arXiv:2408.09112v2 Announce Type: replace Abstract: Reinforcement learning policies parametrized by deep neural networks have achieved strong performance for continuous control, yet even small input perturbations may lead to unpredictable behavior. This sensitivity limits their use in safety-critical domains, where robustness guarantees are required. Our work addresses this gap between state-of-the-art adversarial training methods and formal verification to train verifiably robust agents. Previous works train networks with individual adversarial perturbations, making them only robust against the specific adversarial attacks used. In contrast, our approach propagates entire perturbed input sets, enclosing all possible adversarial attacks within a single network pass. We leverage this to explicitly penalize the size of the output set (minimizing closed-loop uncertainty) and thereby make the actor robust against all possible attacks. This is realized by the use of set-based policy gradients, where each output within the set has a different gradient, thereby balancing the accuracy and robustness of the network. Doing so, we achieve formal verifiability across different verification frameworks for up to 9 times larger input perturbations compared to standard reinforcement learning and improve certified worst-case performance.
Science Journals
arXiv:2607.04609v1 Announce Type: new Abstract: Vision-Language-Action (VLA) policies that execute fixed-length action chunks can exhibit multimodal bifurcation: a cross-chunk inconsistency in which adjacent chunks generated from independent Gaussian latents can converge to incompatible trajectory modes, producing abrupt discontinuities at chunk boundaries. Existing remedies either require backpropagation through the policy at each denoising step, rely on rejection sampling, or require retraining, each trading computational cost or task reliability for smoother transitions. We propose SEAM (Smooth Execution of Action-Chunked Motion), a training-free inference-time method for flow matching VLAs. SEAM exploits a simple synchronous-execution insight: after the robot consumes the executed prefix, the previous chunk's unexecuted tail is already available as an analytic consistency reference. Its core mechanism, Velocity-guided Loss Steering (VLS), derives a time-dependent target from this tail and applies a closed-form correction after each Euler step without backpropagating through the policy network. On LIBERO-10 with pi_0.5, SEAM reduces boundary jerk by 28%, reduces chunk transition discontinuity by 27%, preserves baseline-level task success, and keeps denoising-loop cost near the unguided baseline.
arXiv:2408.13378v5 Announce Type: replace Abstract: Workflows in drug-target interaction (DTI) assessment require integrating heterogeneous data from predictive models, curated resources, and observations from experimental literature. This evidence can be incomplete or conflicting. DrugAgent is a large language model (LLM)-based multi-agent system focused on DTI evidence integration that integrates outputs from machine learning, knowledge graph, and retrieval-augmented generation (RAG) agents. DrugAgent converts agent outputs into interpretable representations, then summarizes conflict across the evidence. We evaluated DrugAgent on kinase screening data of 900 pairs spanning 178 kinases and 42 inhibitors, and an androgen receptor antagonist screening benchmark. On the kinase dataset, LLM-as-a-Judge evaluation indicated outputs were faithful to input evidence in 98.8% of cases. Biological plausibility of returned summarization was high (scores 3-4 out of 5) across ground-truth classes: 79% of Weak activity labels cases (81% for Moderate/77% Strong); Strong cases received higher scores than Weak/Moderate. Label stability showed 98% agreement across runs. Results on the antagonist benchmark were consistent with the kinase dataset. Retrieved literature provided the greatest benefit when direct drug-target evidence was available, highlighting the importance of evidence availability for RAG-based integration. DrugAgent provides heterogeneous evidence-grounded DTI assessment, complementing standalone DTI prediction. We provide strategies to model agreement, conflict, and uncertainty in biomedical evidence integration. Code: https://github.com/sciluna/DrugAgent.
arXiv:2409.14086v2 Announce Type: replace Abstract: There have been several studies on automatically generating piano covers, and recent advancements in deep learning have enabled the creation of more sophisticated covers. However, existing automatic piano cover models still have room for improvement in terms of expressiveness and fidelity to the original. To address these issues, we propose a learning algorithm called AMT-APC, which leverages the capabilities of automatic music transcription models. By utilizing the strengths of well-established automatic music transcription models, we aim to improve the accuracy of piano cover generation. Our experiments demonstrate that the AMT-APC model reproduces original tracks more accurately than any existing models.
