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Hot Jupiters should initially form at considerable distances from host stars and subsequently migrate towards inner regions, supported directly by transit timing variation (TTV). We report the TTV of K2-237b, using reproduced timings fitted from \textit{Kepler} K2 and \textit{TESS} data. The timings span from 2016 to 2021, leading to an observational baseline of 5 years. The timing evolution presents a significant bias to a constant period scenario. The model evidence is evaluated utilizing the Bayesian Information Criterion (BIC), which favours the scenario of period decay with a $\Delta$BIC of 14.1. The detected TTV induces a period decay rate ($\dot{P}$) of -1.14$\pm$0.28$\times$10$^{-8}$ days per day ($-$0.36 s/year). Fitting the spectral energy distribution, we find infrared excess at the significance level of 1.5 $\sigma$ for WISE W1 and W2 bands, and 2 $\sigma$ level for W3 and W4 bands. This potentially reveals the existence of a stellar disk, consisting of hot dust at 800$\pm$300 K, showing a $L_{dust}/L_{\ast}$ of 5$\pm$3$\times$10$^{-3}$. We obtain a stellar age of 1.0$^{+1.4}_{-0.7}$$\times$10$^{9}$ yr from isochrone fitting. The properties of K2-237b potentially serve as a direct observational support to the planet disk migration though more observation are needed., Comment: 5 pages, Accepted for publication in MNRAS Letters

We conduct a comprehensive \textit{ab initio} investigation of electron-electron interactions within the pyrochlore structures of R$_2$Ru$_2$O$_7$, R$_2$Ir$_2$O$_7$, Ca$_2$Ru$_2$O$_7$, and Cd$_2$Ru$_2$O$_7$, where R denotes a rare-earth element. Utilizing a multiorbital Hubbard model, we systematically explore the effects of various rare-earth elements and applied high pressure on the correlation strength in these compounds. Our calculations on the Coulomb interaction parameter $U$ and the bandwidth $W$ reveal that the chemical pressure for R$_2$Ru$_2$O$_7$ and R$_2$Ir$_2$O$_7$ leads to an unusual increase in $U/W$ ratio, hence, increase in correlation strength. Contrary to conventional understanding of bandwidth control, our study identifies that the Hubbard $U$ is more influential than the bandwidth $W$ behind the metal-insulator landscape of R$_2$Ru$_2$O$_7$ and R$_2$Ir$_2$O$_7$, leading to an interaction-controlled metal-insulator transition. We also find unexpected behavior in physical pressure. Whereas physical pressure leads to a decrease in the correlation strength $U/W$ as usual in R$_2$Ru$_2$O$_7$, the effect is notably small in Ca$_2$Ru$_2$O$_7$ and Cd$_2$Ru$_2$O$_7$, which provides an important clue to understanding unusual pressure-induced metal-insulator transition observed experimentally.

Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum circuit optimization is crucial for obtaining useful results. In this paper, we present QuCLEAR, a compilation framework designed to optimize quantum circuits. QuCLEAR significantly reduces both the two-qubit gate count and the circuit depth through two novel optimization steps. First, we introduce the concept of Clifford Extraction, which extracts Clifford subcircuits to the end of the circuit while optimizing the gates. Second, since Clifford circuits are classically simulatable, we propose Clifford Absorption, which efficiently processes the extracted Clifford subcircuits classically. We demonstrate our framework on quantum simulation circuits, which have wide-ranging applications in quantum chemistry simulation, many-body physics, and combinatorial optimization problems. Near-term algorithms such as VQE and QAOA also fall within this category. Experimental results across various benchmarks show that QuCLEAR achieves up to a $77.7\%$ reduction in CNOT gate count and up to an $84.1\%$ reduction in entangling depth compared to state-of-the-art methods., Comment: 13 pages, 9 figures, 2 tables

