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Deep Learning · Everything Else

Marco Federici, Riccardo Del Chiaro, Boris van Breugel, Paul Whatmough, Markus Nagel

Quantization is the key method for reducing inference latency, power and memory footprint of generative AI models. However, accuracy often degrades sharply when activations are at low bit widths. Recent work suggests that invertible linear transformations (e.g. rotations) can aid quantization, by reparameterizing feature channels and weights. In this paper, we propose Sequence Transformation and Mixed Precision (STaMP) quantization, a novel strategy that applies linear transformations along the sequence dimension to exploit the strong local correlation in language and visual data. By keeping a small number of tokens in each intermediate activation at higher precision, we can maintain model accuracy at lower (average) activations bit-widths. We evaluate STaMP on recent LVM and LLM architectures, demonstrating that it significantly improves low bit width activation quantization and complements established activation and weight quantization methods including recent feature transformations.

Optimization · Zero-order and Black-box Optimization

David Stenger, Armin Lindicke, Alexander von Rohr, Sebastian Trimpe

Searching large and complex design spaces for a global optimum can be infeasible and unnecessary. A practical alternative is to iteratively refine the neighborhood of an initial design using local optimization methods such as gradient descent. We propose local entropy search (LES), a Bayesian optimization paradigm that explicitly targets the solutions reachable by the descent sequences of iterative optimizers. The algorithm propagates the posterior belief over the objective through the optimizer, resulting in a probability distribution over descent sequences. It then selects the next evaluation by maximizing mutual information with that distribution, using a combination of analytic entropy calculations and Monte-Carlo sampling of descent sequences. Empirical results on high-complexity synthetic objectives and benchmark problems show that LES achieves strong sample efficiency compared to existing local and global Bayesian optimization methods.

Applications · Language, Speech and Dialog

Bang Xiao, Lingjie Jiang, Shaohan Huang, Tengchao Lv, Yupan Huang, xun wu, Lei Cui, Furu Wei

Large Language Models (LLMs) have become valuable assistants for developers in code-related tasks. While LLMs excel at traditional programming tasks such as code generation and bug fixing, they struggle with visually-oriented coding tasks, often producing suboptimal aesthetics. In this paper, we introduce a new pipeline to enhance the aesthetic quality of LLM-generated code. We first construct AesCode-358K, a large-scale instruction-tuning dataset focused on code aesthetics. Next, we propose agentic reward feedback, a multi-agent system that evaluates executability, static aesthetics, and interactive aesthetics. Building on this, we develop GRPO-AR, which integrates these signals into the GRPO algorithm for joint optimization of functionality and code aesthetics. Finally, we develop OpenDesign, a benchmark for assessing code aesthetics. Experimental results show that combining supervised fine-tuning on AesCode-358K with reinforcement learning using agentic reward feedback significantly improves performance on OpenDesign and enhances results on existing benchmarks such as PandasPlotBench. Notably, our AesCoder-4B surpasses GPT-4o and GPT-4.1, and achieves performance comparable to large open-source models with 480B–685B parameters, underscoring the effectiveness of our approach.

Theory · Learning Theory

Kazushi Mimura, Junichi Takeuchi, Yuto Sumikawa, Yoshiyuki Kabashima, Anthony CC Coolen

Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its dynamical properties have not yet been discussed. In this paper, we analyze the dynamics using an exact approach based on generating functional analysis. We show results on convergence properties of memory retrieval, such as the convergence time and the size of the attraction basins. Our analysis enables a quantitative evaluation of the convergence time and the storage capacity of dense associative memory, which is useful for model design. Unlike the traditional Hopfield model, the retrieval of a pattern does not act as additional noise to itself, suggesting that the structure of modern networks makes recall more robust. Furthermore, the methodology addressed here can be applied to other energy-based models, and thus has the potential to contribute to the design of future architectures.

