This paper introduces a novel reachability problem for the scenario involving two agents, where one agent follows another agent using a feedback strategy. The geometry of the reachable set for an agent, termed \emph{dependent reachable set}, is characterized using the constant bearing pursuit strategy as a case study. Key theoretical results are presented that provide geometric bounds for the associated dependent reachable set. Simulation results are presented to empirically establish the shape of the dependent reachable set. In the process, an original optimization problem is formulated and analyzed for the constant bearing pursuit strategy.

Beyond the commonly recognized optical aberrations, the imaging performance of simplified optical systems--including single-lens and metalens designs--is often further degraded by veiling glare caused by stray-light scattering from non-ideal optical surfaces and coatings, particularly in complex real-world environments. This compound degradation undermines traditional lens aberration correction yet remains underexplored. A major challenge is that conventional scattering models (e.g., for dehazing) fail to fit veiling glare due to its spatial-varying and depth-independent nature. Consequently, paired high-quality data are difficult to prepare via simulation, hindering application of data-driven veiling glare removal models. To this end, we propose VeilGen, a generative model that learns to simulate veiling glare by estimating its underlying optical transmission and glare maps in an unsupervised manner from target images, regularized by Stable Diffusion (SD)-based priors. VeilGen enables paired dataset generation with realistic compound degradation of optical aberrations and veiling glare, while also providing the estimated latent optical transmission and glare maps to guide the veiling glare removal process. We further introduce DeVeiler, a restoration network trained with a reversibility constraint, which utilizes the predicted latent maps to guide an inverse process of the learned scattering model. Extensive experiments on challenging simplified optical systems demonstrate that our approach delivers superior restoration quality and physical fidelity compared with existing methods. These suggest that VeilGen reliably synthesizes realistic veiling glare, and its learned latent maps effectively guide the restoration process in DeVeiler. All code and datasets will be publicly released at https://github.com/XiaolongQian/DeVeiler.

Rare disease diagnosis requires matching variant-bearing genes to complex patient phenotypes across large and heterogeneous evidence sources. This process remains time-intensive in current clinical interpretation pipelines. To overcome these limitations, We present LA-MARRVEL, a knowledge-grounded, language-aware LLM framework and designed for clinical robustness and practical deployment. LA-MARRVEL delivers a 12-15 percentage-point absolute improvement in Recall@1 over established gene prioritization approaches, showing that architectural design can drive substantial accuracy gains. We found that the central contributor is structured, phenotype-rich prompt construction that explicitly encodes patient and disease phenotypes, preserving clinically meaningful context more effectively than disease labels alone. Across three real-world cohorts, LA-MARRVEL consistently improves gene-ranking performance, including in challenging cases where the causal gene was initially ranked lower by first-stage prioritization. For each candidate gene, the system delivers clinically relevant, ACMG-aligned reasoning that integrates phenotype concordance, inheritance patterns, and variant-level evidence into auditable explanations, enabling streamlined clinical review. These findings suggest that knowledge-grounded LLM layer can enhance existing rare-disease gene prioritization workflows without altering established diagnostic pipelines.

Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability analysis tools adapted to them. We propose a novel interval-based reachability method that leverages continuous-time mixed monotonicity techniques for dynamical systems to compute an over-approximation for the neural ODE reachable sets. By exploiting the geometric structure of full initial sets and their boundaries via the homeomorphism property, our approach ensures efficient bound propagation. By embedding neural ODE dynamics into a mixed monotone system, our interval-based reachability approach, implemented in TIRA with single-step, incremental, and boundary-based approaches, provides sound and computationally efficient over-approximations compared with CORA's zonotopes and NNV2.0 star set representations, while trading tightness for efficiency. This trade-off makes our method particularly suited for high-dimensional, real-time, and safety-critical applications. Applying mixed monotonicity to neural ODE reachability analysis paves the way for lightweight formal analysis by leveraging the symmetric structure of monotone embeddings and the geometric simplicity of interval boxes, opening new avenues for scalable verification. This novel approach is illustrated on two numerical examples of a spiral system and a fixed-point attractor system modeled as a neural ODE.

Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression setting, showing that verifier-guided retraining can yield near-term improvements, but ultimately drives the parameter estimate to the verifier's "knowledge center" in the long run. Our theory further predicts that, unless the verifier is perfectly reliable, these early gains will plateau and may even reverse. Indeed, our experiments across linear regression, Variational Autoencoders (VAEs) trained on MNIST, and fining-tuning SmolLM2-135M on the XSUM task confirm these theoretical insights.

