Supervised Learning

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27 papers3 papers in the last four weeks, down 25% on the four weeks before. 0.0% of all new papers.

Oct 7, 2026

MotherTree: Meta-learning on synthetic data improves decision tree training

Conventional decision tree algorithms produce effective, transparent models that can be audited, communicated, and deployed independently of the training data, but require learning every new task from scratch. In contrast, tabular foundation models demonstrate that meta-learning from a synthetic prior distribution enables strong in-context prediction for previously unseen tasks, especially in small-sample regimes. However, this approach does not produce a standalone model that can be inspected in isolation. We introduce MotherTree, a tabular transformer that meta-learns decision tree induction: given a training set for a new task, it outputs a hard, axis-aligned decision tree, equivalent in form to classically trained trees, in a single forward pass. MotherTree is pre-trained on a synthetic prior using stochastic gradient descent without requiring reference trees for supervision. On established benchmarks with controlled sample size, the approach is competitive with size-matched trees from common algorithms: recursive partitioning, gradient-based tree learning, globally optimal trees, and distillation from tabular foundation models. Notably, MotherTree consistently improves over from-scratch gradient-based learning and acts as a strong initializer: task-specific tuning of the generated tree outperforms the corresponding from-scratch learner on all benchmarks and sample sizes. These results show that meta-learning can provide effective inductive biases for learning stand-alone, small decision tree classifiers.

Ziyuan Wang, Fredrik D. Johansson

Chalmers University of Technology University of Gothenburg

Decision Tree Learning Meta-Learning Supervised Learning Tabular Prediction Synthetic Data Pretraining

Oct 3, 2026

Integrated Imputation-Classification for Supervised Learning with Missing Data

We study supervised classification problems with missing feature values. Existing approaches often decouple imputation from classification, producing imputations that may be plausible but uninformative for prediction. Instead, we propose the Integrated Imputation and Classification Network (IICN), which jointly trains an imputer and an

{(n{+}1)}

-classdiscriminator adversarially with a single class supervised classification objective, where the discriminator learns to distinguish among the

n

true classes and an additional ``imputed" class. We prove that at the global optimum, the imputer and discriminator together implement marginalization over missing coordinates and yield a Bayes-optimal classifier. We evaluate IICN on FashionMNIST, CIFAR-10, and tabular datasets with naturally occurring missingness. IICN outperforms classical impute-then-classify pipelines and recent generative baselines, showing strong robustness and accuracy in challenging settings.

Yue Liu, Ben Liang, Ali Tizghadam +1

University of Toronto · TELUS

Learning with Missing Data Supervised Learning Incomplete Data Imputation

Sep 22, 2026

Real-Time Atomic-Resolution Electron Phase Imaging without Probe Calibration via Ptychography-Supervised Learning

Atomic-scale phase imaging is central to resolving defects, interfaces, and weakly scattering atoms that govern the behavior of nanoscale materials. Electron ptychography delivers sub-ångström phase sensitivity but remains an offline technique, because its iterative reconstruction is computationally expensive and sensitive to experimental calibration, preventing live use during data acquisition. Here, a ptychography-supervised local inference framework is presented that converts four-dimensional scanning transmission electron microscopy (4D-STEM) into an acquisition-compatible phase-imaging workflow. Physics-constrained reference phase maps reconstructed from a single experimental AuPd dataset serve as teacher labels for a compact model that predicts local phase patches directly from diffraction measurements, without explicit probe input or online iterative optimization. Full-field images are assembled by deterministic overlap stitching. The workflow reaches an online latency of about 0.27 ms per probe position and a throughput of about 20,000 positions per second, an approximately 1,000-fold speed-up over GPU-accelerated ePIE, while preserving atomic-scale lattice contrast and reciprocal-space fidelity. Without fine-tuning, the same model transfers across materials (WS2), defocus conditions (high-entropy alloy nanoparticles), and instruments (hBN at 300 kV). The approach amortizes ptychographic redundancy into a fast, generalizable workflow that enables real-time atomic-scale phase imaging for materials microscopy.