Applications · Genetics, Cell Biology, Health, etc

Kirill Vishniakov, Karthik Viswanathan, Aleksandr Medvedev, Praveenkumar Kanithi, Marco Pimentel, Ronnie Rajan, Shadab Khan

The success of Large Language Models has inspired the development of Genomic Foundation Models (GFMs) through similar pretraining techniques. However, the relationship between pretraining performance and effectiveness in downstream genomic tasks remains unclear. Additionally, the high computational cost of pretraining raises questions about its cost-efficiency. To assess the usefulness of pretraining in genomics, we evaluated seven different GFMs across 52 diverse genomic tasks, comparing them to their counterparts with randomly initialized weights. Across benchmarks, we find that randomly initialized models provide surprisingly strong baselines and tokenizer and architecture choices strongly shape both these baselines and the gains from pretraining. Specifically, character‑token models often match or exceed the performance of larger pretrained k‑mer or BPE models, whereas subword models appear to benefit from pretraining. We also find that the evaluated GFMs fail to capture clinically relevant genetic mutations, with embeddings and log‑likelihood ratios showing limited sensitivity to annotated variants. For the tasks we study, these results suggest that current NLP‑style pretraining strategies provide modest, tokenizer‑gated improvements over strong random baselines and motivate more biologically informed tokenization and variant‑aware objectives. Our code is available at https://github.com/m42-health/gfm-random-eval.

Deep Learning · Graph Neural Networks

Jun Yin, Senzhang Wang, Ziluowen Luo, Peng Huo, Hao Yan, Hao Miao, Chaozhuo Li, Shirui Pan, Chengqi Zhang

Post-hoc instance-level graph neural network (GNN) explainers are developed to identify a compact subgraph (i.e., explanation) that encompasses the most influential components for each input graph. A fundamental limitation of existing methods lies in the insufficient utilization of structural information during GNN explainer optimization. They typically optimize the explainer by aligning the GNN predictions of input graph and its explanation in the graph label space which inherently lacks expressiveness to describe various graph structures. Motivated by the powerful structural expression ability of vectorized graph representations, we for the first time propose to shift the GNN explainer optimization from the graph label space to the graph representation space. However, the paradigm shift is challenging due to both the entanglement between the explanatory and non-explanatory substructures, and the distributional discrepancy between the input graph and the explanation subgraph. To this end, we meticulously design IDEA, a universal dual-stage optimization framework grounded in a prototypical graph representation space, which can generalize across diverse existing GNN explainer architectures. Specifically, in the Structural Information Disentanglement stage, a graph tokenizer equipped with a structure-aware disentanglement objective is designed to disentangle the explanatory substructures and encapsulate them into explanatory prototypes. In the Explanatory Prototype Alignment stage, IDEA aligns the representational distributions of the input graph and its explanation unified in the prototypical representation space, to optimize the GNN explainer. Comprehensive experiments on real-world and synthetic datasets demonstrate the effectiveness of IDEA, with the average improvements of ROC-AUC by 4.45% and precision by 48.71%. We further integrate IDEA with diverse explainer architectures and achieve an improvement by up to 10.70%, which verifies its generalizability.

Deep Learning · Theory

Ke Sun

The high-dimensional parameter space of deep neural networks --- the neuromanifold --- is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists and practitioners. Focusing on neural classifiers, we return to a low-dimensional space of probability distributions, which we call the core space, and examine the spectrum and envelopes of its Fisher information matrix. We extend our discoveries there to deterministic bounds for the metric tensor on the neuromanifold. We introduce an unbiased random estimator based on Hutchinson's trace method and derive related bounds. It can be evaluated efficiently with a single backward pass per batch, with a standard deviation bounded by the true value up to scaling.

Applications · Language, Speech and Dialog

Waris Quamer, Mu-Ruei Tseng, Ghady Nasrallah, Ricardo Gutierrez-Osuna

Real-time voice conversion and speaker anonymization require causal, low-latency synthesis without sacrificing intelligibility or naturalness. Current systems have a core representational mismatch: content is time-varying, while speaker identity is injected as a static global embedding. We introduce a streamable speech synthesizer that aligns the temporal granularity of identity and content via a content-synchronous, time-varying timbre (TVT) representation. A Global Timbre Memory expands a global timbre instance into multiple compact facets; frame-level content attends to this memory, a gate regulates variation, and spherical interpolation preserves identity geometry while enabling smooth local changes. In addition, a factorized vector-quantized bottleneck regularizes content to reduce residual speaker leakage. The resulting system is streamable end-to-end, with <80 ms GPU latency. Experiments show improvements in naturalness, speaker transfer, and anonymization compared to SOTA streaming baselines, establishing TVT as a scalable approach for privacy-preserving and expressive speech synthesis under strict latency budgets.