Large language models promise a broad set of functions, but when not given a specific objective, they default to generic results. We demonstrate that inferring the user's in-the-moment objective, then rapidly optimizing for that singular objective, enables LLMs to produce specialized tools, interfaces, and responses. Our work introduces just-in-time objectives, which model a user's goals to specialize LLM systems on the fly. We contribute an architecture for automatically inducing such objectives by passively observing user behavior, then steering downstream AI systems through generation and evaluation against this objective. Inducing just-in-time objectives (e.g., "Clarify the abstract's research contribution") enables automatic generation of tools, e.g., those that critique a draft based on relevant HCI methodologies, anticipate related researchers' reactions, or surface ambiguous terminology. In a series of experiments on participants' own tasks, JIT objectives enable LLM outputs that achieve 66-86% win rates over typical LLMs. In-person use sessions confirm that JIT objectives produce specialized tools that are unique to each participant and are rated as significantly higher quality than a standard LLM chat tool.

T cell receptor (TCR) recognition of peptide-MHC (pMHC) complexes is a central component of adaptive immunity, with implications for vaccine design, cancer immunotherapy, and autoimmune disease. While recent advances in machine learning have improved prediction of TCR-pMHC binding, the most effective approaches are black-box transformer models that cannot provide a rationale for predictions. Post-hoc explanation methods can provide insight with respect to the input but do not explicitly model biochemical mechanisms (e.g. known binding regions), as in TCR-pMHC binding. ``Explain-by-design'' models (i.e., with architectural components that can be examined directly after training) have been explored in other domains, but have not been used for TCR-pMHC binding. We propose explainable model layers (TCR-EML) that can be incorporated into protein-language model backbones for TCR-pMHC modeling. Our approach uses prototype layers for amino acid residue contacts drawn from known TCR-pMHC binding mechanisms, enabling high-quality explanations for predicted TCR-pMHC binding. Experiments of our proposed method on large-scale datasets demonstrate competitive predictive accuracy and generalization, and evaluation on the TCR-XAI benchmark demonstrates improved explainability compared with existing approaches.

We present self-speculative masked diffusions, a new class of masked diffusion generative models for discrete data that require significantly fewer function evaluations to generate samples. Standard masked diffusion models predict factorized logits over currently masked positions. A number of masked positions are then sampled, however, the factorization approximation means that sampling too many positions in one go leads to poor sample quality. As a result, many simulation steps and therefore neural network function evaluations are required to generate high-quality data. We reduce the computational burden by generating non-factorized predictions over masked positions. This is achieved by modifying the final transformer attention mask from non-causal to causal, enabling draft token generation and parallel validation via a novel, model-integrated speculative sampling mechanism. This results in a non-factorized predictive distribution over masked positions in a single forward pass. We apply our method to GPT2 scale text modelling and protein sequence generation, finding that we can achieve a ~2x reduction in the required number of network forward passes relative to standard masked diffusion models.

We show that ensembles of deep neural networks, called deep ensembles, can be used to perform quantum parameter estimation while also providing a means for quantifying uncertainty in parameter estimates, which is a key advantage of using Bayesian inference for parameter estimation that is lost when using existing machine learning methods. We show that optimizing for both accurate parameter estimates and well calibrated uncertainty estimates does not lead to degradation in the former as opposed to only optimizing for accuracy. We also show that the drift detection capabilities of these ensemble models can be used to detect drift in the experimental data used during inference. This approach is also shown to provide much faster inference time than both likelihood-based and likelihood-free Bayesian inference. These results suggest that such models could enable accurate, real-time parameter estimation with quantified uncertainty, making them promising candidates for deployment in experimental settings.

Self-supervised learning (SSL) has emerged as a powerful paradigm for representation learning by optimizing geometric objectives, such as invariance to augmentations, variance preservation, and feature decorrelation, without requiring labels. However, most existing methods operate in Euclidean space, limiting their ability to capture nonlinear dependencies and geometric structures. In this work, we propose Kernel VICReg, a novel self-supervised learning framework that pulls the VICReg objective into a Reproducing Kernel Hilbert Space (RKHS). By kernelizing each term of the loss, variance, invariance, and covariance, we obtain a general formulation that operates on double-centered kernel matrices and Hilbert--Schmidt norms, enabling nonlinear feature learning without explicit mappings. We demonstrate that Kernel VICReg mitigates the risk of representational collapse under challenging conditions and improves performance on datasets exhibiting nonlinear structure or limited sample regimes. Empirical evaluations across MNIST, CIFAR-10, STL-10, TinyImageNet, and ImageNet100 show consistent gains over Euclidean VICReg, with particularly strong improvements on datasets where nonlinear structures are prominent. UMAP visualizations are provided only as a qualitative illustration of embedding geometry and are not used as a calibration or statistical validation. Our results suggest that kernelizing SSL objectives is a promising direction for bridging classical kernel methods with modern representation learning.

