arXiv subjects

Dong-Young Lim

Publications and source records attributed to Dong-Young Lim.

17 recordsLinked to original sources

arXiv2026

Don't Lose Entities from Retrieval to Generation: Dual Entity Recovery RAG for multi-hop QA

Retrieval-augmented multi-hop question answering (QA) decomposes a query into sub-questions and decomposes the corpus into smaller retrieval units such as sentences. Both forms of decomposition improve the pipeline, but we show that both share the same vulnerability, the loss of entity information, and that this loss breaks the pipeline at two separate points. The first point is retrieval, where a sub-question loses the entity resolved at the previous hop, leaving the retriever with nothing to match against. The second point is harder to see, because retrieval still appears to succeed. Once a passage is split into sentences, an isolated sentence loses the context that grounds its pronouns, so even with the correct sentence in hand the LLM cannot tell which entity the sentence is about. We isolate this second point as a distinct failure mode that we call lost-in-generation, and a retrieval-controlled experiment shows that it degrades answers even when the gold evidence is fixed in the context. We then propose Dual Entity Recovery RAG (DER-RAG), which keeps the grounding entity explicit from retrieval through to generation with two lightweight components, a two-way query decomposition that carries the resolved entity across sub-questions and a subject entity prefix attached to each sentence at generation time. DER-RAG needs no graph construction, no corpus modification, and no fine-tuning, yet on three multi-hop QA benchmarks it matches or exceeds strong baselines, including graph-based methods that depend on costly offline structures.

cs.CL↗

arXiv2025

Continuum Dropout for Neural Differential Equations

Neural Differential Equations (NDEs) excel at modeling continuous-time dynamics, effectively handling challenges such as irregular observations, missing values, and noise. Despite their advantages, NDEs face a fundamental challenge in adopting dropout, a cornerstone of deep learning regularization, making them susceptible to overfitting. To address this research gap, we introduce Continuum Dropout, a universally applicable regularization technique for NDEs built upon the theory of alternating renewal processes. Continuum Dropout formulates the on-off mechanism of dropout as a stochastic process that alternates between active (evolution) and inactive (paused) states in continuous time. This provides a principled approach to prevent overfitting and enhance the generalization capabilities of NDEs. Moreover, Continuum Dropout offers a structured framework to quantify predictive uncertainty via Monte Carlo sampling at test time. Through extensive experiments, we demonstrate that Continuum Dropout outperforms existing regularization methods for NDEs, achieving superior performance on various time series and image classification tasks. It also yields better-calibrated and more trustworthy probability estimates, highlighting its effectiveness for uncertainty-aware modeling.

stat.ML↗

arXiv2025

FlowPath: Learning Data-Driven Manifolds with Invertible Flows for Robust Irregularly-sampled Time Series Classification

Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly sensitive to the choice of control path constructed from discrete observations. Existing methods commonly employ fixed interpolation schemes, which impose simplistic geometric assumptions that often misrepresent the underlying data manifold, particularly under high missingness. We propose FlowPath, a novel approach that learns the geometry of the control path via an invertible neural flow. Rather than merely connecting observations, FlowPath constructs a continuous and data-adaptive manifold, guided by invertibility constraints that enforce information-preserving and well-behaved transformations. This inductive bias distinguishes FlowPath from prior unconstrained learnable path models. Empirical evaluations on 18 benchmark datasets and a real-world case study demonstrate that FlowPath consistently achieves statistically significant improvements in classification accuracy over baselines using fixed interpolants or non-invertible architectures. These results highlight the importance of modeling not only the dynamics along the path but also the geometry of the path itself, offering a robust and generalizable solution for learning from irregular time series.