Applications · Language, Speech and Dialog

Yuanzhe Hu, Yu Wang, Julian McAuley

Recent benchmarks for Large Language Model (LLM) agents primarily focus on evaluating reasoning, planning, and execution capabilities, while another critical component—memory, encompassing how agents memorize, update, and retrieve long-term information—is under-evaluated due to the lack of benchmarks. We term agents with memory mechanisms as memory agents. In this paper, based on classic theories from memory science and cognitive science, we identify four core competencies essential for memory agents: accurate retrieval, test-time learning, long-range understanding, and selective forgetting. Existing benchmarks either rely on limited context lengths or are tailored for static, long-context settings like book-based QA, which do not reflect the interactive, multi-turn nature of memory agents that incrementally accumulate information. Moreover, no existing benchmarks cover all four competencies. We introduce MemoryAgentBench, a new benchmark specifically designed for memory agents. Our benchmark transforms existing long-context datasets and incorporates newly constructed datasets into a multi-turn format, effectively simulating the incremental information processing characteristic of memory agents. By carefully selecting and curating datasets, our benchmark provides comprehensive coverage of the four core memory competencies outlined above, thereby offering a systematic and challenging testbed for assessing memory quality. We evaluate a diverse set of memory agents, ranging from simple context-based and retrieval-augmented generation (RAG) systems to advanced agents with external memory modules and tool integration. Empirical results reveal that current methods fall short of mastering all four competencies, underscoring the need for further research into comprehensive memory mechanisms for LLM agents.

Deep Learning · Everything Else

Tong Zheng, Hongming Zhang, Wenhao Yu, Xiaoyang Wang, He Xing, Runpeng Dai, Rui Liu, Huiwen Bao, Chengsong Huang, Heng Huang 等

Parallel thinking has emerged as a novel approach for enhancing the reasoning capabilities of large language models (LLMs) by exploring multiple reasoning paths concurrently. However, activating such capabilities through training remains challenging. Existing methods mainly rely on supervised fine-tuning (SFT) over synthetic data, which encourages teacher-forced learning rather than exploration and generalization. To address this issue, we propose **Parallel-R1**, the first reinforcement learning (RL) framework that instills parallel thinking for complex real-world reasoning tasks. Our framework employs a progressive curriculum that addresses the cold-start problem in training parallel thinking with RL. We first use SFT on prompt-generated trajectories from easier tasks to instill the parallel thinking behavior, then transition to RL to explore and generalize this skill on harder problems. Experiments on various math benchmarks, including MATH, AMC23, and AIME, show that Parallel-R1 successfully elicits parallel thinking, leading to 8.4% accuracy improvements over the sequential thinking model trained directly on difficult tasks with RL. Further analysis reveals a distinct shift in the model's thinking patterns: in the early stage, it utilizes parallel thinking as an exploration strategy, while in the later stage, it employs this ability for multi-perspective verification. Most significantly, we validate parallel thinking as a **mid-training exploration scaffold**, where this intermediate phase unlocks a higher performance ceiling after RL, yielding a **42.9%** improvement over the sequential RL baseline.

