Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged as a promising mesh-free approach for approximating their solutions, but in most existing works there is no rigorous guarantee that a small PDE residual implies a small solution error. This paper develops verifiable error bounds for approximate solutions of Lyapunov and HJB equations, with particular emphasis on PINN-based approximations. For both the Lyapunov and HJB PDEs, we show that a verifiable residual bound yields relative error bounds with respect to the true solutions as well as computable a posteriori estimates in terms of the approximate solutions. For the HJB equation, this also yields certified upper and lower bounds on the optimal value function on compact sublevel sets and quantifies the optimality gap of the induced feedback policy. We further show that one-sided residual bounds already imply that the approximation itself defines a valid Lyapunov or control Lyapunov function. We illustrate the results with numerical examples.

Large Language Models (LLMs) rely on optimizations like Automatic Prefix Caching (APC) to accelerate inference. APC works by reusing previously computed states for the beginning part of a request (prefix), when another request starts with the same text. While APC improves throughput, it introduces timing side channels: cache hits are faster than misses, creating observable latency differences. In multi-tenant systems, attackers can exploit these differences to infer sensitive information, e.g., by incrementally reconstructing another user's request by observing hit/miss patterns. Current defenses take a sledgehammer approach: they disable APC and cache sharing, isolating users, and sacrificing efficiency for regular users. This paper presents PrefixWall, a system that secures multi-tenant LLM serving systems against APC side channels without sacrificing performance and efficiency. PrefixWall monitors cache reuse across users, flags suspicious sharing, and selectively isolates prefixes, restricting their reuse only when necessary. Evaluation shows that PrefixWall enables up to 70% higher cache reuse and 30% lower inference latency compared to existing defenses that isolate users. PrefixWall's lightweight design demonstrates how security in LLM serving does not have to come at the cost of unnecessarily reduced performance or unbearable overheads.

Replay attacks remain a critical vulnerability for automatic speaker verification systems, particularly in real-time voice assistant applications. In this work, we propose acoustic maps as a novel spatial feature representation for replay speech detection from multi-channel recordings. Derived from classical beamforming over discrete azimuth and elevation grids, acoustic maps encode directional energy distributions that reflect physical differences between human speech radiation and loudspeaker-based replay. A lightweight convolutional neural network is designed to operate on this representation, achieving competitive performance on the ReMASC dataset with approximately 6k trainable parameters. Experimental results show that acoustic maps provide a compact and physically interpretable feature space for replay attack detection across different devices and acoustic environments.

Attitude and Heading Reference Systems (AHRSs) are broadly applied wherever reliable orientation and motion sensing is required. In this paper, we present an improved Cubature Kalman Filter (CKF) with lower computational cost while maintaining estimation accuracy, which is named "Kaisoku Cubature Kalman Filter (KCKF)". The computationally efficient equations of the KCKF are derived by simplifying those of the CKF, while preserving equivalent mathematical relations. The lightweight prediction equations in the KCKF are derived by expanding the summation terms in the CKF and simplifying the result. This paper shows that the KCKF requires fewer floating-point operations (FLOPs) than the CKF. The controlled experimental results show that the KCKF reduces the computation time by approximately 19% compared to the CKF on a high-performance computer, whereas the KCKF reduces the computation time by approximately 15% compared to the CKF on a low-cost single-board computer. In addition, the KCKF maintains the attitude estimation accuracy of the CKF.

We construct and analyze generative diffusions that transport a point mass to a prescribed target distribution over a finite time horizon using the stochastic interpolant framework. The drift is expressed as a conditional expectation that can be estimated from independent samples without simulating stochastic processes. We show that the diffusion coefficient can be tuned \emph{a~posteriori} without changing the time-marginal distributions. Among all such tunings, we prove that minimizing the impact of estimation error on the path-space Kullback--Leibler divergence selects, in closed form, a Föllmer process -- a diffusion whose path measure minimizes relative entropy with respect to a reference process determined by the interpolation schedules alone. This yields a new variational characterization of Föllmer processes, complementing classical formulations via Schrödinger bridges and stochastic control, and provides a conditional-expectation representation of the Föllmer drift that enables simulation-free estimation from data. We further establish that, under this optimal diffusion coefficient, the path-space Kullback--Leibler divergence becomes independent of the interpolation schedule, rendering different schedules statistically equivalent in this variational sense. We provide numerical experiments to illustrate the impact of path-space variational optimality of Föllmer's processes in probabilistic forecasting and data assimilation applications.