Over the past decade, higher education has undergone successive shifts driven by three major developments: Massive Open Online Courses (MOOCs), Smart Teaching technologies, and AI-enhanced learning. Each paradigm emerged to address specific limitations of traditional education: MOOCs enable ubiquitous access to learning resources; Smart Teaching supports real-time interaction with data-driven insights; and generative AI offers scalable personalization and on-demand content generation. However, these paradigms are often adopted in isolation, limiting their systemic pedagogical potential. This paper proposes a unified instructional framework that integrates these approaches under a coherent teaching-driven logic. The framework distinguishes three complementary dimensions of instructional design: structured exposure (MOOCs), adaptive allocation (Smart Teaching), and efficiency amplification (AI). To operationalize this integration, we formalize the framework as a layered knowledge transformation model and illustrate its behavior through a step-by-step learning example. The results demonstrate how each layer contributes to measurable and functionally distinct gains in knowledge mastery.

CD8+ "killer" T cells and CD4+ "helper" T cells play a central role in the adaptive immune system by recognizing antigens presented by Major Histocompatibility Complex (pMHC) molecules via T Cell Receptors (TCRs). Modeling binding between T cells and the pMHC complex is fundamental to understanding basic mechanisms of human immune response as well as in developing therapies. While transformer-based models such as TULIP have achieved impressive performance in this domain, their black-box nature precludes interpretability and thus limits a deeper mechanistic understanding of T cell response. Most existing post-hoc explainable AI (XAI) methods are confined to encoder-only, co-attention, or model-specific architectures and cannot handle encoder-decoder transformers used in TCR-pMHC modeling. To address this gap, we propose Quantifying Cross-Attention Interaction (QCAI), a new post-hoc method designed to interpret the cross-attention mechanisms in transformer decoders. Quantitative evaluation is a challenge for XAI methods; we have compiled TCR-XAI, a benchmark consisting of 274 experimentally determined TCR-pMHC structures to serve as ground truth for binding. Using these structures we compute physical distances between relevant amino acid residues in the TCR-pMHC interaction region and evaluate how well our method and others estimate the importance of residues in this region across the dataset. We show that QCAI achieves state-of-the-art performance on both interpretability and prediction accuracy under the TCR-XAI benchmark.

Discovering insights from a real-world data lake potentially containing unclean, semi-structured, and unstructured data requires a variety of data processing tasks, ranging from extraction and cleaning to integration, analysis, and modeling. This process often also demands domain knowledge and project-specific insight. While AI models have shown remarkable results in reasoning and code generation, their abilities to design and execute complex pipelines that solve these data-lake-to-insight challenges remain unclear. We introduce KramaBench which consists of 104 manually curated and solved challenges spanning 1700 files, 24 data sources, and 6 domains. KramaBench focuses on testing the end-to-end capabilities of AI systems to solve challenges which require automated orchestration of different data tasks. KramaBench also features a comprehensive evaluation framework assessing the pipeline design and individual data task implementation abilities of AI systems. We evaluate 8 LLMs using our single-agent reference framework DS-Guru, alongside both open- and closed-source single- and multi-agent systems, and find that while current agentic systems may handle isolated data-science tasks and generate plausible draft pipelines, they struggle with producing working end-to-end pipelines. On KramaBench, the best system reaches only 55% end-to-end accuracy in the full data-lake setting. Even with perfect retrieval, the accuracy tops out at 62%. Leading LLMs can identify up to 42% of important data tasks but can only fully implement 20% of individual data tasks. Our code, reference framework, and data are available at https://github.com/mitdbg/KramaBench.