arXiv:2410.20696v3 Announce Type: replace Abstract: Case studies have shown that software disasters snowball from technical issues to catastrophes through humans covering up problems rather than addressing them and empirical research has found the psychological safety of software engineers to discuss and address problems to be foundational to improving project success. However, the failure to do so can be attributed to psychological factors like loss aversion. We conduct a large-scale study of the experiences of 600 software engineers in the UK and USA on project success experiences. Empirical evaluation finds that approaches like ensuring clear requirements before the start of development, when loss aversion is at its lowest, correlated to 97% higher project success. The freedom of software engineers to discuss and address problems correlates with 87% higher success rates. The findings support the development of software development methodologies with a greater focus on human factors in preventing failure.
arXiv:2607.04225v1 Announce Type: new Abstract: Future sixth generation (6G) communications are expected to support robotic control tasks in applications such as industrial automation and emergency response, where sensors, computing units, and robots are interconnected via nervous system-like networks to form sensing-communication-computing-control (SC3) closed loops. However, the limited battery capacities of devices within these SC3 loops constrain operational duration and degrade control efficiency, particularly in remote or post-disaster scenarios. To address this challenge, wireless power transfer (WPT) can be leveraged to provide continuous energy supply for SC3 closed loops. In this paper, we investigate a wireless-powered SC3 system, where a satellite transfers energy via radio frequency (RF) signals to support the communication and computing processes of multiple SC3 closed loops. By accounting for the intricate coupling among computing, communication, and energy transfer, we propose a holistic design framework to enhance overall control performance. Specifically, we adopt the linear quadratic regulator (LQR) cost as the performance metric and formulate a sum LQR cost minimization problem. The uplink/downlink transmit power, bandwidth allocation, computing capability, communication/computing time allocation, and WPT power allocation are jointly optimized. We recast the problem into a more tractable form and develop an iterative algorithm to solve it. For the special case of a single loop, we further analyze the properties of optimal solutions in energy-limited scenarios to provide insights for practical parameter configuration. Simulation results demonstrate the performance gains of the proposed scheme.
arXiv:2607.04287v1 Announce Type: new Abstract: The Weighted Center} problem takes as its input a graph $G=(V,E)$ together with a profile $\pi$ such that every vertex $v$ is mapped to some nonnegative multiplicative weight $\pi(v)$. Its output must be some vertex $c$ minimizing $\max\{\pi(v)d_G(c,v) : v \in V\}$. The classic Center problem corresponds to the case where $\pi(v) =1$ for every vertex $v$. In the literature, various almost linear-time algorithms have been proposed for the Center problem on some well-structured classes of graphs. By contrast, similarly efficient algorithms for the Weighted Center problem have been scarce. We investigate how the Gromov hyperbolicity, alone or in combination with other metric and geometric properties on graphs, can be used in the design of exact and approximate almost linear-time algorithms for the Weighted Center problem. In particular, we derive almost optimal algorithms for the following well-studied classes of graphs: chordal graphs, distance-hereditary graphs (both in $\mathcal{O}(m)$ time), dually chordal graphs and chordal bipartite graphs (both in $\mathcal{O}(m\log{n})$ time).
arXiv:2607.04105v1 Announce Type: new Abstract: The curve shortening--DeTurck flow introduced by Elliott and Fritz (IMA J. Numer. Anal. 37(2): 543--603, 2017) is a reparameterization of the curve shortening flow via the DeTurck trick. For corresponding discrete schemes, although the $H^1$-error estimate has been established, the optimal $L^2$-error estimate remains open due to technical difficulties. In this paper, we prove optimal $L^2$-error estimates for linearized Euler and Crank--Nicolson discretizations combined with finite elements of degree $k\ge 1$ in space. Moreover, we provide an extrinsic approach to derive the curve shortening--DeTurck flow. Numerical experiments are presented to illustrate the mesh distribution properties and to verify the convergence rates in both space and time.
