arXiv subjects

Lingkai Kong

Publications and source records attributed to Lingkai Kong.

At least 55 records · Page 3Linked to original sources

arXiv2024

Convergence of Kinetic Langevin Monte Carlo on Lie groups

Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivialization. We appropriately add tractable noise to the optimization dynamics to turn it into a sampling dynamics, leveraging the advantageous feature that the trivialized momentum variable is Euclidean despite that the potential function lives on a manifold. We then propose a Lie-group MCMC sampler, by delicately discretizing the resulting kinetic-Langevin-type sampling dynamics. The Lie group structure is exactly preserved by this discretization. Exponential convergence with explicit convergence rate for both the continuous dynamics and the discrete sampler are then proved under $W_2$ distance. Only compactness of the Lie group and geodesically $L$-smoothness of the potential function are needed. To the best of our knowledge, this is the first convergence result for kinetic Langevin on curved spaces, and also the first quantitative result that requires no convexity or, at least not explicitly, any common relaxation such as isoperimetry.

math.ST↗

arXiv2024

Time-Series Forecasting for Out-of-Distribution Generalization Using Invariant Learning

Time-series forecasting (TSF) finds broad applications in real-world scenarios. Due to the dynamic nature of time-series data, it is crucial to equip TSF models with out-of-distribution (OOD) generalization abilities, as historical training data and future test data can have different distributions. In this paper, we aim to alleviate the inherent OOD problem in TSF via invariant learning. We identify fundamental challenges of invariant learning for TSF. First, the target variables in TSF may not be sufficiently determined by the input due to unobserved core variables in TSF, breaking the conventional assumption of invariant learning. Second, time-series datasets lack adequate environment labels, while existing environmental inference methods are not suitable for TSF. To address these challenges, we propose FOIL, a model-agnostic framework that enables timeseries Forecasting for Out-of-distribution generalization via Invariant Learning. FOIL employs a novel surrogate loss to mitigate the impact of unobserved variables. Further, FOIL implements a joint optimization by alternately inferring environments effectively with a multi-head network while preserving the temporal adjacency structure, and learning invariant representations across inferred environments for OOD generalized TSF. We demonstrate that the proposed FOIL significantly improves the performance of various TSF models, achieving gains of up to 85%.

cs.LG↗

arXiv2024

Quantitative Convergences of Lie Group Momentum Optimizers

Explicit, momentum-based dynamics that optimize functions defined on Lie groups can be constructed via variational optimization and momentum trivialization. Structure preserving time discretizations can then turn this dynamics into optimization algorithms. This article investigates two types of discretization, Lie Heavy-Ball, which is a known splitting scheme, and Lie NAG-SC, which is newly proposed. Their convergence rates are explicitly quantified under $L$-smoothness and local strong convexity assumptions. Lie NAG-SC provides acceleration over the momentumless case, i.e. Riemannian gradient descent, but Lie Heavy-Ball does not. When compared to existing accelerated optimizers for general manifolds, both Lie Heavy-Ball and Lie NAG-SC are computationally cheaper and easier to implement, thanks to their utilization of group structure. Only gradient oracle and exponential map are required, but not logarithm map or parallel transport which are computational costly.

cs.LG↗

arXiv2024

MUBen: Benchmarking the Uncertainty of Molecular Representation Models

Large molecular representation models pre-trained on massive unlabeled data have shown great success in predicting molecular properties. However, these models may tend to overfit the fine-tuning data, resulting in over-confident predictions on test data that fall outside of the training distribution. To address this issue, uncertainty quantification (UQ) methods can be used to improve the models' calibration of predictions. Although many UQ approaches exist, not all of them lead to improved performance. While some studies have included UQ to improve molecular pre-trained models, the process of selecting suitable backbone and UQ methods for reliable molecular uncertainty estimation remains underexplored. To address this gap, we present MUBen, which evaluates different UQ methods for state-of-the-art backbone molecular representation models to investigate their capabilities. By fine-tuning various backbones using different molecular descriptors as inputs with UQ methods from different categories, we assess the influence of architectural decisions and training strategies. Our study offers insights for selecting UQ for backbone models, which can facilitate research on uncertainty-critical applications in fields such as materials science and drug discovery.

physics.chem-ph↗

arXiv2024

TPD: Enhancing Student Language Model Reasoning via Principle Discovery and Guidance

