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Naichen Shi

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6 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Inv-Entropy: A Fully Probabilistic Framework for Uncertainty Quantification in Language Models

Haoyi Song
Ruihan Ji
Naichen Shi
Fan Lai
Raed Al Kontar

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a fully probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input–output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods.

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JMLR Journal 2024 Journal Article

Personalized PCA: Decoupling Shared and Unique Features

Naichen Shi
Raed Al Kontar

In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining the unique features of each source. To this end, we propose personalized PCA (PerPCA), which uses mutually orthogonal global and local principal components to encode both unique and shared features. We show that, under mild conditions, both unique and shared features can be identified and recovered by a constrained optimization problem, even if the covariance matrices are immensely different. Also, we design a fully federated algorithm inspired by distributed Stiefel gradient descent to solve the problem. The algorithm introduces a new group of operations called generalized retractions to handle orthogonality constraints, and only requires global PCs to be shared across sources. We prove the linear convergence of the algorithm under suitable assumptions. Comprehensive numerical experiments highlight PerPCA's superior performance in feature extraction and prediction from heterogeneous datasets. As a systematic approach to decouple shared and unique features from heterogeneous datasets, PerPCA finds applications in several tasks, including video segmentation, topic extraction, and feature clustering. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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JMLR Journal 2024 Journal Article

Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components

Naichen Shi
Salar Fattahi
Raed Al Kontar

In this work, we study the problem of common and unique feature extraction from noisy data. When we have $N$ observation matrices from $N$ different and associated sources corrupted by sparse and potentially gross noise, can we recover the common and unique components from these noisy observations? This is a challenging task as the number of parameters to estimate is approximately thrice the number of observations. Despite the difficulty, we propose an intuitive alternating minimization algorithm called triple component matrix factorization (TCMF) to recover the three components exactly. TCMF is distinguished from existing works in literature thanks to two salient features. First, TCMF is a principled method to separate the three components given noisy observations provably. Second, the bulk of the computation in TCMF can be distributed. On the technical side, we formulate the problem as a constrained nonconvex nonsmooth optimization problem. Despite the intricate nature of the problem, we provide a Taylor series characterization of its solution by solving the corresponding Karush–Kuhn–Tucker conditions. Using this characterization, we can show that the alternating minimization algorithm makes significant progress at each iteration and converges into the ground truth at a linear rate. Numerical experiments in video segmentation and anomaly detection highlight the superior feature extraction abilities of TCMF. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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NeurIPS Conference 2023 Conference Paper

Personalized Dictionary Learning for Heterogeneous Datasets

Geyu Liang
Naichen Shi
Raed Al Kontar
Salar Fattahi

We introduce a relevant yet challenging problem named Personalized Dictionary Learning (PerDL), where the goal is to learn sparse linear representations from heterogeneous datasets that share some commonality. In PerDL, we model each dataset's shared and unique features as global and local dictionaries. Challenges for PerDL not only are inherited from classical dictionary learning(DL), but also arise due to the unknown nature of the shared and unique features. In this paper, we rigorously formulate this problem and provide conditions under which the global and local dictionaries can be provably disentangled. Under these conditions, we provide a meta-algorithm called Personalized Matching and Averaging (PerMA) that can recover both global and local dictionaries from heterogeneous datasets. PerMA is highly efficient; it converges to the ground truth at a linear rate under suitable conditions. Moreover, it automatically borrows strength from strong learners to improve the prediction of weak learners. As a general framework for extracting global and local dictionaries, we show the application of PerDL in different learning tasks, such as training with imbalanced datasets and video surveillance.

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NeurIPS Conference 2022 Conference Paper

Adam Can Converge Without Any Modification On Update Rules

Yushun Zhang
Congliang Chen
Naichen Shi
Ruoyu Sun
Zhi-Quan Luo

Ever since \citet{reddi2019convergence} pointed out the divergence issue of Adam, many new variants have been designed to obtain convergence. However, vanilla Adam remains exceptionally popular and it works well in practice. Why is there a gap between theory and practice? We point out there is a mismatch between the settings of theory and practice: \citet{reddi2019convergence} pick the problem after picking the hyperparameters of Adam, i. e. , $(\beta_1, \beta_2)$; while practical applications often fix the problem first and then tune $(\beta_1, \beta_2)$. Due to this observation, we conjecture that the empirical convergence can be theoretically justified, only if we change the order of picking the problem and hyperparameter. In this work, we confirm this conjecture. We prove that, when the 2nd-order momentum parameter $\beta_2$ is large and 1st-order momentum parameter $\beta_1 < \sqrt{\beta_2}<1$, Adam converges to the neighborhood of critical points. The size of the neighborhood is propositional to the variance of stochastic gradients. Under an extra condition (strong growth condition), Adam converges to critical points. It is worth mentioning that our results cover a wide range of hyperparameters: as $\beta_2$ increases, our convergence result can cover any $\beta_1 \in [0, 1)$ including $\beta_1=0. 9$, which is the default setting in deep learning libraries. To our knowledge, this is the first result showing that Adam can converge {\it without any modification} on its update rules. Further, our analysis does not require assumptions of bounded gradients or bounded 2nd-order momentum. When $\beta_2$ is small, we further point out a large region of $(\beta_1, \beta_2)$ combinations where Adam can diverge to infinity. Our divergence result considers the same setting (fixing the optimization problem ahead) as our convergence result, indicating that there is a phase transition from divergence to convergence when increasing $\beta_2$. These positive and negative results provide suggestions on how to tune Adam hyperparameters: for instance, when Adam does not work well, we suggest tuning up $\beta_2$ and trying $\beta_1< \sqrt{\beta_2}$.

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ICLR Conference 2021 Conference Paper

RMSprop converges with proper hyper-parameter

Naichen Shi
Dawei Li 0010
Mingyi Hong 0001
Ruoyu Sun 0001

Despite the existence of divergence examples, RMSprop remains one of the most popular algorithms in machine learning. Towards closing the gap between theory and practice, we prove that RMSprop converges with proper choice of hyper-parameters under certain conditions. More specifically, we prove that when the hyper-parameter $\beta_2$ is close enough to $1$, RMSprop and its random shuffling version converge to a bounded region in general, and to critical points in the interpolation regime. It is worth mentioning that our results do not depend on ``bounded gradient" assumption, which is often the key assumption utilized by existing theoretical work for Adam-type adaptive gradient method. Removing this assumption allows us to establish a phase transition from divergence to non-divergence for RMSprop. Finally, based on our theory, we conjecture that in practice there is a critical threshold $\sf{\beta_2^*}$, such that RMSprop generates reasonably good results only if $1>\beta_2\ge \sf{\beta_2^*}$. We provide empirical evidence for such a phase transition in our numerical experiments.

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