The significance of estimating video watch time has been highlighted by the rising importance of (short) video recommendation, which has become a core product of mainstream social media platforms. Modeling video watch time, however, has been challenged by the complexity of user-video interaction, such as different user behavior modes in watching the recommended videos and varying watching probabilities over the video horizon. Despite the importance and challenges, existing literature on modeling video watch time mostly focuses on relatively black-box mechanical enhancement of the classical regression/classification losses, without factoring in user behavior in a principled manner. In this paper, we for the first time take on a user-centric perspective to model video watch time, from which we propose a white-box statistical framework that directly translates various user behavior assumptions in watching (short) videos into statistical watch time models. These behavior assumptions are portrayed by our domain knowledge on users' behavior modes in video watching. We further employ bucketization to cope with user's non-stationary watching probability over the video horizon, which additionally helps to respect the constraint of video length and facilitate the practical compatibility between the continuous regression event of watch time and other binary classification events. We test our models extensively on two public datasets, a large-scale offline industrial dataset, and an online A/B test on a short video platform with hundreds of millions of daily-active users. On all experiments, our models perform competitively against strong relevant baselines, demonstrating the efficacy of our user-centric perspective and proposed framework.

Despite achieving remarkable performance, Federated Learning (FL) encounters two important problems, i.e., low training efficiency and limited computational resources. In this paper, we propose a new FL framework, i.e., FedDUMAP, with three original contributions, to leverage the shared insensitive data on the server in addition to the distributed data in edge devices so as to efficiently train a global model. First, we propose a simple dynamic server update algorithm, which takes advantage of the shared insensitive data on the server while dynamically adjusting the update steps on the server in order to speed up the convergence and improve the accuracy. Second, we propose an adaptive optimization method with the dynamic server update algorithm to exploit the global momentum on the server and each local device for superior accuracy. Third, we develop a layer-adaptive model pruning method to carry out specific pruning operations, which is adapted to the diverse features of each layer so as to attain an excellent trade-off between effectiveness and efficiency. Our proposed FL model, FedDUMAP, combines the three original techniques and has a significantly better performance compared with baseline approaches in terms of efficiency (up to 16.9 times faster), accuracy (up to 20.4% higher), and computational cost (up to 62.6% smaller)., Comment: 27 pages, to appear in TIST

This work presents a novel quantum system characterization and error mitigation framework that applies Pauli check sandwiching (PCS). We motivate our work with prior art in software optimizations for quantum programs like noise-adaptive mapping and multi-programming, and we introduce the concept of PCS while emphasizing design considerations for its practical use. We show that by carefully embedding Pauli checks within a target application (i.e. a quantum circuit), we can learn quantum system noise profiles. Further, PCS combined with multi-programming unlocks non-trivial fidelity improvements in quantum program outcomes.

Long-tailed data is a special type of multi-class imbalanced data with a very large amount of minority/tail classes that have a very significant combined influence. Long-tailed learning aims to build high-performance models on datasets with long-tailed distributions, which can identify all the classes with high accuracy, in particular the minority/tail classes. It is a cutting-edge research direction that has attracted a remarkable amount of research effort in the past few years. In this paper, we present a comprehensive survey of latest advances in long-tailed visual learning. We first propose a new taxonomy for long-tailed learning, which consists of eight different dimensions, including data balancing, neural architecture, feature enrichment, logits adjustment, loss function, bells and whistles, network optimization, and post hoc processing techniques. Based on our proposed taxonomy, we present a systematic review of long-tailed learning methods, discussing their commonalities and alignable differences. We also analyze the differences between imbalance learning and long-tailed learning approaches. Finally, we discuss prospects and future directions in this field., Comment: Current Under Revision at IEEE TNNLS. [This is the long/Full-length version of our Long-Tailed Learning Survey paper]

