arXiv subjects

Mingchen Ma

Publications and source records attributed to Mingchen Ma.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Multi-Index Models: Learning Intersections of Degree-2 PTFs

We give an algorithm for PAC learning intersections of $k$ degree-2 polynomial threshold functions over $R^d$ under a Gaussian distribution. Our algorithm achieves classification error $ε$ using $d^{O(k)}2^{O_k(\log^3(1/ε))}$ time and samples, improving over the $d^{O(k^2/ε^2)}$ running time of the polynomial regression approach. To our knowledge, our result is the first to obtain a dimension exponent independent of the accuracy parameter, even for $k=2$. We complement our algorithmic result with an SQ lower bound showing that the complexity dependence of $d^{Ω(k)}$ is unavoidable. Lifting the input to polynomial features turns the target into an intersection of $k$ halfspaces. This suggests using the first two labeled moments for subspace recovery. In the lifted space, however, these moments can reveal nothing. Our starting point is a Gaussian comparison theorem showing that, for sufficiently regular defining quadratics, the labeled moments needed for subspace recovery are approximately preserved. To handle arbitrary defining quadratics, we establish a new structural result showing that every direction with significant resampling influence can be detected through degree-$O(k)$ moments. These results yield an initial $d^{O(k)}2^{\mathrm{poly}_k(1/ε)}$-time learner using adaptive restrictions. To improve the exponential dependence on $1/ε$, we develop a two-stage dimension-reduction approach that avoids the costly adaptive partitioning. After identifying a subspace containing all directions with large influence, we use generalized regularity and Gaussian comparison to recover the remaining relevant quadratic features through a new derivative-based moment operator. The recovered features support an intersection close to the target. Combining them with robust hinge-loss minimization gives our quasipolynomial-time learner.

cs.LG↗

arXiv2026

Gaussian Partitioning for Reliable Learning of Multi-Index Models

We introduce Gaussian partitioning, an algorithmic primitive for distributions smooth with respect to a Gaussian. It partitions space into polyhedral regions so that almost all mass lies in thin strips restricting a few orthogonal directions. Within each strip, the conditional distribution approximately matches low-degree Gaussian moments in the unrestricted directions. Our construction builds on logconcave partitioning of Diakonikolas, Kane, and Ma (FOCS 2026). Under input marginals smooth with respect to the standard Gaussian, we obtain agnostic learners with error $(1+c)\mathrm{opt}+ε$ for broad classes of Boolean multi-index models, including functions of halfspaces, low-dimensional convex concepts, and low-dimensional polynomial threshold functions. For functions of $k$ halfspaces, both agnostic and testable agnostic learners achieve this error with dimension dependence $d^{\mathrm{poly}(k/c)}$, improving the previous exponential dependence on $k/c$ in the agnostic exponent. For learning from positive examples with imperfect unlabeled data (PUI), we give algorithms and Statistical Query (SQ) lower bounds that qualitatively characterize complexity through Gaussian moment matching. For fixed smoothness and positive-mass parameters, we learn intersections of $k$ halfspaces with dimension dependence $d^{O(\log(k/ε))}$ and matching SQ lower bounds, improving the previous $d^{\mathrm{poly}(1/ε)}$ upper bound even for one halfspace. A general reduction from agnostic reliable learning to PUI yields negative reliable learners for these intersections with the same dimension dependence, for fixed smoothness. Finally, for PQ learning and testable learning with distribution shift, we prove qualitatively optimal SQ lower bounds of $d^{Ω(1/ε^2)}$, even for intersections of two halfspaces with Gaussian training data and arbitrary test distributions.

cs.DS↗

arXiv2026

Robust Learning of Multi-Index Models under Logconcave Distributions via Weak Partial Learners

We develop a new algorithmic framework for learning Boolean concept classes under logconcave distributions. Our framework applies to broad families of multi-index models and yields significantly faster robust learners than were previously known in these settings. It extends to partial classification and testable learning. Consequently, we obtain improved learners for several fundamental concept classes, including functions of halfspaces and multiclass linear classifiers, under logconcave marginals. Our starting point is a new boosting framework based on weak partial learners. Classical boosting approaches require often-intractable distribution-free weak learners or yield weak approximation guarantees. We show instead that weak learners for partial classification, where labels may be undefined on part of the domain, suffice for strong agnostic learning. The key challenge is that boosting requires a weak learner that succeeds under conditioned distributions that are not guaranteed to be logconcave. To address this, we develop a recursive moment-based partitioning procedure: given a logconcave distribution $X$ and a conditional version $X'$, we partition the space into polynomially many convex regions so that, on most regions, the low-degree moments of $X$ and $X'$ approximately agree. On each good region, a well-behaved multi-index model correlates with a low-degree polynomial, giving a weak hypothesis. Combining these hypotheses yields the required weak learner. A key ingredient of our approach is an efficient method for detecting moment discrepancy. Specifically, we show how to find a low-dimensional subspace that captures any non-trivial discrepancy between $X$ and $X'$, if one exists. Our approach combines spectral analysis of moment tensors with recent progress on isoperimetry for logconcave measures. This discrepancy-finding procedure may be of independent interest.