Driven by scaling laws, recommender systems increasingly rely on larger-scale models to capture complex feature interactions and user behaviors, but this trend also leads to prohibitive training and inference costs. While long-sequence models can reuse user-side computation through KV Caching, such reuse is difficult in TokenMixer-based dense feature interaction architectures, where user and group features are deeply entangled and mixed-up across layers. In this work, we present User-Group Separation (UG-Sep), an industrial large-scale framework that enables user-side computation reusable in TokenMixer-based dense interaction models for the first time. UG-Sep explicitly disentangles user-side and item-side information flows within token-mixing layers, ensuring that a subset of tokens preserves purely user-side representations across layers. This design allows the corresponding per-token computations to be reused across multiple samples, significantly reducing redundant inference cost. To compensate for the potential expressive capacity loss induced by masking, we further propose an Information Compensation strategy that adaptively reconstructs suppressed user-item interactions. Moreover, as UG-Sep substantially reduces user-side FLOPs and exposes memory-bound components, we incorporate W8A16 (8-bit weight, 16-bit activation) weight-only quantization to alleviate memory bandwidth bottlenecks and achieve additional acceleration. We conduct extensive offline evaluations and large-scale online A/B experiments at ByteDance to validate the effectiveness of UG-Sep. Results show that UG-Sep reduces inference latency by up to 20% without causing adverse changes to online user experience and commercial metrics on multiple influential business scenarios compared to TokenMixer at ByteDance, including Douyin Feed Recommendation, Hongguo Feed Recommendation, Chuanshanjia Ads, and Qianchuan Ads.

The Model Context Protocol (MCP) is emerging as a standard interface through which large language model (LLM) agents discover and invoke external tools. However, existing MCP evaluations fall short along three key axes: realistic multi-step workflows with cross-server orchestration, breadth across authentic MCP servers rather than mocks, and structured, reproducible claim-level scoring disentangled from agent verbosity or style. We introduce MCP-Atlas, a benchmark for measuring tool-use competency against production MCP servers. MCP-Atlas contains 1,000 natural-language tasks written and verified by human experts spanning 36 real MCP servers and 220 tools. Prompts do not specify servers, tools, or parameters, requiring agents to identify relevant tools among semantically plausible distractors and to compose multi-step, cross-server workflows. Each task is scored with a claim-level rubric, where final answers are scored against atomic factual claims grounded in tool outputs. This answer-centric scoring permits valid alternative tool-call trajectories to receive credit. We pair this with an 11-category diagnostic taxonomy that disentangles tool-call failures from cognitive failures in task understanding, synthesis, parsing, and stopping. Evaluating 20 frontier models from six providers under matched task-level conditions, we find pass rates up to 82.2% at a 0.75 claim coverage threshold and a clear three-tier performance structure. Automated diagnostics show that 63.3% of diagnosed failures are cognitive rather than tool-call related. Notably, several high-performing models fail after successful tool execution due to premature stopping or incorrect synthesis. We release the task schema, containerized harness, claim evaluator, and a 500-task public split, while reserving a 500-task private split to preserve leaderboard integrity. The code is at https://github.com/scaleapi/mcp-atlas.

Multi-agent social dilemmas, such as the tragedy of the commons, capture settings where individual incentives conflict with collective well-being, making these systems highly vulnerable to collapse under disruptions. In this context, this work studies cooperative resilience, understood as the system-level ability to maintain collective well-being under perturbations through adaptive agent behavior. We propose a framework for learning incentive structures aligned with collective well-being in multi-agent reinforcement learning systems, where reward functions shape individual decision-making and collective behavior. A resilience metric is used to score and rank agent trajectories, allowing the inference of reward functions that promote resilient collective behavior. These inferred reward functions are integrated into the multi-agent reinforcement learning process to shape agent interactions in social dilemma settings. The approach is evaluated in resource-sharing environments subject to disruptions, using three incentive structures: individual incentives, resilience-aligned incentives, and a hybrid incentive structure that combines both individual and collective components. The results show that the hybrid incentive structure promotes sustained collective behavior, reduces collapse events associated with resource depletion, and preserves system performance under disruption. These findings highlight the role of incentive design as a mechanism for promoting resilient collective behavior and provide a computational framework for multi-agent social dilemmas under disruptions.