In the proof of the irrationality of $\zeta(3)$ and $\zeta(2)$, Ap\'ery defined two integer sequences through $3$-term recurrences, which are known as the famous Ap\'ery numbers. Zagier, Almkvist--Zudilin and Cooper successively introduced the other $13$ sporadic sequences through variants of Ap\'ery's $3$-term recurrences. All of the $15$ sporadic sequences are called Ap\'ery-like sequences. Motivated by Gessel's congruences mod $24$ for the Ap\'ery numbers, we investigate the congruences in the form $u_n\equiv \alpha^n \pmod{N_{\alpha}}~(\alpha\in \mathbb{Z},N_{\alpha}\in \mathbb{N}^{+})$ for all of the $15$ Ap\'ery-like sequences $\{u_n\}_{n\ge 0}$. Let $N_{\alpha}$ be the largest positive integer such that $u_n\equiv \alpha^n \pmod{N_{\alpha}}$ for all non-negative integers $n$. We determine the values of $\max\{N_{\alpha}|\alpha \in \mathbb{Z}\}$ for all of the $15$ Ap\'ery-like sequences $\{u_n\}_{n\ge 0}$.The binomial transforms of Ap\'ery-like sequences provide us a unified approach to this type of congruences for Ap\'ery-like sequences., Comment: 19 pages

Pauli Check Sandwiching (PCS) is an error mitigation scheme that uses pairs of parity checks to detect errors in the payload circuit. While increasing the number of check pairs improves error detection, it also introduces additional noise to the circuit and exponentially increases the required sampling size. To address these limitations, we propose a novel error mitigation scheme, Pauli Check Extrapolation (PCE), which integrates PCS with an extrapolation technique similar to Zero-Noise Extrapolation (ZNE). However, instead of extrapolating to the `zero-noise' limit, as is done in ZNE, PCE extrapolates to the `maximum check' limit--the number of check pairs theoretically required to achieve unit fidelity. In this study, we focus on applying a linear model for extrapolation and also derive a more general exponential ansatz based on the Markovian error model. We demonstrate the effectiveness of PCE by using it to mitigate errors in the shadow estimation protocol, particularly for states prepared by the variational quantum eigensolver (VQE). Our results show that this method can achieve higher fidelities than the state-of-the-art Robust Shadow (RS) estimation scheme, while significantly reducing the number of required samples by eliminating the need for a calibration procedure. We validate these findings on both fully-connected topologies and simulated IBM hardware backends.

Large Language Models (LLMs) inherently use autoregressive decoding, which lacks parallelism in inference and results in significantly slow inference speeds, especially when hardware parallel accelerators and memory bandwidth are not fully utilized. In this work, we propose Amphista, a speculative decoding algorithm that adheres to a non-autoregressive decoding paradigm. Owing to the increased parallelism, our method demonstrates higher efficiency in inference compared to autoregressive methods. Specifically, Amphista models an Auto-embedding Block capable of parallel inference, incorporating bi-directional attention to enable interaction between different drafting heads. Additionally, Amphista implements Staged Adaptation Layers to facilitate the transition of semantic information from the base model's autoregressive inference to the drafting heads' non-autoregressive speculation, thereby achieving paradigm transformation and feature fusion. We conduct a series of experiments on a suite of Vicuna models using MT-Bench and Spec-Bench. For the Vicuna 33B model, Amphista achieves up to 2.75$\times$ and 1.40$\times$ wall-clock acceleration compared to vanilla autoregressive decoding and Medusa, respectively, while preserving lossless generation quality.

Based on two involutions and a bijection, we completely determine the difference between the number of $\ell$-regular partitions of $n$ into an even number of parts and into an odd number of parts for all positive integers $n$ and $\ell>1$, which extends two recent results due to Ballantine and Merca. As an application, we provide a combinatorial proof of Hickerson's identity on the number of partitions into an even and odd number of parts., Comment: 6 pages

Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work we develop a mapping from dynamic CTQWs to the gate model of computation in the form of an algorithm to convert arbitrary single edge walks and single self loop walks, which are the fundamental building blocks of dynamic CTQWs, to their circuit model counterparts. We use this mapping to introduce an arbitrary quantum state preparation framework based on dynamic CTQWs. Our approach utilizes global information about the target state, relates state preparation to finding the optimal path in a graph, and leads to optimizations in the reduction of controls that are not as obvious in other approaches. Interestingly, classical optimization problems such as the minimal hitting set, minimum spanning tree, and shortest Hamiltonian path problems arise in our framework. We test our methods against uniformly controlled rotations methods, used by Qiskit, and find ours requires fewer CX gates when the target state has a polynomial number of non-zero amplitudes., Comment: Comments are welcome!