H. Yue, C. -C. Chen, C. -N. Hsiao +4

College of Intelligent Robotics and Advanced Manufacturing, Fudan University, Shanghai 200433, China. · Department of Engineering and System Science, National Tsing Hua University, Hsinchu 300044, Taiwan · National Center for Instrumentation Research, National Institutes of Applied Research, Hsinchu 300092, Taiwan +3

Supervised Learning Electron Microscopy Computational Imaging Image Reconstruction Scanning Transmission Electron Microscopy

Sep 9, 2026

Relatively Smart II: Tractable or Semi-Supervised Instance-Optimal Learning

We continue the study of relatively smart learning, introduced by Dughmi and Pour (2026), which asks a supervised learner to compete, marginal by marginal, with every distribution-fixed error guarantee soundly certifiable from unlabeled data. They showed that the One-Inclusion Graph (OIG) learner is relatively smart with a quadratic sample-complexity blowup, and that no relatively smart learner can do better, leaving open whether ERM or another natural or tractable learner achieves comparable guarantees. They also left open whether the blowup can be restricted to unlabeled data. Our firs results shows that ERM---and in fact any proper consistent learner---is relatively smart for binary classification in the distribution-free setting. We show that a small certifiable error with

m

samples implies a similarly small error on the uniform distribution over a random sample of size

O(m^2)

, yielding a cover of size at most

2^{m+1}

on that sample. This suffices to control the error of proper consistent learners with

O(m^2)

samples. We then show that semi-supervised relatively smart learning is information-theoretically possible with a quadratic blowup only in unlabeled sample complexity and no blowup in labeled sample complexity. The learner uses a natural generalization of OIG to a leave-most-out transductive problem, where labels of part of a finite pool are revealed and the remaining labels are predicted. Finally, this label efficiency comes at a cost in simplicity and tractability. If the hypothesis class is accessed only through an agnostic ERM oracle, any semi-supervised relatively smart learner with substantially sub-quadratic labeled-sample blowup requires super-polynomially many oracle calls. This holds even when the marginal is given explicitly, and thus also yields an intractability result for distribution-fixed learning that may be of independent interest.

Shaddin Dughmi, Alireza F. Pour

University of Southern California · University of Waterloo

Classification Semi-Supervised Learning Statistical Learning Theory Supervised Learning

Aug 27, 2026

Algorithmic Principles For Multiclass Learning Are Hard To Come By: Limits of Regularization and Proper Learning

Two of the most fundamental questions in statistical learning theory are the following: which prediction problems are learnable, and how should they be learned? For the former, elegant answers often take the form of combinatorial dimensions. The latter question, however, has proved considerably more elusive: all known general-purpose multiclass learners rely on intricate orientations of exponentially large one-inclusion structures, and familiar algorithmic principles such as proper learning and regularization remain poorly understood. Motivated by prior work, we ask whether learning reduces to proper learning---possibly over a larger hypothesis class---and whether proper or improper multiclass learning can ultimately be captured by suitable regularizers. Our primary results answer both questions negatively, resolving three open problems from prior work. First, we exhibit a learnable multiclass problem that cannot be embedded in any properly learnable class, meaning learning cannot be reduced to proper learning by enlarging the hypothesis class. Second, we demonstrate that proper learning can require training error and characterize this phenomenon precisely: every properly learnable class admits a proper learner making

o(m)

errors on samples of size

m

, but every prescribed sublinear scale

a_m=o(m)

is necessary for some properly learnable problem. Third, regularization is not a general learner: we exhibit a properly learnable class that cannot be learned by any Structural Risk Minimization (SRM) learner, and a learnable class that cannot be learned by any local regularizer. We complement these impossibility results with a positive theory that gives two sufficient conditions for SRM learnability and characterizes SRM representability through integrability of revealed preferences.