cs.LG↗

arXiv2025

Controllable Machine Unlearning via Gradient Pivoting

Machine unlearning (MU) aims to remove the influence of specific data from a trained model. However, approximate unlearning methods, often formulated as a single-objective optimization (SOO) problem, face a critical trade-off between unlearning efficacy and model fidelity. This leads to three primary challenges: the risk of over-forgetting, a lack of fine-grained control over the unlearning process, and the absence of metrics to holistically evaluate the trade-off. To address these issues, we reframe MU as a multi-objective optimization (MOO) problem. We then introduce a novel algorithm, Controllable Unlearning by Pivoting Gradient (CUP), which features a unique pivoting mechanism. Unlike traditional MOO methods that converge to a single solution, CUP's mechanism is designed to controllably navigate the entire Pareto frontier. This navigation is governed by a single intuitive hyperparameter, the `unlearning intensity', which allows for precise selection of a desired trade-off. To evaluate this capability, we adopt the hypervolume indicator, a metric that captures both the quality and diversity of the entire set of solutions an algorithm can generate. Our experimental results demonstrate that CUP produces a superior set of Pareto-optimal solutions, consistently outperforming existing methods across various vision tasks.

cs.LG↗

arXiv2025

Flatness-Aware Stochastic Gradient Langevin Dynamics

Flatness of the loss landscape has been widely studied as an important perspective for understanding the behavior and generalization of deep learning algorithms. Motivated by this view, we propose Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), a first-order optimization method that biases learning its dynamics toward flat basins while retaining the computational and memory efficiency of SGD and SGLD. We provide a non-asymptotic theoretical analysis showing that fSGLD targets a flatness-biased Gibbs distribution under a theoretically prescribed coupling between the noise scale $\sigma$ and the inverse temperature $\beta$, together with explicit excess risk guarantees. We empirically evaluate fSGLD across standard optimizer benchmarks, Bayesian image classification, uncertainty quantification, and out-of-distribution detection, demonstrating consistently strong performance and reliable uncertainty estimates. Additional experiments confirm the effectiveness of the theoretically prescribed $\beta$-$\sigma$ coupling compared to decoupled choices.

cs.LG↗

arXiv2025

Comprehensive Review of Neural Differential Equations for Time Series Analysis

Time series modeling and analysis have become critical in various domains. Conventional methods such as RNNs and Transformers, while effective for discrete-time and regularly sampled data, face significant challenges in capturing the continuous dynamics and irregular sampling patterns inherent in real-world scenarios. Neural Differential Equations (NDEs) represent a paradigm shift by combining the flexibility of neural networks with the mathematical rigor of differential equations. This paper presents a comprehensive review of NDE-based methods for time series analysis, including neural ordinary differential equations, neural controlled differential equations, and neural stochastic differential equations. We provide a detailed discussion of their mathematical formulations, numerical methods, and applications, highlighting their ability to model continuous-time dynamics. Furthermore, we address key challenges and future research directions. This survey serves as a foundation for researchers and practitioners seeking to leverage NDEs for advanced time series analysis.

cs.LG↗

arXiv2025

Modeling Irregular Astronomical Time Series with Neural Stochastic Delay Differential Equations

Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential Equations (Neural SDDEs) that combines stochastic modeling with neural networks to capture delayed temporal dynamics and handle irregular observations. Our approach integrates a delay-aware neural architecture, a numerical solver for SDDEs, and mechanisms to robustly learn from noisy, sparse sequences. Experiments on irregularly sampled astronomical data demonstrate strong classification accuracy and effective detection of novel astrophysical events, even with partial labels. This work highlights Neural SDDEs as a principled and practical tool for time series analysis under observational constraints.

cs.LG↗

arXiv2025

TANDEM: Temporal Attention-guided Neural Differential Equations for Missingness in Time Series Classification

Handling missing data in time series classification remains a significant challenge in various domains. Traditional methods often rely on imputation, which may introduce bias or fail to capture the underlying temporal dynamics. In this paper, we propose TANDEM (Temporal Attention-guided Neural Differential Equations for Missingness), an attention-guided neural differential equation framework that effectively classifies time series data with missing values. Our approach integrates raw observation, interpolated control path, and continuous latent dynamics through a novel attention mechanism, allowing the model to focus on the most informative aspects of the data. We evaluate TANDEM on 30 benchmark datasets and a real-world medical dataset, demonstrating its superiority over existing state-of-the-art methods. Our framework not only improves classification accuracy but also provides insights into the handling of missing data, making it a valuable tool in practice.