DNA language models are increasingly used to represent genomic sequence, yet their effectiveness depends critically on how raw nucleotides are converted into model inputs. Unlike natural language, DNA offers no canonical boundaries, making fixed tokenizations a brittle design choice under shifts, indels, and local repeats. We introduce DNAChunker, a masked DNA language model that incorporates a learnable adaptive segmentation module to produce context-dependent, variable-length units. Building on a dynamic segmentation procedure, DNAChunker learns to allocate finer granularity to functionally enriched regions while compressing repetitive or redundant sequence. We pretrain DNAChunker on the human reference genome and evaluate it across five benchmarks, where it consistently improves over strong fixed-tokenization baselines. Further analyses and ablations indicate that unlike fixed tokenizations, segmentation is learned in a biologically-informed, mutation-resilient manner.

We propose the Consensus-Based Privacy-Preserving Data Distribution (CPPDD) framework, a lightweight and post-setup autonomous protocol for secure multi-client data aggregation. The framework enforces unanimous-release confidentiality through a dual-layer protection mechanism that combines per-client affine masking with priority-driven sequential consensus locking. Decentralized integrity is verified via step (sigma_S) and data (sigma_D) checksums, facilitating autonomous malicious deviation detection and atomic abort without requiring persistent coordination. The design supports scalar, vector, and matrix payloads with O(N*D) computation and communication complexity, optional edge-server offloading, and resistance to collusion under N-1 corruptions. Formal analysis proves correctness, Consensus-Dependent Integrity and Fairness (CDIF) with overwhelming-probability abort on deviation, and IND-CPA security assuming a pseudorandom function family. Empirical evaluations on MNIST-derived vectors demonstrate linear scalability up to N = 500 with sub-millisecond per-client computation times. The framework achieves 100% malicious deviation detection, exact data recovery, and three-to-four orders of magnitude lower FLOPs compared to MPC and HE baselines. CPPDD enables atomic collaboration in secure voting, consortium federated learning, blockchain escrows, and geo-information capacity building, addressing critical gaps in scalability, trust minimization, and verifiable multi-party computation for regulated and resource-constrained environments.

Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior over the continuous-time dynamics and latent state trajectory in state-space form and updating it through a targeted Metropolis-Hastings sampler equipped with a numerical ODE integrator. The resulting posterior samples are used to formulate a scenario-based optimal control problem that accounts for the uncertainty in the dynamics and latent state and is solved using standard nonlinear programming methods. The approach is validated in a numerical case study on glucose regulation using a Type 1 diabetes model.

The identification and classification of collimated particle sprays, or jets, are essential for interpreting data from high-energy collider experiments. While deep learning has improved jet classification, it often lacks interpretability. We introduce the Explainable Particle Chebyshev Network (E-PCN), a graph neural network extending the Particle Chebyshev Network (PCN). E-PCN integrates kinematic variables into jet classification by constructing four graph representations per jet, each weighted by a distinct variable: angular separation ($Δ$), transverse momentum ($k_T$), momentum fraction ($z$), and invariant mass squared ($m^2$). We use the concept of Gradient-weighted Class Activation Mapping (Grad-CAM) to determine which kinematic variables dominate classification outcomes. Analysis reveals that angular separation and transverse momentum collectively account for approximately 76% of classification decisions (40.72% and 35.67%, respectively), with momentum fraction and invariant mass contributing the remaining 24%. Evaluated on the JetClass dataset with 10 signal classes, E-PCN achieves a macro-accuracy of 94.67%, macro-AUC of 96.78%, and macro-AUPR of 86.79%, representing improvements of 2.36%, 4.13%, and 24.88% respectively over the baseline PCN implementation, while demonstrating physically interpretable feature learning.