Applications · Climate

Guowen Li, Xintong Liu, Yang Liu, Mengxuan Chen, Shilei Cao, Xuehe Wang, Juepeng Zheng, Jinxiao Zhang, Haoyuan Liang, Lixian Zhang 等

Accurate Subseasonal-to-Seasonal (S2S) forecasting is vital for decision-making in agriculture, energy production, and emergency management. However, it remains a challenging and underexplored problem due to the chaotic nature of the weather system. Recent data-driven studies have shown promising results, but their performance is limited by the inadequate incorporation of climate states and a model tendency to degrade, progressively losing fine-scale details and yielding over-smoothed forecasts. To overcome these limitations, we propose TianQuan-S2S, a global S2S forecasting model that integrates initial weather states with climatological means via incorporating climatology into patch embedding and enhancing variability capture through an uncertainty-augmented Transformer. Extensive experiments on the Earth Reanalysis 5 (ERA5) reanalysis dataset demonstrate that our model yields a significant improvement in both deterministic and ensemble forecasting over the climatology mean, traditional numerical methods, and data-driven models. Ablation studies empirically show the effectiveness of our model designs. Remarkably, our model outperforms skillful numerical ECMWF-S2S and advanced data-driven Fuxi-S2S in key meteorological variables. The code implementation can be found in https://github.com/zhangminglang42/TianQuan.

Applications · Climate

Shilei Cao, Hehai Lin, Jiashun Cheng, Yang Liu, Guowen Li, Xuehe Wang, Juepeng Zheng, Haoyuan Liang, Meng Jin, Chengwei Qin 等

While recent advances in machine learning have equipped Weather Foundation Models (WFMs) with substantial generalization capabilities across diverse downstream tasks, the escalating computational requirements associated with their expanding scale increasingly hinder practical deployment. Current Parameter-Efficient Fine-Tuning (PEFT) methods, designed for vision or language tasks, fail to address the unique challenges of weather downstream tasks, such as variable heterogeneity, resolution diversity, and spatiotemporal coverage variations, leading to suboptimal performance when applied to WFMs. To bridge this gap, we introduce WeatherPEFT, a novel PEFT framework for WFMs incorporating two synergistic innovations. First, during the forward pass, Task-Adaptive Dynamic Prompting (TADP) dynamically injects the embedding weights within the encoder to the input tokens of the pre-trained backbone via internal and external pattern extraction, enabling context-aware feature recalibration for specific downstream tasks. Furthermore, during backpropagation, Stochastic Fisher-Guided Adaptive Selection (SFAS) not only leverages Fisher information to identify and update the most task-critical parameters, thereby preserving invariant pre-trained knowledge, but also introduces randomness to stabilize the selection. We demonstrate the effectiveness and efficiency of WeatherPEFT on three downstream tasks, where existing PEFT methods show significant gaps versus Full-Tuning, and WeatherPEFT achieves performance parity with Full-Tuning using fewer trainable parameters. The code of this work is available at https://github.com/ShileiCao/WeatherPEFT.

Social Aspects · Trustworthy Machine Learning

Anirudh Bharadwaj, Chaitanya Malaviya, Nitish Joshi, Mark Yatskar

Language models serve as proxies for human preference judgements in alignment and evaluation, yet they exhibit systematic miscalibration, prioritizing superficial patterns over substantive qualities. This bias manifests as overreliance on features like length, structure, and style, leading to issues like reward hacking and unreliable evaluations. However, the connection between training data artifacts and the miscalibrated preferences exhibited by models remains poorly understood. In this work, we systematically investigate the relationship between training data biases and preference model miscalibration across five idiosyncratic features of language model generations: length, structure, jargon, sycophancy and vagueness. Using controlled counterfactual pairs, we first quantify the extent to which preference models favor responses with artificially magnified biases (\textit{skew}), finding this preference occurs in $>60$\% of instances, and model preferences show high \textit{miscalibration} ($\approx 40$\%) compared to human preferences. Notably, bias features only show mild negative correlations to human preference labels (mean $r_{\mathrm{human}} = -0.12$) but show moderately strong positive correlations with labels from a strong reward model (mean $r_{\mathrm{model}} = +0.36$), suggesting that models may overrely on spurious cues. To mitigate these issues, we propose a simple post-training method based on counterfactual data augmentation (CDA) using synthesized contrastive examples. Fine-tuning models with CDA reduces average miscalibration from 39.4\% to 32.5\% and average absolute skew difference from 20.5\% to 10.0\%, while maintaining overall RewardBench performance, indicating that targeted debiasing can strengthen the reliability of preference models within standard alignment pipelines.