cs.LG↗

arXiv2026

The Effect of Layer Ordering in Hybrid Architectures

Hybrid attention is rapidly becoming the dominant architectural choice for frontier models. Despite their successes, such architectures complicate model design by introducing additional choices, including the types and locations of layers. This combinatorially large design space has been studied empirically, but given the vast expense of training and evaluating models with different configurations, a principled understanding of the effects of layer selection and ordering is needed. We provide the first such analysis, showing that the dominant hybrid architecture is highly task-specific. Concretely, for any layer configuration, we prove that there exists a task where we can construct a model with this configuration that provably outperforms any other model of any different configuration under fixed resource constraints. Empirically, we observe that for standard training, learned hybrid architectures exhibit separations between layer orderings that match our theoretical findings. For instance, under the same memory budget, the optimal architecture predicted by our theory for a segmented retrieval task consistently achieves perfect accuracy, whereas the next strongest plateaus below 0.5. These results extend to deeper models, where ``containing'' the dominant architecture for a task indicates whether the model attains high performance. In addition, we investigate the mechanisms learned by hybrids, observing that Transformer layers contribute the largest share of performance on associative recall across architectures. This work establishes insights into task-dependent hybrid architecture design relevant to the training and scaling of frontier-scale hybrids.

cs.LG↗

arXiv2026

Robust Regression of General ReLUs with Queries

We study the task of agnostically learning general (as opposed to homogeneous) ReLUs under the Gaussian distribution with respect to the squared loss. In the passive learning setting, recent work gave a computationally efficient algorithm that uses $poly(d,1/ε)$ labeled examples and outputs a hypothesis with error $O(opt)+ε$, where $opt$ is the squared loss of the best fit ReLU. Here we focus on the interactive setting, where the learner has some form of query access to the labels of unlabeled examples. Our main result is the first computationally efficient learner that uses $d polylog(1/ε)+\tilde{O}(\min\{1/p, 1/ε\})$ black-box label queries, where $p$ is the bias of the target function, and achieves error $O(opt)+ε$. We complement our algorithmic result by showing that its query complexity bound is qualitatively near-optimal, even ignoring computational constraints. Finally, we establish that query access is essentially necessary to improve on the label complexity of passive learning. Specifically, for pool-based active learning, any active learner requires $\tildeΩ(d/ε)$ labels, unless it draws a super-polynomial number of unlabeled examples.

cs.LG↗

arXiv2026

Efficiently Learning Drifting Halfspaces with Massart Noise

We study the problem of learning a drifting concept in the presence of Massart noise. In this framework, an online learner has access to a history of independent samples whose labels are noisy versions of a target concept that may change from round to round. The goal is to output, in each round, a hypothesis with small prediction error. We study the complexity of this learning problem for the fundamental class of margin-separable linear classifiers (halfspaces). On the positive side, we give a computationally efficient learner achieving error $η+ \tilde O(Δ^{1/3}/γ)$, where $η$ upper bounds the Massart noise rate, $Δ$ is the drift rate, and $γ$ is the margin. Interestingly, in the realizable setting, an adaptation of our techniques yields an efficient learner with an improved error rate over prior work. On the lower-bound side, we provide formal evidence of an information-computation tradeoff, strongly suggesting that our algorithm's performance is essentially optimal. Specifically, while the information-theoretically optimal error scales with $Δ^{1/2}$, we prove that $Δ^{1/3}$-scaling is unavoidable for low-degree polynomial tests, even in the special case of random classification noise.

cs.LG↗

arXiv2026

Towards Brain MRI Foundation Models for the Clinic: Findings from the FOMO25 Challenge