Analyzing time series of fluxes from stars, known as stellar light curves, can reveal valuable information about stellar properties. However, most current methods rely on extracting summary statistics, and studies using deep learning have been limited to supervised approaches. In this research, we investigate the scaling law properties that emerge when learning from astronomical time series data using self-supervised techniques. By employing the GPT-2 architecture, we show the learned representation improves as the number of parameters increases from $10^4$ to $10^9$, with no signs of performance plateauing. We demonstrate that a self-supervised Transformer model achieves 3-10 times the sample efficiency compared to the state-of-the-art supervised learning model when inferring the surface gravity of stars as a downstream task. Our research lays the groundwork for analyzing stellar light curves by examining them through large-scale auto-regressive generative models., Comment: 11 pages, 5 figures, ICML 2024 AI4Science workshop

Distributed control of multi-inverter microgrids has attracted considerable attention as it can achieve the combined goals of flexible plug-and-play architecture guaranteeing frequency and voltage regulation while preserving power sharing among nonidentical distributed energy resources (DERs). However, it turns out that cybersecurity has emerged as a serious concern in distributed control schemes. Inspired by quantum communication developments and their security advantages, this paper devises a scalable quantum distributed controller that can guarantee synchronization, and power sharing among DERs. The key innovation lies in the fact that the new quantum distributed scheme allows for exchanging secret information directly through quantum channels among the participating DERs, making microgrids inherently cybersecure. Case studies on two ac and dc microgrids verify the efficacy of the new quantum distributed control strategy.

The multi-line LiDAR is widely used in autonomous vehicles, so point cloud-based 3D detectors are essential for autonomous driving. Extracting rich multi-scale features is crucial for point cloud-based 3D detectors in autonomous driving due to significant differences in the size of different types of objects. However, because of the real-time requirements, large-size convolution kernels are rarely used to extract large-scale features in the backbone. Current 3D detectors commonly use feature pyramid networks to obtain large-scale features; however, some objects containing fewer point clouds are further lost during down-sampling, resulting in degraded performance. Since pillar-based schemes require much less computation than voxel-based schemes, they are more suitable for constructing real-time 3D detectors. Hence, we propose the PillarNeXt, a pillar-based scheme. We redesigned the feature encoding, the backbone, and the neck of the 3D detector. We propose the Voxel2Pillar feature encoding, which uses a sparse convolution constructor to construct pillars with richer point cloud features, especially height features. The Voxel2Pillar adds more learnable parameters to the feature encoding, enabling the initial pillars to have higher performance ability. We extract multi-scale and large-scale features in the proposed fully sparse backbone, which does not utilize large-size convolutional kernels; the backbone consists of the proposed multi-scale feature extraction module. The neck consists of the proposed sparse ConvNeXt, whose simple structure significantly improves the performance. We validate the effectiveness of the proposed PillarNeXt on the Waymo Open Dataset, and the object detection accuracy for vehicles, pedestrians, and cyclists is improved. We also verify the effectiveness of each proposed module in detail through ablation studies.