Large Language Models (LLMs) have recently showcased remarkable reasoning abilities. However, larger models often surpass their smaller counterparts in reasoning tasks, posing the challenge of effectively transferring these capabilities from larger models. Existing approaches heavily rely on extensive fine-tuning data or continuous interactions with a superior teacher LLM during inference. We introduce a principle-based teacher-student framework called ``Teaching via Principle Discovery'' (TPD) to address these limitations. Inspired by human learning mechanisms, TPD mimics the interaction between a teacher and a student using a principle-based approach. The teacher LLM generates problem-solving instructions and corrective principles based on the student LLM's errors. These principles guide the refinement of instructions and the selection of instructive examples from a validation set. This enables the student model to learn from both the teacher's guidance and its own mistakes. Once the student model begins making inferences, TPD requires no further intervention from the teacher LLM or humans. Through extensive experiments across eight reasoning tasks, we demonstrate the effectiveness of TPD. Compared to standard chain-of-thought prompting, TPD significantly improves the student model's performance, achieving $6.2\%$ improvement on average.

cs.CL↗

arXiv2023

When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting

Probabilistic hierarchical time-series forecasting is an important variant of time-series forecasting, where the goal is to model and forecast multivariate time-series that have underlying hierarchical relations. Most methods focus on point predictions and do not provide well-calibrated probabilistic forecasts distributions. Recent state-of-art probabilistic forecasting methods also impose hierarchical relations on point predictions and samples of distribution which does not account for coherency of forecast distributions. Previous works also silently assume that datasets are always consistent with given hierarchical relations and do not adapt to real-world datasets that show deviation from this assumption. We close both these gap and propose PROFHiT, which is a fully probabilistic hierarchical forecasting model that jointly models forecast distribution of entire hierarchy. PROFHiT uses a flexible probabilistic Bayesian approach and introduces a novel Distributional Coherency regularization to learn from hierarchical relations for entire forecast distribution that enables robust and calibrated forecasts as well as adapt to datasets of varying hierarchical consistency. On evaluating PROFHiT over wide range of datasets, we observed 41-88% better performance in accuracy and significantly better calibration. Due to modeling the coherency over full distribution, we observed that PROFHiT can robustly provide reliable forecasts even if up to 10% of input time-series data is missing where other methods' performance severely degrade by over 70%.

cs.LG↗

arXiv2023

When Rigidity Hurts: Soft Consistency Regularization for Probabilistic Hierarchical Time Series Forecasting

cs.LG↗

arXiv2023

Autoregressive Diffusion Model for Graph Generation

Diffusion-based graph generative models have recently obtained promising results for graph generation. However, existing diffusion-based graph generative models are mostly one-shot generative models that apply Gaussian diffusion in the dequantized adjacency matrix space. Such a strategy can suffer from difficulty in model training, slow sampling speed, and incapability of incorporating constraints. We propose an \emph{autoregressive diffusion} model for graph generation. Unlike existing methods, we define a node-absorbing diffusion process that operates directly in the discrete graph space. For forward diffusion, we design a \emph{diffusion ordering network}, which learns a data-dependent node absorbing ordering from graph topology. For reverse generation, we design a \emph{denoising network} that uses the reverse node ordering to efficiently reconstruct the graph by predicting the node type of the new node and its edges with previously denoised nodes at a time. Based on the permutation invariance of graph, we show that the two networks can be jointly trained by optimizing a simple lower bound of data likelihood. Our experiments on six diverse generic graph datasets and two molecule datasets show that our model achieves better or comparable generation performance with previous state-of-the-art, and meanwhile enjoys fast generation speed.

cs.AI↗

arXiv2023

DyGen: Learning from Noisy Labels via Dynamics-Enhanced Generative Modeling

Learning from noisy labels is a challenge that arises in many real-world applications where training data can contain incorrect or corrupted labels. When fine-tuning language models with noisy labels, models can easily overfit the label noise, leading to decreased performance. Most existing methods for learning from noisy labels use static input features for denoising, but these methods are limited by the information they can provide on true label distributions and can result in biased or incorrect predictions. In this work, we propose the Dynamics-Enhanced Generative Model (DyGen), which uses dynamic patterns in the embedding space during the fine-tuning process of language models to improve noisy label predictions. DyGen uses the variational auto-encoding framework to infer the posterior distributions of true labels from noisy labels and training dynamics. Additionally, a co-regularization mechanism is used to minimize the impact of potentially noisy labels and priors. DyGen demonstrates an average accuracy improvement of 3.10% on two synthetic noise datasets and 1.48% on three real-world noise datasets compared to the previous state-of-the-art. Extensive experiments and analyses show the effectiveness of each component in DyGen. Our code is available for reproducibility on GitHub.

