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Lijie Hu

Lijie Hu contributes to research discovery and scholarly infrastructure.

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Machine Learning Cryptography and Security Computer Vision math.OC

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preprint2026arXiv

In-Context Learning Operates as Concept Subspace Learning

Regression and Bayesian accounts of in-context learning (ICL) explain how demonstrations can induce predictors, while mechanistic analyses often identify compact activation directions that steer prompted behavior. However, it remains unclear whether structured demonstrations induce low-dimensional concept inference. We study this question through a concept-subspace view of ICL, in which tasks vary only along intrinsic concept coordinates, although inputs are observed in a high-dimensional ambient space. For ridge and least-squares ICL proxies, prediction decomposes exactly into concept-coordinate regression and off-subspace leakage. Under block-diagonal or near-block-diagonal covariance assumptions, the leading estimation and nuisance-sensitivity terms scale with the dimension of the concept subspace, while residual effects are controlled by cross-subspace coupling. This separation gives a mechanistic prediction: recoverable task information should concentrate in a low-dimensional, task-aligned activation subspace. On CounterFact-derived multi-relation prompts with Llama-3-8B, a 68--73-dimensional subspace of the 4096-dimensional residual stream restores 78.8% of the clean--corrupted accuracy gap, whereas patching the complementary subspace restores 0%. Concept swaps redirect predictions toward injected relations, while random and cross-task matched-rank controls are largely ineffective. Additional experiments on Qwen2.5-7B and a controlled cross-lingual rule task show the same qualitative pattern. These results support concept subspaces as compact, task-aligned mediators of recoverable ICL behavior in structured task families, without implying full-circuit recovery.

preprint2026arXiv

MedFM-Robust: Benchmarking Robustness of Medical Foundation Models

Medical foundation models (MedFMs) have emerged as transformative tools in healthcare, demonstrating capabilities across diverse clinical applications. These models can be broadly categorized into two paradigms: Medical Vision-Language Models (Med-VLMs) and segmentation foundation models. Med-VLMs range from medical-specialized models such as LLaVA-Med and MedGemma, to general-purpose models like GPT-4o and Gemini, all capable of medical image understanding tasks including visual question answering (VQA), report generation, and visual grounding. Concurrently, the Segment Anything Model (SAM) has catalyzed a new generation of medical segmentation models, with adaptations like SAM-Med2D and MedSAM. The widespread clinical deployment of these models thus necessitates rigorous evaluation of their reliability under real-world conditions.

preprint2022arXiv

Differentially Private (Gradient) Expectation Maximization Algorithm with Statistical Guarantees

(Gradient) Expectation Maximization (EM) is a widely used algorithm for estimating the maximum likelihood of mixture models or incomplete data problems. A major challenge facing this popular technique is how to effectively preserve the privacy of sensitive data. Previous research on this problem has already lead to the discovery of some Differentially Private (DP) algorithms for (Gradient) EM. However, unlike in the non-private case, existing techniques are not yet able to provide finite sample statistical guarantees. To address this issue, we propose in this paper the first DP version of (Gradient) EM algorithm with statistical guarantees. Moreover, we apply our general framework to three canonical models: Gaussian Mixture Model (GMM), Mixture of Regressions Model (MRM) and Linear Regression with Missing Covariates (RMC). Specifically, for GMM in the DP model, our estimation error is near optimal in some cases. For the other two models, we provide the first finite sample statistical guarantees. Our theory is supported by thorough numerical experiments.

preprint2022arXiv

Estimating Smooth GLM in Non-interactive Local Differential Privacy Model with Public Unlabeled Data

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLMs) in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical setting, our model allows the server to access some additional public but unlabeled data. In the first part of the paper we focus on GLMs. Specifically, we first consider the case where each data record is i.i.d. sampled from a zero-mean multivariate Gaussian distribution. Motivated by the Stein's lemma, we present an $(ε, δ)$-NLDP algorithm for GLMs. Moreover, the sample complexity of public and private data for the algorithm to achieve an $\ell_2$-norm estimation error of $α$ (with high probability) is ${O}(p α^{-2})$ and $\tilde{O}(p^3α^{-2}ε^{-2})$ respectively, where $p$ is the dimension of the feature vector. This is a significant improvement over the previously known exponential or quasi-polynomial in $α^{-1}$, or exponential in $p$ sample complexities of GLMs with no public data. Then we consider a more general setting where each data record is i.i.d. sampled from some sub-Gaussian distribution with bounded $\ell_1$-norm. Based on a variant of Stein's lemma, we propose an $(ε, δ)$-NLDP algorithm for GLMs whose sample complexity of public and private data to achieve an $\ell_\infty$-norm estimation error of $α$ is ${O}(p^2α^{-2})$ and $\tilde{O}(p^2α^{-2}ε^{-2})$ respectively, under some mild assumptions and if $α$ is not too small ({\em i.e.,} $α\geq Ω(\frac{1}{\sqrt{p}})$). In the second part of the paper, we extend our idea to the problem of estimating non-linear regressions and show similar results as in GLMs for both multivariate Gaussian and sub-Gaussian cases. Finally, we demonstrate the effectiveness of our algorithms through experiments on both synthetic and real-world datasets.

preprint2022arXiv

Faster Rates of Private Stochastic Convex Optimization

In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) and provide excess population risks for some special classes of functions that are faster than the previous results of general convex and strongly convex functions. In the first part of the paper, we study the case where the population risk function satisfies the Tysbakov Noise Condition (TNC) with some parameter $θ>1$. Specifically, we first show that under some mild assumptions on the loss functions, there is an algorithm whose output could achieve an upper bound of $\tilde{O}((\frac{1}{\sqrt{n}}+\frac{\sqrt{d\log \frac{1}δ}}{nε})^\fracθ{θ-1})$ for $(ε, δ)$-DP when $θ\geq 2$, here $n$ is the sample size and $d$ is the dimension of the space. Then we address the inefficiency issue, improve the upper bounds by $\text{Poly}(\log n)$ factors and extend to the case where $θ\geq \barθ>1$ for some known $\barθ$. Next we show that the excess population risk of population functions satisfying TNC with parameter $θ\geq 2$ is always lower bounded by $Ω((\frac{d}{nε})^\fracθ{θ-1}) $ and $Ω((\frac{\sqrt{d\log \frac{1}δ}}{nε})^\fracθ{θ-1})$ for $ε$-DP and $(ε, δ)$-DP, respectively. In the second part, we focus on a special case where the population risk function is strongly convex. Unlike the previous studies, here we assume the loss function is {\em non-negative} and {\em the optimal value of population risk is sufficiently small}. With these additional assumptions, we propose a new method whose output could achieve an upper bound of $O(\frac{d\log\frac{1}δ}{n^2ε^2}+\frac{1}{n^τ})$ for any $τ\geq 1$ in $(ε,δ)$-DP model if the sample size $n$ is sufficiently large.

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