Variational inference (VI) is a cornerstone of modern Bayesian learning, enabling approximate inference in complex models. However, its formulation depends on expectations and divergences defined through high-dimensional integrals, often rendering analytical treatment impossible and necessitating heavy reliance on approximations. Possibility theory, an imprecise probability framework, allows us to directly model epistemic uncertainty instead of relying on a subjective interpretation of probabilities. While this framework provides robustness and interpretability under sparse or imprecise information, adapting VI to the possibilistic setting requires rethinking core concepts such as divergences, which presuppose additivity. In this work, we develop a principled formulation for performing possibilistic VI by establishing a maxitive analogue of the classical Donsker-Varadhan formulation. The resulting framework enables us to derive a learning rule for possibilistic VI with exponential-family candidates and practical update rules for neural-network training, giving rise to a family of optimizers termed CBOpt. Finally, we demonstrate that CBOpt achieves competitive performance on both in-domain and out-of-domain image classification tasks.

Large Language Models (LLMs) are increasingly capable of generating complete applications from natural language instructions, creating new opportunities in science and education. In these domains, interactive scientific demonstrations are particularly valuable for explaining concepts, supporting new teaching methods, and presenting research findings. Generating such demonstrations requires models to combine accurate scientific knowledge with the ability to implement interactive front-end code that behaves correctly and responds to user actions. This capability goes beyond the scope of existing benchmarks, which typically evaluate either knowledge question answering without grounding in code or static web code generation without scientific interactivity. To evaluate this integrated ability, we design a hybrid framework that combines programmatic functional testing to rigorously verify interaction logic with visually-grounded qualitative testing to assess rendered outputs against reference snapshots. Building on this framework, we present InteractScience, a benchmark consisting of a substantial set of carefully designed questions across five scientific domains, each paired with unit tests, reference snapshots, and checklists. We evaluate 30 leading open- and closed-source LLMs and report results that highlight ongoing weaknesses in integrating domain knowledge with interactive front-end coding. Our work positions InteractScience as the first benchmark to automatically measure this combined capability with realistic interactive operations, providing a foundation for advancing reliable and educationally useful scientific demonstration code generation. All code and data are publicly available at https://github.com/open-compass/InteractScience.

We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters, and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.

Large language models (LLMs) distinguish themselves from previous technologies by functioning as collaborative ``thought partners,'' capable of engaging more fluidly in natural language on a range of tasks. As LLMs increasingly influence consequential decisions across diverse domains from healthcare to personal advice, the risk of overreliance -- relying on LLMs beyond their capabilities -- grows. This paper argues that measuring and mitigating overreliance must become central to LLM research and deployment. First, we consolidate risks from overreliance at both the individual and societal levels, including high-stakes errors, governance challenges, and cognitive deskilling. Then, we explore LLM characteristics, system design features, and user cognitive biases that together raise serious and unique concerns about overreliance on LLMs in practice. We also examine historical approaches for measuring overreliance, identifying three important gaps and proposing three promising directions to improve measurement. Finally, we propose mitigation strategies that can be pursued to ensure LLMs augment rather than undermine human capabilities.

In this work, we present the \texttt{LLM ORDER BY} semantic operator as a logical abstraction and conduct a systematic study of its physical implementations. First, we propose several improvements to existing semantic sorting algorithms and introduce a semantic-aware external merge sort algorithm. Our extensive evaluation reveals that no single implementation offers universal optimality on all datasets. From our evaluations, we observe a general test-time scaling relationship between sorting cost and the ordering quality for comparison-based algorithms. Building on these insights, we design a budget-aware optimizer that utilizes heuristic rules, LLM-as-Judge evaluation, and consensus aggregation to dynamically select the near-optimal access path for LLM ORDER BY. In our extensive evaluations, our optimizer consistently achieves ranking accuracy on par with or superior to the best static methods across all benchmarks. We believe that this work provides foundational insights into the principled optimization of semantic operators essential for building robust, large-scale LLM-powered analytic systems.