arXiv:2410.24053v4 Announce Type: replace Abstract: We demonstrate the inter-translatability of proofs between the most prominent sequent-based formalisms for G\"odel-L\"ob provability logic. In particular, we consider Sambin and Valentini's sequent system GLseq, Shamkanov's non-wellfounded and cyclic sequent systems GL$\infty$ and GLcirc, Poggiolesi's tree-hypersequent system CSGL$^{*}$, and Negri's labeled sequent system G3KGL. Shamkanov provided proof-theoretic correspondences between GLseq, GL$\infty$, and GLcirc, and Gor\'e and Ramanayake showed how proofs could be transformed between CSGL$^{*}$ and G3KGL; however, the exact nature of proof transformations between the former three systems and the latter two systems has remained an open problem. We solve this open problem by showing how to restructure tree-hypersequent proofs into an end-active form and introduce a novel 'linearization technique' that transforms such proofs into linear nested sequent proofs. As a result, we obtain a new proof-theoretic tool for extracting linear nested sequent systems from tree-hypersequent systems, which yields the first cut-free linear nested sequent calculus LNGL for G\"odel-L\"ob provability logic. We show how to transform proofs in LNGL into a certain normal form, where proofs repeat in stages of modal and local rule applications, and which are translatable into GLseq and G3KGL proofs. These new syntactic transformations, together with those mentioned above, establish full proof-theoretic correspondences between GLseq, GL$\infty$, GLcirc, CSGL$^{*}$, G3KGL, and LNGL while also giving (to the best of the author's knowledge) the first constructive proof mappings between structural (viz. labeled, tree-hypersequent, and linear nested sequent) systems and a cyclic sequent system.
arXiv:2607.04147v1 Announce Type: new Abstract: Automated fine-grained perception of calligraphy styles--a task vital to cultural heritage preservation--remains a critical challenge for Large Vision-Language Models (LVLMs), largely constrained by existing datasets that suffer from modal mixture and flattened labels. To bridge this gap, we introduce HCSU, the first comprehensive dataset tailored for fine-grained Historical Calligraphy Style Understanding. HCSU comprises 39,307 meticulously curated character images from 49 historically prominent calligraphers across 10 dynasties, systematically decoupling authentic ink manuscripts (Tie) from stone rubbings (Bei) to resolve the long-standing modal mixture problem. Moving beyond conventional flattened labels, HCSU provides hierarchical expert-written aesthetic descriptions, enabling two rigorous evaluation protocols: fine-grained style discrimination and interpretable aesthetic reasoning. Extensive evaluations reveal a persistent gap between calligraphy-related knowledge and visually grounded style perception: state-of-the-art LVLMs show non-trivial performance but remain sensitive to script-level, textual, and source-specific cues, and often struggle to ground aesthetic judgments in fine-grained brushwork evidence. Ultimately, the HCSU benchmark exposes fundamental limitations in current multimodal architectures, aiming to inspire the evolution of expert-level visual reasoning for cultural heritage preservation. The dataset is available at https://huggingface.co/datasets/Tongji209/HCSU.
arXiv:2411.11449v3 Announce Type: replace Abstract: Deploying AI systems in public institutions can have far-reaching consequences for many people, making it a matter of public interest. Providing opportunities for stakeholders to come together, understand these systems, and debate their merits and harms is thus essential. Explainable AI often focuses on individuals, but deliberation benefits from group settings, which are underexplored. To address this gap, we present findings from an interview study with 8 focus groups and 12 individuals. Our findings provide insight into how explanations support AI novices in deliberating alone and in groups. Participants used modular explanations with four information categories to solve tasks and decide about an AI system's deployment. We found that the explanations supported groups in creating shared understanding and in finding arguments for and against the system's deployment. In comparison, individual participants engaged with explanations in more depth and performed better in the study tasks, but missed an exchange with others. Based on our findings, we provide suggestions on how explanations should be designed to work in group settings and describe their potential use in real-world contexts. With this, our contributions inform XAI research that aims to enable AI novices to understand and deliberate AI systems in the public sector.
arXiv:2412.00393v3 Announce Type: replace Abstract: Analyzing process data at varying levels of granularity is important to derive actionable insights and support informed decision-making. Object-Centric Event Data (OCED) enhances process mining by capturing interactions among events and multiple objects, leading to the discovery of more detailed and realistic yet complex process models. The lack of methods to adjust the granularity of the analysis prevents users from leveraging the full potential of Object-Centric Process Mining (OCPM). To address this gap, we propose four operations: drill-down, roll-up, unfold, and fold, which enable analysts to change the granularity of analysis when working with Object-Centric Event Logs (OCEL). These operations allow analysts to seamlessly transition between detailed and aggregated process models, facilitating the discovery of insights that require varying levels of abstraction. We formally define these operations and implement them in an open-source Python library. To validate their utility, we applied the approach to real-world OCEL data extracted from a learning management system, covering a four-year period and approximately 400 students, as a case of object-centric educational process mining. This case study shows significant improvements in the precision and fitness of the discovered models after applying the operations. In addition, we evaluate the scalability of the operators on large, publicly available OCELs derived from the Business Process Intelligence Challenge datasets, demonstrating that the operations remain computationally feasible on industrial-scale event logs. This approach can empower analysts to perform more flexible and comprehensive process exploration, unlocking actionable insights through flexible granularity adjustments.
