the conceptual front, we identify connections between these three problems and present a framework that brings all these challenges under a common umbrella. We then present a (randomized) algorithm for reviewer assignment that can optimally solve the reviewer-assignment problem under any given constraints on the probability of assignment for any reviewer-paper pair.

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

Recent advances in 3D Gaussian splatting have significantly improved real-time novel view synthesis, yet insufficient geometric constraints during scene optimization often result in blurred reconstructions of fine-grained details, particularly in regions with high-frequency textures and sharp discontinuities. To address this, we propose a comprehensive optimization framework integrating multisample anti-aliasing (MSAA) with dual geometric constraints. Our system computes pixel colors through adaptive blending of quadruple subsamples, effectively reducing aliasing artifacts in high-frequency components. The framework introduces two constraints: (a) an adaptive weighting strategy that prioritizes under-reconstructed regions through dynamic gradient analysis, and (b) gradient differential constraints enforcing geometric regularization at object boundaries. This targeted optimization enables the model to allocate computational resources preferentially to critical regions requiring refinement while maintaining global consistency. Extensive experimental evaluations across multiple benchmarks demonstrate that our method achieves state-of-the-art performance in detail preservation, particularly in preserving high-frequency textures and sharp discontinuities, while maintaining real-time rendering efficiency. Quantitative metrics and perceptual studies confirm statistically significant improvements over baseline approaches in both structural similarity (SSIM) and perceptual quality (LPIPS).

Internet of Things (IoT) systems increasingly operate in environments where devices must respond in real time while managing fluctuating resource constraints, including energy and bandwidth. Yet, current approaches often fall short in addressing scenarios where operational constraints evolve over time. To address these limitations, we propose a novel Budgeted Multi-Armed Bandit framework tailored for IoT applications with dynamic operational limits. Our model introduces a decaying violation budget, which permits limited constraint violations early in the learning process and gradually enforces stricter compliance over time. We present the Budgeted Upper Confidence Bound (UCB) algorithm, which adaptively balances performance optimization and compliance with time-varying constraints. We provide theoretical guarantees showing that Budgeted UCB achieves sublinear regret and logarithmic constraint violations over the learning horizon. Extensive simulations in a wireless communication setting show that our approach achieves faster adaptation and better constraint satisfaction than standard online learning methods. These results highlight the framework's potential for building adaptive, resource-aware IoT systems.