Clinical deployment of automated brain MRI analysis faces a fundamental challenge: clinical data is heterogeneous and noisy, and high-quality labels are prohibitively costly to obtain. Self-supervised learning (SSL) can address this by leveraging the vast amounts of unlabeled data produced in clinical workflows to train robust \textit{foundation models} that adapt out-of-domain with minimal supervision. However, the development of foundation models for brain MRI has been limited by small pretraining datasets and in-domain benchmarking focused on high-quality, research-grade data. To address this gap, we organized the FOMO25 challenge as a satellite event at MICCAI 2025. FOMO25 provided participants with a large pretraining dataset, FOMO60K, and evaluated models on data sourced directly from clinical workflows in few-shot and out-of-domain settings. Tasks covered infarct classification, meningioma segmentation, and brain age regression, and considered both models trained on FOMO60K (method track) and any data (open track). Nineteen foundation models from sixteen teams were evaluated using a standardized containerized pipeline. Results show that (a) self-supervised pretraining improves generalization on clinical data under domain shift, with the strongest models trained \textit{out-of-domain} surpassing supervised baselines trained \textit{in-domain}. (b) No single pretraining objective benefits all tasks: MAE favors segmentation, hybrid reconstruction-contrastive objectives favor classification, and (c) strong performance was achieved by small pretrained models, and improvements from scaling model size and training duration did not yield reliable benefits.

cs.CV↗

arXiv2026

Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals

We study the task of agnostic learning of multiclass linear classifiers under the Gaussian distribution. Given labeled examples $(x, y)$ from a distribution over $\mathbb{R}^d \times [k]$, with Gaussian $x$-marginal, the goal is to output a hypothesis whose error is comparable to that of the best $k$-class linear classifier. While the binary case $k=2$ has a well-developed algorithmic theory, much less is known for $k \ge 3$. Even for $k=3$, prior robust algorithms incur exponential dependence on the inverse of the desired accuracy in both complexity and representation size. In this work, we develop new structural results for multiclass linear classifiers and use them to design fully polynomial-time robust learners with dimension-independent error guarantees. Our first result shows that the standard multiclass perceptron algorithm requires super-polynomially many samples and updates, even with clean labels and Gaussian marginals, revealing a basic obstruction absent in the binary case. Our main positive result is a pairwise improper-learning framework which yields an efficient learner with error $\widetilde O(k^{3/2}\sqrt{\mathrm{opt}})+ε$ for general $k$. Additionally, we develop a sharper localization-based framework which leads to error $O(\mathrm{opt})+ε$ for $k=3$, and error $\mathrm{poly}(k)\mathrm{opt}+ε$ for geometrically regular $k$-class linear classifiers.

cs.LG↗

arXiv2026

Skilled AI Agents for Embedded and IoT Systems Development

Large language models (LLMs) and agentic systems have shown promise for automated software development, but applying them to hardware-in-the-loop (HIL) embedded and Internet-of-Things (IoT) systems remains challenging due to the tight coupling between software logic and physical hardware behavior. Code that compiles successfully may still fail when deployed on real devices because of timing constraints, peripheral initialization requirements, or hardware-specific behaviors. To address this challenge, we introduce a skills-based agentic framework for HIL embedded development together with IoT-SkillsBench, a benchmark designed to systematically evaluate AI agents in real embedded programming environments. IoT-SkillsBench spans three representative embedded platforms, 23 peripherals, and 42 tasks across three difficulty levels, where each task is evaluated under three agent configurations (no-skills, LLM-generated skills, and human-expert skills) and validated through real hardware execution. Across 378 hardware validated experiments, we show that concise human-expert skills with structured expert knowledge enable near-perfect success rates across platforms.

cs.SE↗

arXiv2026

Expressivity-Efficiency Tradeoffs for Hybrid Sequence Models

Hybrid sequence models--combining Transformer and state-space model layers--seek to gain the expressive versatility of attention as well as the computational efficiency of state-space model layers. Despite burgeoning interest in hybrid models, we lack a basic understanding of the settings where--and underlying mechanisms through which--they offer benefits over their constituent models. In this paper, we study this question, focusing on a broad family of core synthetic tasks. For this family of tasks, we prove the existence of fundamental limitations for non-hybrid models. Specifically, any Transformer or state-space model that solves the underlying task requires either a large number of parameters or a large working memory. On the other hand, for two prototypical tasks within this family--namely selective copying and associative recall--we construct hybrid models of small size and working memory that provably solve these tasks, thus achieving the best of both worlds. Our experimental evaluation empirically validates our theoretical findings. Importantly, going beyond the settings in our theoretical analysis, we empirically show that learned--rather than constructed--hybrids outperform non-hybrid models with up to 6x as many parameters. We additionally demonstrate that hybrid models exhibit stronger length generalization and out-of-distribution robustness than non-hybrids.