Code large language models (CodeLLMs) and agents are increasingly being integrated into complex software engineering tasks spanning the entire Software Development Life Cycle (SDLC). Benchmarking is critical for rigorously evaluating these capabilities. However, despite their growing significance, there remains a lack of comprehensive reviews that examine these benchmarks from an SDLC perspective. To bridge this gap, we propose a tiered analysis framework to systematically review 178 benchmarks from 461 papers, comprehensively characterizing them from the perspective of the SDLC. Our findings reveal a notable imbalance in the coverage of current benchmarks, with approximately 61\% focused on the software implementation phase in SDLC, while requirements engineering and software design phases receive minimal attention at only 5\% and 3\%, respectively. % Additionally, anti-contamination strategies are largely absent from current benchmarks, leading to an increased risk of data leakage. Furthermore, current benchmarks lack effective anti-contamination strategies, posing significant risks of data leakage and potentially inflated performance assessments. Finally, we identify key open challenges in current research and outline future directions to narrow the gap between the theoretical capabilities of CodeLLMs and agents and their practical effectiveness in real-world scenarios.

The growing luminosity frontier at the Large Hadron Collider is challenging the reconstruction and analysis of particle collision events. Increased particle multiplicities are straining latency and storage requirements at the data acquisition stage, while new complications are emerging, including higher background levels and more frequent particle vertex misassociations. This in turn necessitates the development of more holistic and scalable reconstruction methods that take advantage of recent advances in machine learning. We propose a novel Heterogeneous Graph Neural Network (HGNN) architecture featuring unique representations for diverse particle collision relationships and integrated graph pruning layers for scalability. Trained with a multi-task paradigm in an environment mimicking the LHCb experiment, this HGNN significantly improves beauty hadron reconstruction performance. Notably, it concurrently performs particle vertex association and graph pruning within a single framework. We quantify reconstruction and pruning performance, demonstrate enhanced inference time scaling with event complexity, and mitigate potential performance loss using a weighted message passing scheme.

Tabular data embedded in PDF files, web pages, and other types of documents is prevalent in various domains. These tables, which we call human-centric tables (HCTs for short), are dense in information but often exhibit complex structural and semantic layouts. To query these HCTs, some existing solutions focus on transforming them into relational formats. However, they fail to handle the diverse and complex layouts of HCTs, making them not amenable to easy querying with SQL-based approaches. Another emerging option is to use Large Language Models (LLMs) and Vision Language Models (VLMs). However, there is a lack of standard evaluation benchmarks to measure and compare the performance of models to query HCTs using natural language. To address this gap, we propose the HumanCentric Tables Question-Answering extensive benchmark (HCTQA) consisting of thousands of HCTs with several thousands of natural language questions with their respective answers. More specifically, HCT-QA includes 1,880 real-world HCTs with 9,835 QA pairs in addition to 4,679 synthetic HCTs with 67.7K QA pairs. Also, we show through extensive experiments the performance of 25 and 9 different LLMS and VLMs, respectively, in an answering HCT-QA's questions. In addition, we show how finetuning an LLM on HCT-QA improves F1 scores by up to 25 percentage points compared to the off-the-shelf model. Compared to existing benchmarks, HCT-QA stands out for its broad complexity and diversity of covered HCTs and generated questions, its comprehensive metadata enabling deeper insight and analysis, and its novel synthetic data and QA generator.

In this paper, we adopt a survivor-centered approach to locate and dissect the role of sociotechnical AI governance in preventing AI-Generated Non-Consensual Intimate Images (AIG-NCII) of adults, colloquially known as "deep fake pornography." We identify a "malicious technical ecosystem" or "MTE," comprising of open-source face-swapping models and nearly 200 "nudifying" software programs that allow non-technical users to create AIG-NCII within minutes. Then, using the National Institute of Standards and Technology (NIST) AI 100-4 report as a reflection of current synthetic content governance methods, we show how the current landscape of practices fails to effectively regulate the MTE for adult AIG-NCII, as well as flawed assumptions explaining these gaps.

Image and video quality metrics, such as SSIM, LPIPS, and VMAF, aim to predict perceived visual quality and are often assumed to reflect principles of human vision. However, relatively few metrics explicitly incorporate models of human perception, with most relying on hand-crafted formulas or data-driven training to approximate perceptual alignment. In this paper, we introduce a set of tests for full-reference quality metrics that evaluate their ability to capture key aspects of low-level human vision: contrast sensitivity, contrast masking, and contrast matching. These tests provide an additional framework for assessing both established and newly proposed metrics. We apply the tests to 34 existing quality metrics and highlight patterns in their behavior, including the ability of LPIPS and MS-SSIM to predict contrast masking and the tendency of SSIM to overemphasize high spatial frequencies, which is mitigated in MS-SSIM, and the general inability of metrics to model supra-threshold contrast constancy. Our results demonstrate how these tests can reveal properties of quality metrics that are not easily observed with standard evaluation protocols.