arXiv:2607.04156v1 Announce Type: new Abstract: Scientific equation discovery must combine broad domain priors with strict numerical testing. Symbolic regression supplies numerical grounding but faces a combinatorial search space, whereas many language-model systems ask the model to propose or select formulas directly. We test a different division of labour. We compare role specifications in which the language model acts as equation author, candidate decider or search controller, alongside end-to-end language-model and purely numerical baselines. In the controller setting we propose here, implemented as LLM-PySR, language models specify variables, operators, transformations and search depth; symbolic regression enumerates and fits expressions; and deterministic metrics govern retention. Across 74 AI-Feynman equations and seven complex formula-recovery tasks, search control achieved the strongest observed balance of accuracy, complexity, stability and cost. On an independent battery dataset, LLM-PySR identified a compact piecewise-linear relation between early voltage-curve displacement and cycle life. The results suggest that language models should shape hypothesis exploration rather than decide which equations survive.
arXiv:2607.04163v1 Announce Type: new Abstract: Large Vision-Language Models (LVLMs) have achieved remarkable progress in visual understanding tasks such as image captioning and visual question answering. However, they remain susceptible to hallucinations, generating content that is inconsistent with the actual visual input. Existing methods primarily intervene at the decoding stage, while overlooking a critical source of hallucinations: irrelevant or noisy visual tokens that mislead the decoding process. To address this issue, we propose SeeMe, a training-free framework that introduces the concept of feature engineering from traditional machine learning into LVLMs. SeeMe restructures visual tokens through a three-stage token engineering process to suppress hallucination sources while preserving informative visual evidence. Experiments on MME, POPE, and AMBER benchmarks across four LVLMs demonstrate that SeeMe consistently reduces hallucinations and improves output consistency, providing a novel perspective for mitigating hallucinations in LVLMs.
arXiv:2412.20750v4 Announce Type: replace Abstract: Large-scale Vision-Language Models (VLMs) have achieved notable progress in aligning visual inputs with text. However, their ability to deeply understand the unique physical properties of non-RGB vision sensor images remains limited. In this paper, we revisit and analyze these limitations and introduce a novel, cost-efficient paradigm that significantly advances sensor image understanding-without requiring extensive training data or any modifications to the existing VLM architectures. Specifically, we propose Sensor-Aware Attributes Fine-Tuning (SAFT) with the Diverse Negative Attributes (DNA) optimization, which leverages minimal sensor-specific data to enable robust learning of non-RGB characteristics and overcome RGB-centric biases inherent in current VLMs. In addition, we present VS-TDX-the first comprehensive, public benchmark designed to rigorously evaluate VLMs' sensor-specific understanding across diverse and realistic scenarios. Through extensive experiments on VLMs and various sensor modalities, we validate that our method consistently delivers superior performance and generalization under resource-constrained and architecture-invariant settings. Our approach provides a practical advance towards scalable deployment of VLMs in increasingly sensor-diverse real-world environments.
arXiv:2501.14750v3 Announce Type: replace Abstract: Carbon emissions significantly contribute to climate change, and carbon credits have emerged as a key tool for mitigating environmental damage and helping organizations manage their carbon footprint. Despite their growing importance across sectors, fully leveraging carbon credits remains challenging. This study explores engineering practices and fintech solutions to enhance carbon emission management. We first review the negative impacts of carbon emission non-disclosure, revealing its adverse effects on financial stability and market value. Organizations are encouraged to actively manage emissions and disclose relevant data to mitigate risks. Next, we analyze factors influencing carbon prices and review advanced prediction algorithms that optimize carbon credit purchasing strategies, reducing costs and improving efficiency. Additionally, we examine corporate carbon emission prediction models, which offer accurate performance assessments and aid in planning future carbon credit needs. By integrating carbon price and emission predictions, we propose research directions, including corporate carbon management cost forecasting. This study provides a foundation for future quantitative research on the financial and market impacts of carbon management practices and is the first systematic review focusing on computing solutions and engineering practices for carbon credits.