cs.CL↗

arXiv2023

AdaPlanner: Adaptive Planning from Feedback with Language Models

Large language models (LLMs) have recently demonstrated the potential in acting as autonomous agents for sequential decision-making tasks. However, most existing methods either take actions greedily without planning or rely on static plans that are not adaptable to environmental feedback. Consequently, the sequential decision-making performance of LLM agents degenerates with problem complexity and plan horizons increase. We propose a closed-loop approach, AdaPlanner, which allows the LLM agent to refine its self-generated plan adaptively in response to environmental feedback. In AdaPlanner, the LLM agent adaptively refines its plan from feedback with both in-plan and out-of-plan refinement strategies. To mitigate hallucination, we develop a code-style LLM prompt structure that facilitates plan generation across a variety of tasks, environments, and agent capabilities. Furthermore, we propose a skill discovery mechanism that leverages successful plans as few-shot exemplars, enabling the agent to plan and refine with fewer task demonstrations. Our experiments in the ALFWorld and MiniWoB++ environments demonstrate that AdaPlanner outperforms state-of-the-art baselines by 3.73% and 4.11% while utilizing 2x and 600x fewer samples, respectively.

cs.CL↗

arXiv2023

Momentum Stiefel Optimizer, with Applications to Suitably-Orthogonal Attention, and Optimal Transport

The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a new approach is proposed based on, for the first time, an interplay between thoughtfully designed continuous and discrete dynamics. It leads to a gradient-based optimizer with intrinsically added momentum. This method exactly preserves the manifold structure but does not require additional operation to keep momentum in the changing (co)tangent space, and thus has low computational cost and pleasant accuracy. Its generalization to adaptive learning rates is also demonstrated. Notable performances are observed in practical tasks. For instance, we found that placing orthogonal constraints on attention heads of trained-from-scratch Vision Transformer [Dosovitskiy et al. 2022] could markedly improve its performance, when our optimizer is used, and it is better that each head is made orthogonal within itself but not necessarily to other heads. This optimizer also makes the useful notion of Projection Robust Wasserstein Distance [Paty & Cuturi 2019; Lin et al. 2020] for high-dim. optimal transport even more effective.

cs.LG↗

arXiv2022

End-to-End Stochastic Optimization with Energy-Based Model

Decision-focused learning (DFL) was recently proposed for stochastic optimization problems that involve unknown parameters. By integrating predictive modeling with an implicitly differentiable optimization layer, DFL has shown superior performance to the standard two-stage predict-then-optimize pipeline. However, most existing DFL methods are only applicable to convex problems or a subset of nonconvex problems that can be easily relaxed to convex ones. Further, they can be inefficient in training due to the requirement of solving and differentiating through the optimization problem in every training iteration. We propose SO-EBM, a general and efficient DFL method for stochastic optimization using energy-based models. Instead of relying on KKT conditions to induce an implicit optimization layer, SO-EBM explicitly parameterizes the original optimization problem using a differentiable optimization layer based on energy functions. To better approximate the optimization landscape, we propose a coupled training objective that uses a maximum likelihood loss to capture the optimum location and a distribution-based regularizer to capture the overall energy landscape. Finally, we propose an efficient training procedure for SO-EBM with a self-normalized importance sampler based on a Gaussian mixture proposal. We evaluate SO-EBM in three applications: power scheduling, COVID-19 resource allocation, and non-convex adversarial security game, demonstrating the effectiveness and efficiency of SO-EBM.

cs.LG↗

arXiv2022

AcTune: Uncertainty-aware Active Self-Training for Semi-Supervised Active Learning with Pretrained Language Models

While pre-trained language model (PLM) fine-tuning has achieved strong performance in many NLP tasks, the fine-tuning stage can be still demanding in labeled data. Recent works have resorted to active fine-tuning to improve the label efficiency of PLM fine-tuning, but none of them investigate the potential of unlabeled data. We propose {\ours}, a new framework that leverages unlabeled data to improve the label efficiency of active PLM fine-tuning. AcTune switches between data annotation and model self-training based on uncertainty: it selects high-uncertainty unlabeled samples for active annotation and low-uncertainty ones for model self-training. Under this framework, we design (1) a region-aware sampling strategy that reduces redundancy when actively querying for annotations and (2) a momentum-based memory bank that dynamically aggregates the model's pseudo labels to suppress label noise in self-training. Experiments on 6 text classification datasets show that AcTune outperforms the strongest active learning and self-training baselines and improves the label efficiency of PLM fine-tuning by 56.2\% on average. Our implementation will be available at \url{https://github.com/yueyu1030/actune}.

