arXiv subjects

Justin Baker

Publications and source records attributed to Justin Baker.

13 recordsLinked to original sources

arXiv2026

From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier

Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages. However, current systems remain fundamentally limited in tackling frontier research mathematics, such as discovering new theorems or resolving open conjectures, which are often open-ended, under-specified, and involve multiple layers of abstraction. We argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning. In this position paper, we provide a systematic review of the field, covering datasets, auto-formalization, and proof synthesis. More importantly, we identify core limitations of existing systems in serving as mathematical research agents, examining issues across datasets, relational structure, mathematical exploration, tool ecosystem, and human-AI collaboration, outlining a strategic road-map for the future of AI4Math.

cs.CL↗

arXiv2026

Advanced Control of Electron Beams: Tailoring X-ray Production with Programmable Laser Shaping

Leveraging the full scientific capabilities of next-generation high-repetition-rate free-electron lasers requires programmable control over electron-beam properties at their source. The photoinjector drive laser defines the electron beam's initial six-dimensional phase-space distribution, yet has historically been limited to Gaussian or static flat-top profiles, with most manipulation occurring downstream. Here we demonstrate software-programmable ultraviolet pulse shaping at the LCLS-II photoinjector as a source-level actuator that complements traditional accelerator controls. Using a coupled architecture combining dispersion-controlled nonlinear frequency conversion with spatial-light-modulator spectral shaping, we generate user-defined temporal structures and observe their imprint on electron bunches through high-resolution time-domain diagnostics. Laser-imposed multi-peaked modulation persists through acceleration, magnetic compression, and undulator transport with shot-to-shot repeatability, producing clearly resolved current structure in the compressed beam. Variance-based reconstruction from transverse deflecting cavity measurements reveals structured X-ray emission profiles exhibiting temporal features consistent with the programmed laser waveform. By providing rapid, software-controlled reconfiguration of electron-beam initial conditions, this source-level control approach establishes a programmable upstream actuator for future adaptive optimization and autonomous facility operation at high-repetition-rate light sources.

physics.acc-ph↗

arXiv2026

Towards Multiscale Graph-based Protein Learning with Geometric Secondary Structural Motifs

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale representations and modeling long-range dependencies efficiently. In this work, we propose an efficient multiscale graph-based learning framework tailored to proteins. Our proposed framework contains two crucial components: (1) It constructs a hierarchical graph representation comprising a collection of fine-grained subgraphs, each corresponding to a secondary structure motif (e.g., $\alpha$-helices, $\beta$-strands, loops), and a single coarse-grained graph that connects these motifs based on their spatial arrangement and relative orientation. (2) It employs two GNNs for feature learning: the first operates within individual secondary motifs to capture local interactions, and the second models higher-level structural relationships across motifs. Our modular framework allows a flexible choice of GNN in each stage. Theoretically, we show that our hierarchical framework preserves the desired maximal expressiveness, ensuring no loss of critical structural information. Empirically, we demonstrate that integrating baseline GNNs into our multiscale framework remarkably improves prediction accuracy and reduces computational cost across various benchmarks.

cs.LG↗

arXiv2026

Upstream Laser-based Longitudinal Enhancement of Relativistic Photoelectrons

Controlling the longitudinal phase space of high-brightness relativistic electron beams is crucial for advancing a broad spectrum of charged-particle-based instrumentation and scientific frontiers. A generalized method for achieving this control involves manipulating the photoemission laser's temporal distribution at the picosecond level, a long-standing technical challenge. Recent developments in laser shaping have enabled the creation of high-power, picosecond-scale symmetrical and asymmetrical temporal profiles, capable of fine-tuning complex space-charge dynamics and external field effects in relativistic charged-particle beams. Here, we demonstrate that rather than deviations from theorized, idealized laser distributions, a controlled asymmetry can be harnessed to counteract accelerator-induced distortions. By implementing spatiotemporal shaping of the ultraviolet photocathode laser at the LCLS-II superconducting injector, we achieve deterministic control over the longitudinal phase space without downstream corrections. We find that this optical asymmetry induces a self-linearizing effect across both low (40 pC) and high (80 pC) charge regimes, effectively suppressing nonlinear compression and energy chirp. Consequently, this approach is expected to preserve a low emittance comparable to that of ideal flattop or regular Gaussian profiles, while delivering superior current uniformity and shot-to-shot stability. These results establish spatiotemporal laser shaping as a compact, generalizable tool for directly optimizing beam brightness at the source.