Quantum error mitigation plays a crucial role in the current noisy-intermediate-scale-quantum (NISQ) era. As we advance towards achieving a practical quantum advantage in the near term, error mitigation emerges as an indispensable component. One notable prior work, Jigsaw, demonstrates that measurement crosstalk errors can be effectively mitigated by measuring subsets of qubits. Jigsaw operates by running multiple copies of the original circuit, each time measuring only a subset of qubits. The localized distributions yielded from measurement subsetting suffer from less crosstalk and are then used to update the global distribution, thereby achieving improved output fidelity. Inspired by the idea of measurement subsetting, we propose QuTracer, a framework designed to mitigate both gate and measurement errors in subsets of qubits by tracing the states of qubit subsets throughout the computational process. In order to achieve this goal, we introduce a technique, qubit subsetting Pauli checks (QSPC), which utilizes circuit cutting and Pauli Check Sandwiching (PCS) to trace the qubit subsets distribution to mitigate errors. The QuTracer framework can be applied to various algorithms including, but not limited to, VQE, QAOA, quantum arithmetic circuits, QPE, and Hamiltonian simulations. In our experiments, we perform both noisy simulations and real device experiments to demonstrate that QuTracer is scalable and significantly outperforms the state-of-the-art approaches.

Andrews and Merca [J. Combin. Theory Ser. A 203 (2024), Art. 105849] recently obtained two interesting results on the sum of the parts with the same parity in the partitions of $n$ (the modulo $2$ case), the proof of which relies on generating functions. Motivated by Andrews and Merca's results, we define six statistics related to the partitions of $n$ and show that the two triples of the six statistics are equidistributed. From this equidistributed result, we derive modulo $m$ extensions of Andrews and Merca's results for all integers $m\ge 2$. The proof of the main result is based on a general bijection on the set of partitions of $n$., Comment: The bijection constructed in this paper already exists in the known literature

Osburn, Sahu and Straub introduced the numbers: \begin{align*} A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t, \end{align*} for non-negative integers $n,r,s,t$ with $r\ge 2$, which includes two kinds of Ap\'ery numbers and four kinds of Ap\'ery-like numbers as special cases, and showed that the numbers $\{A_n^{(r,s,t)}\}_{n\ge 0}$ satisfy the Gauss congruences of order $3$. We establish an extension of Osburn--Sahu--Straub congruence through Bernoulli numbers, which is one step deep congruence of the Gauss congruence for $A_n^{(r,s,t)}$., Comment: 26 pages

Motivated by Berkovich's nine $q$-binomial identities involving the Legendre symbol $(\frac{d}{3})$, we establish a unified form of $q$-binomial identities of this type through a combinatorial approach. This unified form includes Berkovich's nine identities as special cases. Many such identities can be also deduced from this unified form., Comment: 10 pages

Lane detection is a fundamental task in autonomous driving, and has achieved great progress as deep learning emerges. Previous anchor-based methods often design dense anchors, which highly depend on the training dataset and remain fixed during inference. We analyze that dense anchors are not necessary for lane detection, and propose a transformer-based lane detection framework based on a sparse anchor mechanism. To this end, we generate sparse anchors with position-aware lane queries and angle queries instead of traditional explicit anchors. We adopt Horizontal Perceptual Attention (HPA) to aggregate the lane features along the horizontal direction, and adopt Lane-Angle Cross Attention (LACA) to perform interactions between lane queries and angle queries. We also propose Lane Perceptual Attention (LPA) based on deformable cross attention to further refine the lane predictions. Our method, named Sparse Laneformer, is easy-to-implement and end-to-end trainable. Extensive experiments demonstrate that Sparse Laneformer performs favorably against the state-of-the-art methods, e.g., surpassing Laneformer by 3.0% F1 score and O2SFormer by 0.7% F1 score with fewer MACs on CULane with the same ResNet-34 backbone.