cs.LG↗

arXiv2025

Learning Intersections of Two Margin Halfspaces under Factorizable Distributions

Learning intersections of halfspaces is a central problem in Computational Learning Theory. Even for just two halfspaces, it remains a major open question whether learning is possible in polynomial time with respect to the margin $γ$ of the data points and their dimensionality $d$. The best-known algorithms run in quasi-polynomial time $d^{O(\log(1/γ))}$, and it has been shown that this complexity is unavoidable for any algorithm relying solely on correlational statistical queries (CSQ). In this work, we introduce a novel algorithm that provably circumvents the CSQ hardness barrier. Our approach applies to a broad class of distributions satisfying a natural, previously studied, factorizability assumption. Factorizable distributions lie between distribution-specific and distribution-free settings, and significantly extend previously known tractable cases. Under these distributions, we show that CSQ-based methods still require quasipolynomial time even for weakly learning, whereas our algorithm achieves $poly(d,1/γ)$ time by leveraging more general statistical queries (SQ), establishing a strong separation between CSQ and SQ for this simple realizable PAC learning problem. Our result is grounded in a rigorous analysis utilizing a novel duality framework that characterizes the moment tensor structure induced by the marginal distributions. Building on these structural insights, we propose new, efficient learning algorithms. These algorithms combine a refined variant of Jennrich's Algorithm with PCA over random projections of the moment tensor, along with a gradient-descent-based non-convex optimization framework.

cs.LG↗

arXiv2025

ProGress: Structured Music Generation via Graph Diffusion and Hierarchical Music Analysis

Artificial Intelligence (AI) for music generation is undergoing rapid developments, with recent symbolic models leveraging sophisticated deep learning and diffusion model algorithms. One drawback with existing models is that they lack structural cohesion, particularly on harmonic-melodic structure. Furthermore, such existing models are largely "black-box" in nature and are not musically interpretable. This paper addresses these limitations via a novel generative music framework that incorporates concepts of Schenkerian analysis (SchA) in concert with a diffusion modeling framework. This framework, which we call ProGress (Prolongation-enhanced DiGress), adapts state-of-the-art deep models for discrete diffusion (in particular, the DiGress model of Vignac et al., 2023) for interpretable and structured music generation. Concretely, our contributions include 1) novel adaptations of the DiGress model for music generation, 2) a novel SchA-inspired phrase fusion methodology, and 3) a framework allowing users to control various aspects of the generation process to create coherent musical compositions. Results from human experiments suggest superior performance to existing state-of-the-art methods.

cs.SD↗

arXiv2025

IoT-MCP: Bridging LLMs and IoT Systems Through Model Context Protocol

The integration of Large Language Models (LLMs) with Internet-of-Things (IoT) systems faces significant challenges in hardware heterogeneity and control complexity. The Model Context Protocol (MCP) emerges as a critical enabler, providing standardized communication between LLMs and physical devices. We propose IoT-MCP, a novel framework that implements MCP through edge-deployed servers to bridge LLMs and IoT ecosystems. To support rigorous evaluation, we introduce IoT-MCP Bench, the first benchmark containing 114 Basic Tasks (e.g., ``What is the current temperature?'') and 1,140 Complex Tasks (e.g., ``I feel so hot, do you have any ideas?'') for IoT-enabled LLMs. Experimental validation across 22 sensor types and 6 microcontroller units demonstrates IoT-MCP's 100% task success rate to generate tool calls that fully meet expectations and obtain completely accurate results, 205ms average response time, and 74KB peak memory footprint. This work delivers both an open-source integration framework (https://github.com/Duke-CEI-Center/IoT-MCP-Servers) and a standardized evaluation methodology for LLM-IoT systems.

cs.DC↗

arXiv2025

Statistical Query Hardness of Multiclass Linear Classification with Random Classification Noise

We study the task of Multiclass Linear Classification (MLC) in the distribution-free PAC model with Random Classification Noise (RCN). Specifically, the learner is given a set of labeled examples $(x, y)$, where $x$ is drawn from an unknown distribution on $R^d$ and the labels are generated by a multiclass linear classifier corrupted with RCN. That is, the label $y$ is flipped from $i$ to $j$ with probability $H_{ij}$ according to a known noise matrix $H$ with non-negative separation $σ: = \min_{i \neq j} H_{ii}-H_{ij}$. The goal is to compute a hypothesis with small 0-1 error. For the special case of two labels, prior work has given polynomial-time algorithms achieving the optimal error. Surprisingly, little is known about the complexity of this task even for three labels. As our main contribution, we show that the complexity of MLC with RCN becomes drastically different in the presence of three or more labels. Specifically, we prove super-polynomial Statistical Query (SQ) lower bounds for this problem. In more detail, even for three labels and constant separation, we give a super-polynomial lower bound on the complexity of any SQ algorithm achieving optimal error. For a larger number of labels and smaller separation, we show a super-polynomial SQ lower bound even for the weaker goal of achieving any constant factor approximation to the optimal loss or even beating the trivial hypothesis.