arXiv:2607.04169v1 Announce Type: new Abstract: Recent research has achieved remarkable novel view rendering and scene reconstruction results with Neural Radiance Field (NeRF), including extensions to the LiDAR modality. Few studies have, however, explored the key design differences between RGB NeRFs and LiDAR NeRFs, particularly considering their underlying working principles. In this work, we provide both theoretical and empirical evidence suggesting that the density of volume sampling plays a significant role in LiDAR NeRF. Based on this finding, we propose a novel Neural LiDAR Bundle Adjustment (NeLD-BA) algorithm, which is tailored using efficient volume sampling of LiDAR rays for joint optimization of LiDAR map and poses. Extensive experiments are performed using the Newer College and FusionPortable datasets to demonstrate the proposed NeLD-BA's state-of-the-art performance in multi-view point cloud registration and 3D mapping. We will open-source our code for the community.
arXiv:2607.04808v1 Announce Type: new Abstract: We introduce an adjoint-based reduced-order model framework for fast and accurate estimation of quantities of interest for many-query linear problems. The method builds a reduced-order model with respect to the adjoint problem, thus bypassing the solution of the primal problem and drastically reducing computational cost. It creates a surrogate model that is independent of the loading configurations. It enables fast evaluation across multiple load cases and the generation of virtual charts to support decision-making. Numerical experiments on the Poisson equation and a plane-stress elasticity problem demonstrate that the adjoint reduced-order model converges rapidly, outperforms its primal counterpart, and provides reliable estimates of the quantities of interest. Importantly, it is often more practical to parameterize a kernel function than an entire set of external loads, making the method generic and particularly suited for early-stage prototyping and design optimization.
arXiv:2503.02368v4 Announce Type: replace Abstract: While guided decoding, especially value-guided methods, has emerged as a cost-effective alternative for controlling language model outputs without re-training models, its effectiveness is limited by the accuracy of the value function. We identify that this inaccuracy stems from a core distributional gap: existing methods train static value functions on trajectories sampled exclusively from the base policy, which inherently confines their training to a narrow and suboptimal view of the potential output space. We propose Iterative Value Refinement, a evolutionary framework designed to narrow this gap. It employs Value Exploration to provide a more comprehensive and robust training signal, complemented by Iterative Self-Refinement, which uses the improved value function from one iteration to guide the generation of higher-quality data for the next. Extensive experiments on text summarization, multi-turn dialogue, and instruction following demonstrate the effectiveness of our framework in aligning language models. Our approach not only achieves alignment but also significantly reduces computational costs by leveraging principled value function optimization for efficient and effective control.
arXiv:2607.04235v1 Announce Type: new Abstract: Large language model agents operate in partially observable, long-horizon settings where obtaining supervision remains a major bottleneck. We address this by utilizing a source of supervision overlooked in existing post-training methods: unintended yet successful goals embedded within agent rollouts. Specifically, we introduce Hindsight Supervised Learning (HSL), where an auxiliary LLM reviews each completed trajectory and relabels it with all of the natural-language goals the agent actually achieved. HSL then pairs the trajectory with its relabeled goals and uses these pairs for additional fine-tuning. To mitigate suboptimality in the relabeled data, we propose two learning techniques for HSL, irrelevant-action masking and sample reweighting. Our experiments show that HSL is flexible and compatible with existing post-training pipelines. It improves both SFT and DPO, with larger gains on long-horizon tasks with more diverse goal spaces. Moreover, HSL is sample-efficient: on ALFWorld, it surpasses baselines trained on the full dataset while using only one quarter of the ground-truth demonstrations.
arXiv:2607.04247v1 Announce Type: new Abstract: Spectral Galerkin methods are renowned for high-precision eigenvalue approximation, yet a rigorous lower bound obtained directly from a spectral discretisation has remained unavailable: the classical Kato and Weinstein--Temple enclosures do apply, but require a~priori information on a neighbouring eigenvalue. This paper resolves the issue by extending the author's projection-based framework for guaranteed lower eigenvalue bounds -- so far realised only through finite element methods -- to conforming spectral Galerkin methods. For trial spaces of exact eigenfunctions the required projection constant is the closed-form optimal value $C_N=\lambda_{M+1}^{-1/2}$, the inverse square root of the first omitted eigenvalue. For $-\Delta+V$ with $0\le V\in L^\infty$, a \emph{projection-gap estimate} yields an explicit constant for the standard Galerkin matrix (exact at $V=0$), and a composite discretisation removes the $||V||_{L^\infty}$-dependence for large potentials. With Neumann domain truncation these give certified two-sided bounds on $R^d$; for two benchmark potentials on $R^2$ the spectral enclosures match or surpass certified finite element ones at two orders of magnitude fewer degrees of freedom. The same auxiliary-projector mechanism extends to singular potentials with an unbounded $L^\infty$ norm -- in particular to attractive Coulomb singularities in three dimensions, via a localised Hardy inequality -- which we develop in a companion paper.