Adversarial robustness in quantum classifiers is a critical area of study, providing insights into their performance compared to classical models and uncovering potential advantages inherent to quantum machine learning. In the NISQ era of quantum computing, circuit cutting is a notable technique for simulating circuits that exceed the qubit limitations of current devices, enabling the distribution of a quantum circuit's execution across multiple quantum processing units through classical communication. In contrast, when quantum communication is available, teleportation-based methods can be used to support the distribution of the quantum circuit. We study the robustness of partitioned quantum classifiers to adversarial perturbations targeting wire cutting or quantum state teleportation and show a link between such perturbations and implementing adversarial gates within intermediate layers of a quantum classifier. We then proceed to study the latter problem from both a theoretical and experimental perspective.

While LLM-based TTS models exhibit zero-shot emotion and speaker cloning, their cloning fidelity and pronunciation clarity degrade on unseen domains. Fine-tuning is essential for adaptation, yet uniform approaches overlook specific parameter contributions. Uniform tuning on limited data causes slow training and catastrophic forgetting, leading to degraded pronunciation accuracy. To address this, we propose CSP-FT, a characteristic-specific partial fine-tuning strategy. By dynamically analyzing layer contributions via a weighted sum, we selectively fine-tune only the two layers capturing the most and least emotion and speaker information, maximizing the utility of the former while explicitly strengthening the capacity of the latter. Experiments on a combined corpus of 11 datasets show CSP-FT matches or exceeds the fidelity and intelligibility of full fine-tuning while updating only ~8% of parameters, accelerating training by ~2x, and significantly mitigating catastrophic forgetting.

Seismic exploration remains the most critical method for characterizing subsurface structures in geophysics. However, complex surface conditions often cause a non-uniform distribution of seismic receivers along survey lines, leading to irregularly acquired seismic data, which affects subsequent processing and inversion. Prior deep learning-based seismic data reconstruction methods typically rely on datasets for supervised training. While some existing methods avoid extra data, they lack effective constraints on reconstructed data, leading to unstable performance. In this study, we propose a self-supervised self-consistency learning strategy with a lightweight network for seismic data reconstruction. Our method requires no extra datasets, and it leverages inter-component correlations in seismic data to design a loss function, optimizing a network with only 188,849 learnable parameters. Validated on two public seismic datasets, results demonstrate our approach yields high-quality reconstruction, providing significant value for large-scale and complex seismic exploration tasks.

A project (e.g., writing a collaborative research paper) is often a group effort. At the end, each contributor identifies their contribution, often verbally. The reward, however, is very frequently financial. It leads to the question of what (percentage) share in the creation of the paper is due to individual authors. Different authors may have various opinions on the matter; even worse, their opinions may have different relevance. In this paper, we present simple models that allow aggregation of experts' views, linking the priority of his preference directly to the assessment made by other experts. In this approach, the more significant the contribution of a given expert, the greater the importance of his opinion. The presented method can be considered an attempt to find consensus among peers involved in the same project. Hence, its applications may go beyond the proposed study example of writing a scientific paper.

This paper introduces a novel two-stage active learning (AL) pipeline for automatic speech recognition (ASR), combining unsupervised and supervised AL methods. The first stage utilizes unsupervised AL by using x-vectors clustering for diverse sample selection from unlabeled speech data, thus establishing a robust initial dataset for the subsequent supervised AL. The second stage incorporates a supervised AL strategy, with a batch AL method specifically developed for ASR, aimed at selecting diverse and informative batches of samples. Here, sample diversity is also achieved using x-vectors clustering, while the most informative samples are identified using a Bayesian AL method tailored for ASR with an adaptation of Monte Carlo dropout to approximate Bayesian inference. This approach enables precise uncertainty estimation, thereby enhancing ASR model training with significantly reduced data requirements. Our method has shown superior performance compared to competing methods on homogeneous, heterogeneous, and OOD test sets, demonstrating that strategic sample selection and innovative Bayesian modeling can substantially optimize both labeling effort and data utilization in deep learning-based ASR applications.