cs.LG↗

arXiv2025

AutoCBT: An Autonomous Multi-agent Framework for Cognitive Behavioral Therapy in Psychological Counseling

Traditional in-person psychological counseling remains primarily niche, often chosen by individuals with psychological issues, while online automated counseling offers a potential solution for those hesitant to seek help due to feelings of shame. Cognitive Behavioral Therapy (CBT) is an essential and widely used approach in psychological counseling. The advent of large language models (LLMs) and agent technology enables automatic CBT diagnosis and treatment. However, current LLM-based CBT systems use agents with a fixed structure, limiting their self-optimization capabilities, or providing hollow, unhelpful suggestions due to redundant response patterns. In this work, we utilize Quora-like and YiXinLi single-round consultation models to build a general agent framework that generates high-quality responses for single-turn psychological consultation scenarios. We use a bilingual dataset to evaluate the quality of single-response consultations generated by each framework. Then, we incorporate dynamic routing and supervisory mechanisms inspired by real psychological counseling to construct a CBT-oriented autonomous multi-agent framework, demonstrating its general applicability. Experimental results indicate that AutoCBT can provide higher-quality automated psychological counseling services.

cs.CL↗

arXiv2024

Active Learning of General Halfspaces: Label Queries vs Membership Queries

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces under the Gaussian distribution on $R^d$ in the presence of some form of query access. In the classical pool-based active learning model, where the algorithm is allowed to make adaptive label queries to previously sampled points, we establish a strong information-theoretic lower bound ruling out non-trivial improvements over the passive setting. Specifically, we show that any active learner requires label complexity of $\tildeΩ(d/(\log(m)ε))$, where $m$ is the number of unlabeled examples. Specifically, to beat the passive label complexity of $\tilde{O} (d/ε)$, an active learner requires a pool of $2^{poly(d)}$ unlabeled samples. On the positive side, we show that this lower bound can be circumvented with membership query access, even in the agnostic model. Specifically, we give a computationally efficient learner with query complexity of $\tilde{O}(\min\{1/p, 1/ε\} + d\cdot polylog(1/ε))$ achieving error guarantee of $O(opt)+ε$. Here $p \in [0, 1/2]$ is the bias and $opt$ is the 0-1 loss of the optimal halfspace. As a corollary, we obtain a strong separation between the active and membership query models. Taken together, our results characterize the complexity of learning general halfspaces under Gaussian marginals in these models.

cs.LG↗

arXiv2024

Active Learning with Simple Questions

We consider an active learning setting where a learner is presented with a pool S of n unlabeled examples belonging to a domain X and asks queries to find the underlying labeling that agrees with a target concept h^* \in H. In contrast to traditional active learning that queries a single example for its label, we study more general region queries that allow the learner to pick a subset of the domain T \subset X and a target label y and ask a labeler whether h^*(x) = y for every example in the set T \cap S. Such more powerful queries allow us to bypass the limitations of traditional active learning and use significantly fewer rounds of interactions to learn but can potentially lead to a significantly more complex query language. Our main contribution is quantifying the trade-off between the number of queries and the complexity of the query language used by the learner. We measure the complexity of the region queries via the VC dimension of the family of regions. We show that given any hypothesis class H with VC dimension d, one can design a region query family Q with VC dimension O(d) such that for every set of n examples S \subset X and every h^* \in H, a learner can submit O(d log n) queries from Q to a labeler and perfectly label S. We show a matching lower bound by designing a hypothesis class H with VC dimension d and a dataset S \subset X of size n such that any learning algorithm using any query class with VC dimension less than O(d) must make poly(n) queries to label S perfectly. Finally, we focus on well-studied hypothesis classes including unions of intervals, high-dimensional boxes, and d-dimensional halfspaces, and obtain stronger results. In particular, we design learning algorithms that (i) are computationally efficient and (ii) work even when the queries are not answered based on the learner's pool of examples S but on some unknown superset L of S

cs.LG↗

arXiv2023

Buying Information for Stochastic Optimization

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a $2$-competitive deterministic algorithm and a $e/(e-1)$-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an $8$-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

cs.DS↗