cs.LG↗

arXiv2025

DGSAM: Domain Generalization via Individual Sharpness-Aware Minimization

Domain generalization (DG) aims to learn models that perform well on unseen target domains by training on multiple source domains. Sharpness-Aware Minimization (SAM), known for finding flat minima that improve generalization, has therefore been widely adopted in DG. However, our analysis reveals that SAM in DG may converge to \textit{fake flat minima}, where the total loss surface appears flat in terms of global sharpness but remains sharp with respect to individual source domains. To understand this phenomenon more precisely, we formalize the average worst-case domain risk as the maximum loss under domain distribution shifts within a bounded divergence, and derive a generalization bound that reveals the limitations of global sharpness-aware minimization. In contrast, we show that individual sharpness provides a valid upper bound on this risk, making it a more suitable proxy for robust domain generalization. Motivated by these insights, we shift the DG paradigm toward minimizing individual sharpness across source domains. We propose \textit{Decreased-overhead Gradual SAM (DGSAM)}, which applies gradual domain-wise perturbations in a computationally efficient manner to consistently reduce individual sharpness. Extensive experiments demonstrate that DGSAM not only improves average accuracy but also reduces performance variance across domains, while incurring less computational overhead than SAM.

stat.ML↗

arXiv2025

A Neural Frequency-Severity Model and Its Application to Insurance Claims

This paper proposes a flexible and analytically tractable class of frequency and severity models for predicting insurance claims. The proposed model is able to capture nonlinear relationships in explanatory variables by characterizing the logarithmic mean functions of frequency and severity distributions as neural networks. Moreover, a potential dependence between the claim frequency and severity can be incorporated. In particular, the paper provides analytic formulas for mean and variance of the total claim cost, making our model ideal for many applications such as pricing insurance contracts and the pure premium. A simulation study demonstrates that our method successfully recovers nonlinear features of explanatory variables as well as the dependency between frequency and severity. Then, this paper uses a French auto insurance claim dataset to illustrate that the proposed model is superior to the existing methods in fitting and predicting the claim frequency, severity, and the total claim loss. Numerical results indicate that the proposed model helps in maintaining the competitiveness of an insurer by accurately predicting insurance claims and avoiding adverse selection.

econ.EM↗

arXiv2025

On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation is made of Lipschitz continuous functions avoiding any Lipschitzness assumption on the score function. We demonstrate via a motivating example, sampling from a Gaussian distribution with unknown mean, the powerfulness of our approach. In this case, explicit estimates are provided for the associated optimization problem, i.e. score approximation, while these are combined with the corresponding sampling estimates. As a result, we obtain the best known upper bound estimates in terms of key quantities of interest, such as the dimension and rates of convergence, for the Wasserstein-2 distance between the data distribution (Gaussian with unknown mean) and our sampling algorithm. Beyond the motivating example and in order to allow for the use of a diverse range of stochastic optimizers, we present our results using an $L^2$-accurate score estimation assumption, which crucially is formed under an expectation with respect to the stochastic optimizer and our novel auxiliary process that uses only known information. This approach yields the best known convergence rate for our sampling algorithm.

cs.LG↗

arXiv2025

Dual Cone Gradient Descent for Training Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their remarkable empirical performance in various scientific computing tasks, PINNs often fail to generate reasonable solutions, and such pathological behaviors remain difficult to explain and resolve. In this paper, we identify that PINNs can be adversely trained when gradients of each loss function exhibit a significant imbalance in their magnitudes and present a negative inner product value. To address these issues, we propose a novel optimization framework, Dual Cone Gradient Descent (DCGD), which adjusts the direction of the updated gradient to ensure it falls within a dual cone region. This region is defined as a set of vectors where the inner products with both the gradients of the PDE residual loss and the boundary loss are non-negative. Theoretically, we analyze the convergence properties of DCGD algorithms in a non-convex setting. On a variety of benchmark equations, we demonstrate that DCGD outperforms other optimization algorithms in terms of various evaluation metrics. In particular, DCGD achieves superior predictive accuracy and enhances the stability of training for failure modes of PINNs and complex PDEs, compared to existing optimally tuned models. Moreover, DCGD can be further improved by combining it with popular strategies for PINNs, including learning rate annealing and the Neural Tangent Kernel (NTK).