physics.optics↗

arXiv2025

Structured Light at the Extreme: Harnessing Spatiotemporal Control for High-Field Laser-Matter Interactions

This review charts the emerging paradigm of intelligent structured light for high-field laser-matter interactions, where the precise spatiotemporal and vectorial control of light is a critical degree of freedom. We outline a transformative framework built upon three synergistic pillars. First, we survey the advanced electromagnetic toolkit, moving beyond conventional spatial light modulators to include robust static optics and the promising frontier of plasma light modulators. Second, we detail the optimization engine for this high-dimensional design space, focusing on physics-informed digital twins and AI-driven inverse design to automate the discovery of optimal light structures. Finally, we explore the groundbreaking applications enabled by this integrated approach, including programmable electron beams, orbital-angular-momentum-carrying {\gamma}-rays, compact THz accelerators, and robust communications. The path forward necessitates overcoming grand challenges in material science, real-time adaptive control at MHz rates, and the extension of these principles to the quantum realm. This review serves as a call to action for a coordinated, interdisciplinary effort to command, rather than merely observe, light-matter interactions at the extreme.

physics.optics↗

arXiv2025

Deep Learning Assisted Modeling for $\chi^{(2)}$ Nonlinear Optics

Modeling second-order ($\chi^{(2)}$) nonlinear optical processes remains computationally expensive due to the need to resolve fast field oscillations and simulate wave propagation using methods like the split-step Fourier method (SSFM). This can become a bottleneck in real-time applications, such as high-repetition-rate laser systems requiring rapid feedback and control. We present an LSTM-based surrogate model trained on SSFM simulations generated from a start-to-end model of the photocathode drive laser at SLAC National Accelerator Laboratory's Linac Coherent Light Source II. The model achieves over 250x speedup while maintaining high fidelity, enabling future real-time optimization and laying the foundation for data-integrated modeling frameworks and digital twins of laser systems.

physics.optics↗

arXiv2025

LLAMADRS: Evaluating Open-Source LLMs on Real Clinical Interviews--To Reason or Not to Reason?

Large language models (LLMs) excel on many NLP benchmarks, but their behavior on real-world, semi-structured prediction remains underexplored. We present LlaMADRS, a benchmark for structured clinical assessment from dialogue built on the CAMI corpus of psychiatric interviews, comprising 5,804 expert annotations across 541 sessions. We evaluate 25 open-source models (standard and reasoning-augmented; 0.6B--400B parameters) and generate over 400,000 predictions. Our results demonstrate that strong open-source LLMs achieve item-level accuracy with residual error below clinically substantial thresholds. Additionally, an Item-then-Sum (ItS) strategy, assessing symptoms individually through discrete LLM calls before synthesizing final scores, significantly reduces error relative to Direct Total Score (DTS) prediction across most model architectures and scales, despite reasoning models attempting similar decomposition in the reasoning traces of their DTS predictions. In fact, we find that performance gains attributed to "reasoning" depend fundamentally on prompt design: standard models equipped with structured task definitions and examples match reasoning-augmented counterparts. Among the latter, longer reasoning traces correlate with reduced error; while higher model scale does across both architectures. Our results clarify when and why reasoning helps and offer actionable guidance for deploying LLMs in semi-structured clinical assessment.

cs.HC↗

arXiv2024

Learning to Control the Smoothness of Graph Convolutional Network Features

The pioneering work of Oono and Suzuki [ICLR, 2020] and Cai and Wang [arXiv:2006.13318] initializes the analysis of the smoothness of graph convolutional network (GCN) features. Their results reveal an intricate empirical correlation between node classification accuracy and the ratio of smooth to non-smooth feature components. However, the optimal ratio that favors node classification is unknown, and the non-smooth features of deep GCN with ReLU or leaky ReLU activation function diminish. In this paper, we propose a new strategy to let GCN learn node features with a desired smoothness -- adapting to data and tasks -- to enhance node classification. Our approach has three key steps: (1) We establish a geometric relationship between the input and output of ReLU or leaky ReLU. (2) Building on our geometric insights, we augment the message-passing process of graph convolutional layers (GCLs) with a learnable term to modulate the smoothness of node features with computational efficiency. (3) We investigate the achievable ratio between smooth and non-smooth feature components for GCNs with the augmented message-passing scheme. Our extensive numerical results show that the augmented message-passing schemes significantly improve node classification for GCN and some related models.