Recent remarkable advancements in geometric deep generative models, coupled with accumulated structural data, enable structure-based drug design (SBDD) using only target protein information. However, existing models often struggle to balance multiple objectives, excelling only in specific tasks. BInD, a diffusion model with knowledge-based guidance, is introduced to address this limitation by co-generating molecules and their interactions with a target protein. This approach ensures balanced consideration of key objectives, including target-specific interactions, molecular properties, and local geometry. Comprehensive evaluations demonstrate that BInD achieves robust performance across all objectives, matching or surpassing state-of-the-art methods. Additionally, an NCI-driven molecule design and optimization method is proposed, enabling the enhancement of target binding and specificity by elaborating the adequate interaction patterns.

Scientific articles play a crucial role in advancing knowledge and informing research directions. One key aspect of evaluating scientific articles is the analysis of citations, which provides insights into the impact and reception of the cited works. This article introduces the innovative use of large language models, particularly ChatGPT, for comprehensive sentiment analysis of citations within scientific articles. By leveraging advanced natural language processing (NLP) techniques, ChatGPT can discern the nuanced positivity or negativity of citations, offering insights into the reception and impact of cited works. Furthermore, ChatGPT's capabilities extend to detecting potential biases and conflicts of interest in citations, enhancing the objectivity and reliability of scientific literature evaluation. This study showcases the transformative potential of artificial intelligence (AI)-powered tools in enhancing citation analysis and promoting integrity in scholarly research.

We conduct experiments with algorithmic pricing agents based on Large Language Models (LLMs). In oligopoly settings, LLM-based pricing agents quickly and autonomously reach supracompetitive prices and profits. Variation in seemingly innocuous phrases in LLM instructions ("prompts") substantially influence the degree of supracompetitive pricing. We develop novel techniques for behavioral analysis of LLMs and use them to uncover price-war concerns as a contributing factor. Our results extend to auction settings. Our findings uncover unique challenges to any future regulation of LLM-based pricing agents, and AI-based pricing agents more broadly.

A dramatic increase in the number of outbreaks of Dengue has recently been reported, and climate change is likely to extend the geographical spread of the disease. In this context, this paper shows how a neural network approach can incorporate Dengue and COVID-19 data as well as external factors (such as social behaviour or climate variables), to develop predictive models that could improve our knowledge and provide useful tools for health policy makers. Through the use of neural networks with different social and natural parameters, in this paper we define a Correlation Model through which we show that the number of cases of COVID-19 and Dengue have very similar trends. We then illustrate the relevance of our model by extending it to a Long short-term memory model (LSTM) that incorporates both diseases, and using this to estimate Dengue infections via COVID-19 data in countries that lack sufficient Dengue data.

Selecting an appropriate statistical model to forecast exchange rates is still today a relevant issue for policymakers and central bankers. The so-called Meese and Rogoff puzzle assesses that exchange rate fluctuations are unpredictable. In the literature, a lot of studies tried to solve the puzzle finding alternative predictors and statistical models based on temporal aggregation. In this paper, we propose an approach based on mixed frequency models to overcome the lack of information caused by temporal aggregation. We show the effectiveness of our approach in comparison with other proposed methods by performing CAD/USD exchange rate predictions.

We present a formalism for semiclassical time evolution in quantum mechanics, building on a century of work. We identify complex saddle points in real time, real saddle points in complex time, and complex saddle points in complex time that reproduce the known answers in classic problems. For the decay of a metastable state, we find finite time and finite energy analogs of the "bounce" which do not have strict zero or negative modes. The one-loop phase of the wave function and the multiplicity of bounce solutions at late times are discussed. The motivation of this work is to learn how to compute decay rates in quantum field theory in situations with non-trivial time dependence, by first taking a humble step backwards to the fascinating world of quantum mechanics.

We introduce and analyze a broad class of continuous directed polymers in $\mathbb{R}^d$ driven by Gaussian environments that are white in time and spatially correlated, under Dalang's condition. Using an Itô-renormalized stochastic-heat-equation representation, we establish structural properties of the partition function, including positivity, stationarity, scaling, homogeneity, and a Chapman--Kolmogorov relation. On finite time intervals, we prove Brownian-type pathwise behavior, namely Hölder continuity and identification of the quadratic variation. We then obtain a sharp measure-theoretic dichotomy: the quenched polymer measure is singular with respect to Wiener measure if and only if $\widehat f(\mathbb{R}^d)=\infty$ (equivalently, the noise is non-trace-class), and it is equivalent otherwise. Finally, in dimension $d\ge 3$, we prove diffusive behavior at large times in the high-temperature regime. This extends the Alberts--Khanin--Quastel framework from the $1+1$ white-noise setting to higher-dimensional Gaussian environments with general spatial covariance.