cs.LG↗

arXiv2024

Langevin dynamics based algorithm e-TH$\varepsilon$O POULA for stochastic optimization problems with discontinuous stochastic gradient

We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We demonstrate both theoretically and numerically the applicability of the e-TH$\varepsilon$O POULA algorithm. More precisely, under the conditions that the stochastic gradient is locally Lipschitz in average and satisfies a certain convexity at infinity condition, we establish non-asymptotic error bounds for e-TH$\varepsilon$O POULA in Wasserstein distances and provide a non-asymptotic estimate for the expected excess risk, which can be controlled to be arbitrarily small. Three key applications in finance and insurance are provided, namely, multi-period portfolio optimization, transfer learning in multi-period portfolio optimization, and insurance claim prediction, which involve neural networks with (Leaky)-ReLU activation functions. Numerical experiments conducted using real-world datasets illustrate the superior empirical performance of e-TH$\varepsilon$O POULA compared to SGLD, TUSLA, ADAM, and AMSGrad in terms of model accuracy.

math.OC↗

arXiv2024

Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks

We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models. Its underpinning theory relies on recent advances of Euler's polygonal approximations for stochastic differential equations (SDEs) with monotone coefficients. As a result, it inherits the stability properties of tamed algorithms, while it addresses other known issues, e.g. vanishing gradients in neural networks. In particular, we provide a nonasymptotic analysis and full theoretical guarantees for the convergence properties of an algorithm of this novel class, which we named TH$\varepsilon$O POULA (or, simply, TheoPouLa). Finally, several experiments are presented with different types of deep learning models, which show the superior performance of TheoPouLa over many popular adaptive optimization algorithms.

cs.LG↗

arXiv2024

Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Data

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

cs.LG↗

arXiv2024

DualDynamics: Synergizing Implicit and Explicit Methods for Robust Irregular Time Series Analysis

Real-world time series analysis faces significant challenges when dealing with irregular and incomplete data. While Neural Differential Equation (NDE) based methods have shown promise, they struggle with limited expressiveness, scalability issues, and stability concerns. Conversely, Neural Flows offer stability but falter with irregular data. We introduce 'DualDynamics', a novel framework that synergistically combines NDE-based method and Neural Flow-based method. This approach enhances expressive power while balancing computational demands, addressing critical limitations of existing techniques. We demonstrate DualDynamics' effectiveness across diverse tasks: classification of robustness to dataset shift, irregularly-sampled series analysis, interpolation of missing data, and forecasting with partial observations. Our results show consistent outperformance over state-of-the-art methods, indicating DualDynamics' potential to advance irregular time series analysis significantly.

cs.LG↗

arXiv2023

Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function

We consider non-convex stochastic optimization problems where the objective functions have super-linearly growing and discontinuous stochastic gradients. In such a setting, we provide a non-asymptotic analysis for the tamed unadjusted stochastic Langevin algorithm (TUSLA) introduced in Lovas et al. (2020). In particular, we establish non-asymptotic error bounds for the TUSLA algorithm in Wasserstein-1 and Wasserstein-2 distances. The latter result enables us to further derive non-asymptotic estimates for the expected excess risk. To illustrate the applicability of the main results, we consider an example from transfer learning with ReLU neural networks, which represents a key paradigm in machine learning. Numerical experiments are presented for the aforementioned example which support our theoretical findings. Hence, in this setting, we demonstrate both theoretically and numerically that the TUSLA algorithm can solve the optimization problem involving neural networks with ReLU activation function. Besides, we provide simulation results for synthetic examples where popular algorithms, e.g. ADAM, AMSGrad, RMSProp, and (vanilla) stochastic gradient descent (SGD) algorithm, may fail to find the minimizer of the objective functions due to the super-linear growth and the discontinuity of the corresponding stochastic gradient, while the TUSLA algorithm converges rapidly to the optimal solution. Moreover, we provide an empirical comparison of the performance of TUSLA with popular stochastic optimizers on real-world datasets, as well as investigate the effect of the key hyperparameters of TUSLA on its performance.

math.OC↗