Strongly correlated electron systems with a kagome lattice can host abundant exotic quantum states such as superconductivity and spin/charge density waves (CDW) due to the complicated interactions between different degrees of freedoms in the framework of a unique two-dimensional geometrically frustrated lattice structure. Recently, successive orders of A-type antiferromagnetism (AFM), $2\times2\times2$ CDW and canted double-cone AFM have been manifested upon cooling in magnetic kagome FeGe. However, the mechanism of the CDW order and its interaction with magnetism are presently enigmatic at best. Here we investigate the evolution of CDW order with temperature across the spin canting transition in FeGe by single-crystal x-ray diffraction. Refinements of its modulated structure are presented using the superspace approach. Interestingly, the superlattice reflections originating from CDW-induced long-range structural modulation become extremely weak after the system enters the canted AFM while a $2\times2$ CDW in the $ab$ plane persists as a long-range order demonstrated by strong electronic modulation in the d$I$/d$V$ map of scanning tunneling spectroscopy. We discovered a novel CDW order without long-range structural modulation in FeGe probably because of the competition between CDW and canted AFM in determining the underlying crystal structure. In addition, occupational modulations of Ge1 atoms located in the kagome plane and displacive modulations of all the atoms were extracted from the refinements, confirming the existence of Ge atom dimerization along the $c$ axis as the major distortion and indicating a dynamic transformation between different CDW domains., Comment: 22 pages, 6 figures. Comments on the manuscript are welcome

While centralized servers pose a risk of being a single point of failure, decentralized approaches like blockchain offer a compelling solution by implementing a consensus mechanism among multiple entities. Merging distributed computing with cryptographic techniques, decentralized technologies introduce a novel computing paradigm. Blockchain ensures secure, transparent, and tamper-proof data management by validating and recording transactions via consensus across network nodes. Federated Learning (FL), as a distributed machine learning framework, enables participants to collaboratively train models while safeguarding data privacy by avoiding direct raw data exchange. Despite the growing interest in decentralized methods, their application in FL remains underexplored. This paper presents a thorough investigation into Blockchain-based FL (BCFL), spotlighting the synergy between blockchain's security features and FL's privacy-preserving model training capabilities. First, we present the taxonomy of BCFL from three aspects, including decentralized, separate networks, and reputation-based architectures. Then, we summarize the general architecture of BCFL systems, providing a comprehensive perspective on FL architectures informed by blockchain. Afterward, we analyze the application of BCFL in healthcare, IoT, and other privacy-sensitive areas. Finally, we identify future research directions of BCFL., Comment: 25 pages, accepted by KAIS 2024

We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed., Comment: 10 pages

This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These constructed graphs possess maximum vertex and edge connectivity, and more importantly, exhibit large algebraic connectivity of an optimal order provided they are not sparse. These properties guarantee fast and resilient consensus processes over these graphs.

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory. Recent advances at the intersection of control and RL follow a two-stage, safety filter approach to enforcing hard safety constraints: model-free RL is used to learn a potentially unsafe controller, whose actions are projected onto safe sets prescribed, for example, by a control barrier function. Though safe, such approaches lose any convergence guarantees enjoyed by the underlying RL methods. In this paper, we develop a single-stage, sampling-based approach to hard constraint satisfaction that learns RL controllers enjoying classical convergence guarantees while satisfying hard safety constraints throughout training and deployment. We validate the efficacy of our approach in simulation, including safe control of a quadcopter in a challenging obstacle avoidance problem, and demonstrate that it outperforms existing benchmarks., Comment: 20 pages, 7 figures

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among these, the Quantum Approximate Optimization Algorithm (QAOA) stands out for its potential to efficiently solve the Max-Cut problem, a quintessential example of combinatorial optimization. However, practical application faces challenges due to current limitations on quantum computational resource. Our work optimizes QAOA initialization, using Graph Neural Networks (GNN) as a warm-start technique. This sacrifices affordable computational resource on classical computer to reduce quantum computational resource overhead, enhancing QAOA's effectiveness. Experiments with various GNN architectures demonstrate the adaptability and stability of our framework, highlighting the synergy between quantum algorithms and machine learning. Our findings show GNN's potential in improving QAOA performance, opening new avenues for hybrid quantum-classical approaches in quantum computing and contributing to practical applications.