This work presents a novel reinforcement learning (RL) algorithm based on Y-wise Affine Neural Networks (YANNs). YANNs provide an interpretable neural network which can exactly represent known piecewise affine functions of arbitrary input and output dimensions defined on any amount of polytopic subdomains. One representative application of YANNs is to reformulate explicit solutions of multi-parametric linear model predictive control. Built on this, we propose the use of YANNs to initialize RL actor and critic networks, which enables the resulting YANN-RL control algorithm to start with the confidence of linear optimal control. The YANN-actor is initialized by representing the multi-parametric control solutions obtained via offline computation using an approximated linear system model. The YANN-critic represents the explicit form of the state-action value function for the linear system and the reward function as the objective in an optimal control problem (OCP). Additional network layers are injected to extend YANNs for nonlinear expressions, which can be trained online by directly interacting with the true complex nonlinear system. In this way, both the policy and state-value functions exactly represent a linear OCP initially and are able to eventually learn the solution of a general nonlinear OCP. Continuous policy improvement is also implemented to provide heuristic confidence that the linear OCP solution serves as an effective lower bound to the performance of RL policy. The YANN-RL algorithm is demonstrated on a clipped pendulum and a safety-critical chemical-reactive system. Our results show that YANN-RL significantly outperforms the modern RL algorithm using deep deterministic policy gradient, especially when considering safety constraints.

Distrust of public serving institutions and anti-establishment views are on the rise (especially in the U.S.). As people turn to social media for information, it is imperative to understand whether and how social media environments may be contributing to distrust of institutions. In social media, content creators, influencers, and other opinion leaders often position themselves as having expertise and authority on a range of topics from health to politics, and in many cases devalue and dismiss institutional expertise to build a following and increase their own visibility. However, the extent to which this content appears and whether such content increases engagement is unclear. This study analyzes the prevalence of anti-establishment sentiment (AES) on the social media platform TikTok. Despite its popularity as a source of information, TikTok remains relatively understudied and may provide important insights into how people form attitudes towards institutions. We employ a computational approach to label TikTok posts as containing AES or not across topical domains where content creators tend to frame themselves as experts: finance and wellness. As a comparison, we also consider the topic of conspiracy theories, where AES is expected to be common. We find that AES is most prevalent in conspiracy theory content, and relatively rare in content related to the other two topics. However, we find that engagement patterns with such content varies by area, and that there may be platform incentives for users to post content that expresses anti-establishment sentiment.

We investigate Machine-Learned Force Fields (MLFFs) trained on approximate Density Functional Theory (DFT) and Coupled Cluster (CC) level potential energy surfaces for the carbon diamond and lithium hydride solids. We assess the accuracy and precision of the MLFFs by calculating phonon dispersions and vibrational densities of states (VDOS) that are compared to experiment and reference ab initio results. To overcome limitations from long-range effects and the lack of atomic forces in the CC training data, a delta-learning approach based on the difference between CC and DFT results, as well as a charge aware MLFF approach is explored. Compared to DFT, MLFFs trained on CC theory yield higher vibrational frequencies for optical modes, agreeing better with experiment. Furthermore, the MLFFs are used to estimate anharmonic effects on the VDOS of lithium hydride at the level of CC theory.

Variational Quantum Algorithms are promising candidates for near-term quantum computing, yet they face scalability challenges due to barren plateaus, where gradients vanish exponentially relative to system size. Recent conjectures suggest that avoiding these plateaus might inherently lead to classical simulability, thereby limiting the opportunities for quantum advantage. In this work, we advance the theoretical understanding of the relationship between gradient scalability at initialization and the computational complexity of variational quantum algorithms. We first present the Taylor surrogate, a classical simulation technique that matches Pauli path runtime guarantees on near-Clifford regions while offering runtime advantages in specific regimes. Leveraging this surrogate, we prove that beyond previously established classically simulable regions, the computational complexity is at least super-polynomial. Next, we introduce the Linear Clifford Encoder, a classically efficient ansatz modifier that ensures constant-scaling gradients within landscape regions close to Clifford circuits. Finally, numerical experiments on these modified landscapes provide preliminary empirical evidence of a transition zone where constant-scaling gradients may decay polynomially in super-polynomially complex regions rather than exponentially. These findings suggest speculative instances where non-vanishing gradients and super-polynomial complexity could potentially coexist, vindicating the need for future formal proofs.