General Machine Learning · Transfer, Multitask and Meta-learning

Haoyuan Gao, Zicong Zhang, Yuqi Wei, Linglan Zhao, Guilin Li, Yexin Li, Bo Wang, Linghe Kong, Weiran Huang

Vision-Language Models (VLMs) represent a significant breakthrough in artificial intelligence by integrating visual and textual modalities to achieve impressive zero-shot capabilities. However, VLMs are susceptible to catastrophic forgetting when sequentially fine-tuned on multiple downstream tasks. Existing continual learning methods for VLMs face various limitations, often relying on additional reference datasets, compromising zero-shot performance, or being restricted to parameter-efficient fine-tuning scenarios. In this paper, we propose a novel Continual Decoupling-Unifying (ConDU) approach that pioneers the use of model fusion for continual learning in VLMs. Specifically, ConDU maintains a unified model along with task triggers and prototype sets, employing an iterative process of decoupling task experts for previous tasks and unifying them with the task expert for the newly learned task. Additionally, we introduce an inference strategy for zero-shot scenarios by aggregating predictions from multiple decoupled task experts. Extensive experiments on the MTIL benchmark show that ConDU achieves up to a 2\% improvement in average performance across all seen tasks compared to state-of-the-art baselines, while also enhancing zero-shot capabilities relative to the original VLM. Our code is available at https://github.com/zhangzicong518/ConDU.

Deep Learning · Generative Models and Autoencoders

Yiming Huang, Tolga Birdal

Graph generation is a critical yet challenging task, as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant advances in graph generation, but these models are typically adapted from image generation frameworks and overlook inherent higher-order topology, limiting their ability to capture graph topology. In this work, we propose Higher-order Guided Diffusion (HOG-Diff), a principled framework that progressively generates plausible graphs with inherent topological structures. HOG-Diff follows a coarse-to-fine generation curriculum, guided by higher-order topology and implemented via diffusion bridges. We further prove that our model admits stronger theoretical guarantees than classical diffusion frameworks. Extensive experiments across eight graph generation benchmarks, spanning diverse domains and including large-scale settings, demonstrate the scalability of our method and its superior performance on both pairwise and higher-order topological metrics. Our project page is available [here](https://circle-group.github.io/research/hog-diff/).

Minsang Park, Gyuwon Sim, Hyungho Na, Jiseok Kwak, Sumin Lee, Richard Kim, Donghyeok Shin, Byeonghu Na, Yeongmin Kim, Il-chul Moon

Diffusion-based generative models have recently achieved state-of-the-art performance in high-fidelity image synthesis. These models learn a sequence of denoising transition kernels that gradually transform a simple prior distribution into a complex data distribution. However, requiring many transitions not only slows down sampling but also accumulates approximation errors. We introduce the Accelerator-Corrector Sampler (AC-Sampler), which accelerates and corrects diffusion sampling without fine-tuning. It generates samples directly from intermediate timesteps using the Metropolis–Hastings (MH) algorithm while correcting them to target the true data distribution. We derive a tractable density ratio for arbitrary timesteps with a discriminator, enabling computation of MH acceptance probabilities. Theoretically, our method yields samples better aligned with the true data distribution than the original model distribution. Empirically, AC-Sampler achieves FID 2.38 with only 15.8 NFEs, compared to the base sampler’s FID 3.23 with 17 NFEs on unconditional CIFAR-10. On CelebA-HQ 256×256, it attains FID 6.6 with 98.3 NFEs. AC-Sampler can be combined with existing acceleration and correction techniques, demonstrating its flexibility and broad applicability. Our code is available at \href{https://github.com/aailab-kaist/AC-Sampler}{https://github.com/aailab-kaist/AC-Sampler.}

Jiaqi Han, Austin Wang, Minkai Xu, Wenda Chu, Meihua Dang, Haotian Ye, Huayu Chen, Yisong Yue, Stefano Ermon