cs.CL↗

arXiv2022

CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting

Probabilistic time-series forecasting enables reliable decision making across many domains. Most forecasting problems have diverse sources of data containing multiple modalities and structures. Leveraging information as well as uncertainty from these data sources for well-calibrated and accurate forecasts is an important challenging problem. Most previous work on multi-modal learning and forecasting simply aggregate intermediate representations from each data view by simple methods of summation or concatenation and do not explicitly model uncertainty for each data-view. We propose a general probabilistic multi-view forecasting framework CAMul, that can learn representations and uncertainty from diverse data sources. It integrates the knowledge and uncertainty from each data view in a dynamic context-specific manner assigning more importance to useful views to model a well-calibrated forecast distribution. We use CAMul for multiple domains with varied sources and modalities and show that CAMul outperforms other state-of-art probabilistic forecasting models by over 25\% in accuracy and calibration.

cs.LG↗

arXiv2021

When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting

Accurate and trustworthy epidemic forecasting is an important problem that has impact on public health planning and disease mitigation. Most existing epidemic forecasting models disregard uncertainty quantification, resulting in mis-calibrated predictions. Recent works in deep neural models for uncertainty-aware time-series forecasting also have several limitations; e.g. it is difficult to specify meaningful priors in Bayesian NNs, while methods like deep ensembling are computationally expensive in practice. In this paper, we fill this important gap. We model the forecasting task as a probabilistic generative process and propose a functional neural process model called EPIFNP, which directly models the probability density of the forecast value. EPIFNP leverages a dynamic stochastic correlation graph to model the correlations between sequences in a non-parametric way, and designs different stochastic latent variables to capture functional uncertainty from different perspectives. Our extensive experiments in a real-time flu forecasting setting show that EPIFNP significantly outperforms previous state-of-the-art models in both accuracy and calibration metrics, up to 2.5x in accuracy and 2.4x in calibration. Additionally, due to properties of its generative process,EPIFNP learns the relations between the current season and similar patterns of historical seasons,enabling interpretable forecasts. Beyond epidemic forecasting, the EPIFNP can be of independent interest for advancing principled uncertainty quantification in deep sequential models for predictive analytics

cs.LG↗

arXiv2020

Stochasticity of Deterministic Gradient Descent: Large Learning Rate for Multiscale Objective Function

This article suggests that deterministic Gradient Descent, which does not use any stochastic gradient approximation, can still exhibit stochastic behaviors. In particular, it shows that if the objective function exhibit multiscale behaviors, then in a large learning rate regime which only resolves the macroscopic but not the microscopic details of the objective, the deterministic GD dynamics can become chaotic and convergent not to a local minimizer but to a statistical distribution. A sufficient condition is also established for approximating this long-time statistical limit by a rescaled Gibbs distribution. Both theoretical and numerical demonstrations are provided, and the theoretical part relies on the construction of a stochastic map that uses bounded noise (as opposed to discretized diffusions).

cs.LG↗

arXiv2020

Calibrated Language Model Fine-Tuning for In- and Out-of-Distribution Data

Fine-tuned pre-trained language models can suffer from severe miscalibration for both in-distribution and out-of-distribution (OOD) data due to over-parameterization. To mitigate this issue, we propose a regularized fine-tuning method. Our method introduces two types of regularization for better calibration: (1) On-manifold regularization, which generates pseudo on-manifold samples through interpolation within the data manifold. Augmented training with these pseudo samples imposes a smoothness regularization to improve in-distribution calibration. (2) Off-manifold regularization, which encourages the model to output uniform distributions for pseudo off-manifold samples to address the over-confidence issue for OOD data. Our experiments demonstrate that the proposed method outperforms existing calibration methods for text classification in terms of expectation calibration error, misclassification detection, and OOD detection on six datasets. Our code can be found at https://github.com/Lingkai-Kong/Calibrated-BERT-Fine-Tuning.

cs.CL↗

arXiv2020

SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large number of parameters. Non-Bayesian methods are simple to implement but often conflate different sources of uncertainties and require huge computing resources. We propose a new method for quantifying uncertainties of DNNs from a dynamical system perspective. The core of our method is to view DNN transformations as state evolution of a stochastic dynamical system and introduce a Brownian motion term for capturing epistemic uncertainty. Based on this perspective, we propose a neural stochastic differential equation model (SDE-Net) which consists of (1) a drift net that controls the system to fit the predictive function; and (2) a diffusion net that captures epistemic uncertainty. We theoretically analyze the existence and uniqueness of the solution to SDE-Net. Our experiments demonstrate that the SDE-Net model can outperform existing uncertainty estimation methods across a series of tasks where uncertainty plays a fundamental role.

cs.LG↗