Large-scale clinical databases offer opportunities for medical research, but their complexity creates barriers to effective use. The Medical Information Mart for Intensive Care (MIMIC-IV), one of the world's largest open-source electronic health record databases, traditionally requires both SQL proficiency and clinical domain expertise. We introduce M3, a system that enables natural language querying of MIMIC-IV data through the Model Context Protocol. With a single command, M3 retrieves MIMIC-IV from PhysioNet, launches a local SQLite instance or connects to hosted BigQuery, and allows researchers to pose clinical questions in plain English. We evaluated M3 using samples from the EHRSQL 2024 benchmark with two language models. On one hundred answerable questions, the proprietary Claude Sonnet 4 achieved 94% accuracy and the open-weights gpt-oss-20B (deployable locally on consumer hardware) achieved 93%; on a matched sample of one hundred unanswerable questions, where correct behavior is to abstain rather than produce SQL, gpt-oss-20B correctly abstained on 69%. Both models translate natural language into SQL, execute queries against MIMIC-IV, and return structured results alongside the underlying query for verification. Error analysis revealed that most failures stemmed from complex temporal reasoning or ambiguous question phrasing rather than fundamental architectural limitations. The comparable performance of a smaller open-weights model demonstrates that privacy-preserving local deployment is viable for sensitive clinical data analysis. M3 lowers technical barriers to critical care data analysis and is designed with security measures including OAuth2 authentication, query validation, and audit logging.

This work formally introduces Y-wise Affine Neural Networks (YANNs), a fully-explainable network architecture that continuously and efficiently represent piecewise affine functions with polytopic subdomains. Following from the proofs, it is shown that the development of YANNs requires no training to achieve the functionally equivalent representation. YANNs thus maintain all mathematical properties of the original formulations. Multi-parametric model predictive control is utilized as an application showcase of YANNs, which theoretically computes optimal control laws as a piecewise affine function of states, outputs, setpoints, and disturbances. With the exact representation of multi-parametric control laws, YANNs retain essential control-theoretic guarantees such as recursive feasibility and stability. This sets YANNs apart from the existing works which apply neural networks for approximating optimal control laws instead of exactly representing them. By optimizing the inference speed of the networks, YANNs can evaluate substantially faster in real-time compared to traditional piecewise affine function calculations. Numerical case studies are presented to demonstrate the algorithmic scalability with respect to the input/output dimensions and the number of subdomains. YANNs represent a significant advancement in control as the first neural network-based controller that inherently ensures both feasibility and stability. Future applications can leverage them as an efficient and interpretable starting point for data-driven modeling/control.

Topological insulators (TIs) and topological crystalline insulators (TCIs) are materials with unconventional electronic properties, making their discovery highly valuable for practical applications. However, such materials, particularly those with a full band gap, remain scarce. Given the limitations of traditional approaches that scan known materials for candidates, we focus on the generation of new topological materials through a generative model. Specifically, we apply reinforcement fine-tuning (ReFT) to a pre-trained generative model, thereby aligning the model's objectives with our material design goals. We demonstrate that ReFT is effective in enhancing the model's ability to generate TIs and TCIs, with minimal compromise on the stability of the generated materials. Using the fine-tuned model, we successfully identify a large number of new topological materials, with Ge$_2$Bi$_2$O$_6$ serving as a representative example--a TI with a full band gap of 0.26 eV, ranking among the largest known in this category.

The rapid advancements in Large Language Models (LLMs) have unlocked transformative possibilities in natural language processing, particularly within the financial sector. Financial data is often embedded in intricate relationships across textual content, numerical tables, and visual charts, posing challenges that traditional methods struggle to address effectively. However, the emergence of LLMs offers new pathways for processing and analyzing this multifaceted data with increased efficiency and insight. Despite the fast pace of innovation in LLM research, there remains a significant gap in their practical adoption within the finance industry, where cautious integration and long-term validation are prioritized. This disparity has led to a slower implementation of emerging LLM techniques, despite their immense potential in financial applications. As a result, many of the latest advancements in LLM technology remain underexplored or not fully utilized in this domain. This survey seeks to bridge this gap by providing a comprehensive overview of recent developments in LLM research and examining their applicability to the financial sector. Building on previous survey literature, we highlight several novel LLM methodologies, exploring their distinctive capabilities and their potential relevance to financial data analysis. By synthesizing insights from a broad range of studies, this paper aims to serve as a valuable resource for researchers and practitioners, offering direction on promising research avenues and outlining future opportunities for advancing LLM applications in finance.