Discrete diffusion models have demonstrated great promise in modeling various sequence data, ranging from human language to biological sequences. Inspired by the success of RL in language models, there is growing interest in further improving the models by alignment with a certain reward. In this work, we propose an offline preference optimization method to approach trajectory alignment for discrete diffusion models. Instead of applying the reward on the final output and backpropagating the gradient to the entire denoising process, we decompose the problem into a set of stepwise alignment objectives by matching the per-step posterior. This framework enables efficient diffusion optimization, is compatible with arbitrary reward functions, and importantly, yields an equivalent optimal solution under additive factorization of the trajectory reward. Experiments across multiple domains including DNA sequence design, protein inverse folding, and language modeling consistently demonstrate the superiority of our approach. Notably, it achieves an up to 12\% improvement over the most competitive RL-based baseline in terms of predicted activity on DNA sequence design, and further improves the GSM8K score from 78.6 to 81.2 on LLaDA-8B-Instruct for language modeling.

Applications · Chemistry and Drug Discovery

Emily Jin, Andrei Nica, Mikhail Galkin, Jarrid Rector-Brooks, Kin Long Kelvin Lee, Santiago Miret, Frances Arnold, Michael Bronstein, Joey Bose, Alexander Tong 等

Accurately predicting experimentally realizable 3D molecular crystal structures from their 2D chemical graphs is a long-standing open challenge in computational chemistry called crystal structure prediction (CSP). Efficiently solving this problem has implications ranging from pharmaceuticals to organic semiconductors, as crystal packing directly governs the physical and chemical properties of organic solids. In this paper, we introduce OXtal, a large-scale 100M parameter all-atom diffusion model that directly learns the conditional joint distribution over intramolecular conformations and periodic packing. To efficiently scale OXtal, we abandon explicit equivariant architectures imposing inductive bias arising from crystal symmetries in favor of data augmentation strategies. We further propose a novel crystallization-inspired lattice-free training scheme, Stoichiometric Stochastic Shell Sampling ($S^4$), that efficiently captures long-range interactions while sidestepping explicit lattice parametrization---thus enabling more scalable architectural choices at all-atom resolution. By leveraging a large dataset of 600K experimentally validated crystal structures (including rigid and flexible molecules, co-crystals, and solvates), OXtal achieves orders-of-magnitude improvements over prior ab initio machine learning CSP methods, while remaining orders of magnitude cheaper than traditional quantum-chemical approaches. Specifically, OXtal recovers experimental structures with conformer $\mathrm{RMSD}_1<0.5$ Å and attains over 80% packing similarity rate, demonstrating its ability to model both thermodynamic and kinetic regularities of molecular crystallization.

Applications · Language, Speech and Dialog

Ahmadreza Jeddi, Marco Ciccone, Babak Taati

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Applications · Chemistry and Drug Discovery

Xinzhe Yuan, Zhuo Chen, Jianshu Zhang, Huan Xiong, Nanyang Ye, Yuqiang Li, Qinying Gu

Scientific discovery is increasingly constrained by costly experiments and limited budgets, making efficient optimization essential for AI for science. Bayesian Optimization (BO), while widely adopted for balancing exploration and exploitation, suffers from slow cold-start performance and poor scalability in high-dimensional settings, limiting its effectiveness in real-world scientific applications. To address these challenges, we propose LLM-Guided Bayesian Optimization (LGBO), the first LLM preference-guided BO framework that continuously integrates the semantic reasoning of large language models (LLMs) into the optimization loop. Unlike prior works that use LLMs only for warm-start initialization or candidate generation, LGBO introduces a region-lifted preference mechanism that embeds LLM-driven preferences into every iteration, shifting the surrogate mean in a stable and controllable way. Theoretically, we prove that LGBO is not perform significantly worse than standard BO in the worst case, while achieving significantly faster convergence when preferences align with the objective. Empirically, LGBO achieves consistent improvements across diverse dry benchmarks in physics, chemistry, biology, and materials science. Most notably, in a new wet-lab optimization of Fe–Cr battery electrolytes, LGBO reaches \textbf{90\% of the best observed value within 6 iterations}, whereas standard BO and existing LLM-augmented baselines require more than 10 iterations. Together, the results suggest that LGBO offers a promising direction for integrating LLMs into scientific optimization workflows.