cs.LG↗

arXiv2023

Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain

Inverse scattering has a broad applicability in quantum mechanics, remote sensing, geophysical, and medical imaging. This paper presents a robust direct reduced order model (ROM) method for solving inverse scattering problems based on an efficient approximation of the resolvent operator regularizing the Lippmann-Schwinger-Lanczos (LSL) algorithm. We show that the efficiency of the method relies upon the weak dependence of the orthogonalized basis on the unknown potential in the Schr\"odinger equation by demonstrating that the Lanczos orthogonalization is equivalent to performing Gram-Schmidt on the ROM time snapshots. We then develop the LSL algorithm in the frequency domain with two levels of regularization. We show that the same procedure can be extended beyond the Schr\"odinger formulation to the Helmholtz equation, e.g., to imaging the conductivity using diffusive electromagnetic fields in conductive media with localized positive conductivity perturbations. Numerical experiments for Helmholtz and Schr\"odinger problems show that the proposed bi-level regularization scheme significantly improves the performance of the LSL algorithm, allowing for good reconstructions with noisy data and large data sets.

math.NA↗

arXiv2022

Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs

Learning neural ODEs often requires solving very stiff ODE systems, primarily using explicit adaptive step size ODE solvers. These solvers are computationally expensive, requiring the use of tiny step sizes for numerical stability and accuracy guarantees. This paper considers learning neural ODEs using implicit ODE solvers of different orders leveraging proximal operators. The proximal implicit solver consists of inner-outer iterations: the inner iterations approximate each implicit update step using a fast optimization algorithm, and the outer iterations solve the ODE system over time. The proximal implicit ODE solver guarantees superiority over explicit solvers in numerical stability and computational efficiency. We validate the advantages of proximal implicit solvers over existing popular neural ODE solvers on various challenging benchmark tasks, including learning continuous-depth graph neural networks and continuous normalizing flows.

math.NA↗

arXiv2022

Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning algorithms enable learning POD-based dynamics from data and making accurate and fast predictions of dynamical systems. In this paper, we leverage the recently proposed heavy-ball neural ODEs (HBNODEs) [Xia et al. NeurIPS, 2021] for learning data-driven reduced-order models (ROMs) in the POD context, in particular, for learning dynamics of time-varying coefficients generated by the POD analysis on training snapshots generated from solving full order models. HBNODE enjoys several practical advantages for learning POD-based ROMs with theoretical guarantees, including 1) HBNODE can learn long-term dependencies effectively from sequential observations and 2) HBNODE is computationally efficient in both training and testing. We compare HBNODE with other popular ROMs on several complex dynamical systems, including the von K\'{a}rm\'{a}n Street flow, the Kurganov-Petrova-Popov equation, and the one-dimensional Euler equations for fluids modeling.

cs.LG↗

arXiv2019

Quantum Computing at the Frontiers of Biological Sciences

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.

quant-ph↗

arXiv2017

Deducing the severity of psychiatric symptoms from the human voice

Psychiatric illnesses are often associated with multiple symptoms, whose severity must be graded for accurate diagnosis and treatment. This grading is usually done by trained clinicians based on human observations and judgments made within doctor-patient sessions. Current research provides sufficient reason to expect that the human voice may carry biomarkers or signatures of many, if not all, these symptoms. Based on this conjecture, we explore the possibility of objectively and automatically grading the symptoms of psychiatric illnesses with reference to various standard psychiatric rating scales. Using acoustic data from several clinician-patient interviews within hospital settings, we use non-parametric models to learn and predict the relations between symptom-ratings and voice. In the process, we show that different articulatory-phonetic units of speech are able to capture the effects of different symptoms differently, and use this to establish a plausible methodology that could be employed for automatically grading psychiatric symptoms for clinical purposes.

cs.SD↗