arXiv:2503.06643v2 Announce Type: replace Abstract: In this paper, we tackle a critical challenge in model evaluation: how to keep code benchmarks useful when models might have already seen them during training. We introduce a novel solution, dynamic benchmarking framework, to address this challenge. Given a code understanding or reasoning benchmark, our framework dynamically transforms each input, i.e., programs, with various semantic-preserving mutations to build a syntactically new while semantically identical benchmark. We evaluated 10 popular language models on our dynamic benchmarks. Our evaluation reveals several interesting or surprising findings: (1) all models perform significantly worse than before, (2) the ranking between some models shifts dramatically, and (3) dynamic benchmarks can resist against the data contamination problem.
arXiv:2607.04255v1 Announce Type: new Abstract: With the development of low altitude intelligent systems, multiple unmanned aerial vehicles (UAVs) can collaboratively execute more complex tasks. Conventional task allocation methods usually regard tasks and UAVs as isolated entities, making it difficult to capture task dependencies and UAV communication relationships. To address this issue, this paper proposes a dual heterogeneous graph learning based UAV task allocation method. A directed task graph is constructed to represent task dependencies and encode task resource requirements, while an undirected UAV communication graph is built to model communication relationships and encode UAV resource states. The task allocation problem is formulated as a structural matching problem between the task graph and the UAV communication graph. A graph attention network based feature extraction method is introduced to learn structural representations from both graphs through message passing. A cross attention mechanism is further integrated with proximal policy optimization to optimize the matching between task nodes and UAV nodes for task allocation. Simulation results demonstrate that the proposed method achieves a higher task completion rate and shorter task completion time than benchmark methods under different evaluation settings. Furthermore, a UAV sensing and computing application is developed on the AirSim simulation platform. A large language model is employed to convert natural language task requirements into a structured task graph for autonomous UAV task execution, demonstrating the potential of the proposed framework for natural language driven UAV mission planning and execution.
arXiv:2503.20666v2 Announce Type: replace Abstract: Thematic analysis (TA) is a widely used qualitative approach for uncovering latent meanings in unstructured text data. TA provides valuable insights in healthcare but is resource-intensive. Large Language Models (LLMs) have been introduced to perform TA, yet their applications in high-stakes healthcare settings, particularly for qualitative clinical interview analysis, remain limited. Here, we propose TAMA: A Human-AI Collaborative Thematic Analysis framework using Multi-Agent LLMs for clinical interviews. We leverage the scalability and coherence of multi-agent systems through structured conversations between agents and coordinate the expertise of cardiac experts in TA. Using interview transcripts from parents of children with Anomalous Aortic Origin of a Coronary Artery (AAOCA), a rare congenital heart disease, we demonstrate that TAMA outperforms single-agent LLM TA approaches, achieving higher thematic hit rate, coverage, and distinctiveness. TAMA demonstrates strong potential for automated TA in clinical settings by leveraging multi-agent LLM systems with human-in-the-loop integration by enhancing quality while significantly reducing manual workload. The full implementation is publicly available at https://github.com/Charlie-Yi-SJ/TAMA.
arXiv:2607.04356v1 Announce Type: new Abstract: Bayesian Optimization (BO) generally begins with an initialization phase: a batch of $n_0$ uninformed evaluations. The choice of $n_0$ remains largely heuristic, and we empirically observe that the total cost (random initial points plus BO iterations needed to find the global optimum) is U-shaped in $n_0$, i.e., a practitioner wastes resources by selecting either too low or too high a value of $n_0$. We find this tradeoff persists across MLE, Bayesian MCMC, and exact GP hyperparameters, as well as across acquisition functions. Toward the latter, Thompson Sampling appears an exception, with both total cost and simple regret essentially $n_0$-agnostic, though higher in our experiments. We attribute this U-shape to the known boundary issue of variance-driven BO: BO burns early budget on corners of the hypercube before turning inward. We demonstrate this effect using a 3D BO trajectory where the exact hyperparameters are known. We conclude with practical recommendations: use multi-step lookahead BO where possible; otherwise use Thompson Sampling when $n_0$ cannot be tuned, and a generously large $n_0$ when it can.