We address the problem of selecting $k$ representative nodes from a network, aiming to achieve two objectives: identifying the most influential nodes and ensuring the selection proportionally reflects the network's diversity. We propose two approaches to accomplish this, analyze them theoretically, and demonstrate their effectiveness through a series of experiments.

In graph-based data analysis, $k$-nearest neighbor ($k$NN) graphs are widely used due to their adaptivity to local data densities. Allowing weighted edges in the graph, the kernelized graph affinity provides a more general type of $k$NN graph where the $k$NN distance is used to set the kernel bandwidth adaptively. In this work, we consider a general class of $k$NN graph where the graph affinity is $W_{ij} = ε^{-d/2} k_0 ( \| x_i - x_j \|^2 / εϕ( \hat ρ(x_i), \hat ρ(x_j) )^2 ) $, with $\hatρ(x)$ being the (rescaled) $k$NN distance at the point $x$, $ϕ$ a symmetric bi-variate function, and $k_0$ a non-negative function on $[0,\infty)$. Under the manifold data setting, where $N$ i.i.d. samples $x_i$ are drawn from a density $p$ on a $d$-dimensional unknown manifold embedded in a high dimensional Euclidean space, we prove the operator pointwise convergence of the $k$NN graph Laplacian to the limiting manifold operator (depending on $p$) at the rate of $O(N^{-2/(d+6)})$, up to a log factor, when $k_0$ and $ϕ$ have $C^3$ regularity and satisfy other technical conditions. This is obtained when $ε\sim N^{-2/(d+6)}$ and $k \sim N^{6/(d+6)}$, both at the optimal order to balance the theoretical bias and variance errors. Our improved convergence rate is based on a refined analysis of the $k$NN estimator, which can be of independent interest. We validate our theory by numerical experiments on simulated data.

The ability to discover new materials with desirable properties is critical for numerous applications from helping mitigate climate change to advances in next generation computing hardware. AI has the potential to accelerate materials discovery and design by more effectively exploring the chemical space compared to other computational methods or by trial-and-error. While substantial progress has been made on AI for materials data, benchmarks, and models, a barrier that has emerged is the lack of publicly available training data and open pre-trained models. To address this, we present a Meta FAIR release of the Open Materials 2024 (OMat24) large-scale open dataset and an accompanying set of pre-trained models. OMat24 contains over 110 million density functional theory (DFT) calculations focused on structural and compositional diversity. Our EquiformerV2 models achieve state-of-the-art performance on the Matbench Discovery leaderboard and are capable of predicting ground-state stability and formation energies to an F1 score above 0.9 and an accuracy of 20 meV/atom, respectively. We explore the impact of model size, auxiliary denoising objectives, and fine-tuning on performance across a range of datasets including OMat24, MPtraj, and Alexandria. The open release of the OMat24 dataset and models enables the research community to build upon our efforts and drive further advancements in AI-assisted materials science.

Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high-dimensional data. Despite its success and widespread adoption, the primary limitation of the MMD test has been its quadratic-time complexity, which poses challenges for large-scale analysis. While various approaches have been proposed to expedite the procedure, it has been unclear whether it is possible to attain the same power guarantee as the MMD test at sub-quadratic time cost. To fill this gap, we revisit the approximated MMD test using random Fourier features, and investigate its computational-statistical trade-off. We start by revealing that the approximated MMD test is pointwise consistent in power only when the number of random features approaches infinity. We then consider the uniform power of the test and study the time-power trade-off under the minimax testing framework. Our result shows that, by carefully choosing the number of random features, it is possible to attain the same minimax separation rates as the MMD test within sub-quadratic time. We demonstrate this point under different distributional assumptions such as densities in a Sobolev ball. Our theoretical findings are corroborated by simulation studies.

Quantum state tomography is a crucial technique for characterizing the state of a quantum system, which is essential for many applications in quantum technologies. In recent years, there has been growing interest in leveraging neural networks to enhance the efficiency and accuracy of quantum state tomography. However, versatile methods that are broadly applicable across diverse reconstruction scenarios remain relatively underexplored. In this paper, we present two neural network-based reconstruction approaches for both pure and mixed quantum state tomography: Restricted Feature Based Neural Network and Mixed States Neural Network. By leveraging class information during reconstruction, we are able to achieve state-of-the-art performance of tomography for both pure and mixed quantum states.