arXiv:2603.01077v1 Announce Type: cross Abstract: We extend the unified kernel framework for transport equations and Koopman eigenfunctions, developed in previous work by the authors for deterministic systems, to stochastic differential equations (SDEs). In the deterministic setting, three analytically grounded constructions-Lions-type variational principles, Green’s function convolution, and resolvent operators along characteristic flows–were shown to yield identical reproducing kernels. For stochastic systems, the Koopman generator includes a second-order diffusion term, transforming the first-order hyperbolic transport equation into a second-order elliptic-parabolic […]

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Wireless communications face both opportunities and challenges due to the coexistence of 5G New Radio (NR) high-band, 5G mid-band, and 5G low-band technologies. Each technology uses both licensed and unlicensed spectrum to operate in separate frequency bands. For example, 5G NR uses the high-band of 24+ GHz, the mid-band of 2-6 GHz, or the low-band of less than 2 GHz, including the 5 GHz band via Licensed-Assisted Access (LAA). With the use of sophisticated coexistence mechanisms and optimization […]

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arXiv:2601.18840v1 Announce Type: new Abstract: Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic programming, this approach has received relatively less attention, mainly because it is often less efficient in practice and can be more difficult to extend to model-free settings such as reinforcement learning. Nonetheless, Bellman residual minimization has several advantages that make it worth investigating, such […]

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arXiv:2601.20882v1 Announce Type: new Abstract: Even though demonstrating extraordinary capabilities in code generation and software issue resolving, AI agents’ capabilities in the full software DevOps cycle are still unknown. Different from pure code generation, handling the DevOps cycle in real-world software, including developing, deploying, and managing, requires analyzing large-scale projects, understanding dynamic program behaviors, leveraging domain-specific tools, and making sequential decisions. However, existing benchmarks focus on isolated problems and lack environments and tool interfaces for DevOps. We introduce […]

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arXiv:2506.17764v2 Announce Type: replace Abstract: Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for band-limited functions from noisy input-output measurements, by working in a Paley-Wiener reproducing kernel Hilbert space. Kernel norm bounds are tightened using a uniformly-randomized Hoeffding’s inequality for small samples and an empirical Bernstein bound for larger ones. We derive an approximate threshold, based […]

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arXiv:2510.15337v2 Announce Type: replace Abstract: Transfer learning is a key component of modern machine learning, enhancing the performance of target tasks by leveraging diverse data sources. Simultaneously, overparameterized models such as the minimum-$ell_2$-norm interpolator (MNI) in high-dimensional linear regression have garnered significant attention for their remarkable generalization capabilities, a property known as benign overfitting. Despite their individual importance, the intersection of transfer learning and MNI remains largely unexplored. Our research bridges this gap by proposing a novel two-step […]

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Unsupervised multi-view clustering (MVC) aims to partition data into meaningful groups by leveraging complementary information from multiple views without labels, yet a central challenge is to obtain a reliable shared structural signal to guide representation learning and cross-view alignment under view discrepancy and noise. Existing approaches often rely on magnitude-only affinities or early pseudo targets, which can be unstable when different views induce relations with comparable strengths but contradictory directional tendencies, thereby distorting the global spectral geometry and […]

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The most counterintuitive secret about startups is that it’s often easier to succeed with a hard startup than an easy one.  A hard startup requires a lot more money, time, coordination, or technological development than most startups. A good hard startup is one that will be valuable if it works (not all hard problems are worth solving!). I remember when Instagram started to get really popular—it felt like you couldn’t go a day without hearing about another photo […]

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arXiv:2601.09718v1 Announce Type: new Abstract: This study investigates how to efficiently build a domain-specialized large language model (LLM) for statistics using the lightweight LLaMA-3.2-3B family as the foundation model (FM). We systematically compare three multi-stage training pipelines, starting from a base FM with no instruction-following capability, a base FM augmented with post-hoc instruction tuning, and an instruction-tuned FM with strong general reasoning abilities across continual pretraining, supervised fine-tuning (SFT), reinforcement learning from human feedback (RLHF) preference alignment, and […]

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