Julian Asilis, Shaddin Dughmi, Vatsal Sharan +3

USC · University of Chicago · Northwestern University

Statistical Learning Theory Multiclass Classification Supervised Learning

Aug 25, 2026

Toward Machine Learning with the Unit as a Primitive: Learning from Unit-Linked Events

Machine learning is usually formalized through samples, while the persistent individual to which multiple observed or possible events refer often remains implicit. We propose the unit as an explicit primitive at the level of task semantics. A learning task first declares a population of persistent referents and a sameness criterion; the realized value

u

denotes the selected referent. Supervised learning is the main formal specialization. Its semantic object is a family of unit-conditioned response laws. Homogeneity is the special case in which those laws coincide; a sample-only conditional is silent as to whether the world is homogeneous or the observed law is only the marginal of a heterogeneous family. What is learned from data is a pair

(T_φ,R_θ)

: a tokenizer that produces a contextual unit token and one shared response-law form that reads it. The structured class takes that form to be a simple relation in the token; a linear predictor is the running instance. The token is the learner-side representation through which the task-side unit affects prediction, while a learner specification that omits unit information is unit-insensitive; homogeneity remains a property of the world-side response family. When identity is unresolved, the world-side law mixes unit-conditioned targets, while the learner composes its shared form with a token. A trusted resolver may fix the unit and supply a lookup token; otherwise unit abduction forms a token of the same type from factual evidence. Unlinked single-row observations can fail to distinguish a heterogeneous unit world from a homogeneous pooled world; trusted same-unit pairs separate a restricted witness. The formal results concern this supervised specialization.

Heyang Gong

Supervised Learning

Aug 17, 2026

Hide&Seek: Learning to Explain in an End-to-End Differentiable Network

Instance-wise feature selection is a valuable tool for interpreting labeled data and the predictions of black-box models. In contrast to global feature selection techniques, instance-wise methods dynamically identify important features for each instance. A growing number of methods learn a selector, which identifies important features, and a predictor, which uses these to make predictions. However, these pioneering methods face challenges including information leakage and lack of differentiability, which can slow training. In this paper, we present Hide&Seek, an end-to-end differentiable model for instance-wise feature selection. We jointly learn feature selection and prediction under a single objective without information leakage. Hide&Seek outperforms existing state-of-the-art models across a range of experiments and is fast to train. We achieve this by reformulating feature removal as a differentiable operation where instead of discretely removing features, we replace a proportion of each feature. Training is further stabilized via a parsimony-weight annealing framework.

Tal Ellinson, Hadi Mohasel Afshar, Sally Cripps

Human Technology Institute; School of Mathematical and Physical Sciences, University of Technology Sydney, Australia.

Feature Selection Interpretable ML Supervised Learning

Jul 31, 2026

Transpiler Autotuning with Predictive Models for Quantum Circuit Optimization

Quantum software engineering is an emerging research field focusing on efficiently embedding the quantum programming paradigm into existing software ecosystems. A key aspect of this field is the realization of quantum algorithms using gate-based programming and the subsequent low-level optimization of the resulting quantum circuits, a process that is commonly performed by so-called transpilation pipelines. One significant challenge in these pipelines is determining which optimizations to apply to a given circuit. This decision is usually based on fixed default configurations that are uniformly applied to all circuits, frequently resulting in missed opportunities for more aggressive circuit optimization. In this work, we tackle this challenge by applying autotuning with supervised machine learning to develop an automated method for selection of transpiler passes. To train our machine-learning models, we employ feature-model based sampling to generate a representative dataset that examines how different combinations of Qiskit transpiler passes perform across thousands of circuits drawn from the state-of-the-art benchmarking suite MQT Bench. Using these data, we build a predictive model extension for the Qiskit transpilation pipeline that uses a machine learning model to automatically select combinations of transpiler passes aiming to achieve a maximum reduction in two-qubit gates. Our empirical evaluation shows that the combinations selected by our model are never outperformed by Qiskit's optimization levels, achieve on average an additional 19.1

\%

- 32.4

\%

reduction in two-qubit gates, and for some circuits finds reductions of up to

95.8\%

in cases where Qiskit achieves no reduction at all.

Piotr Malkowski, Domenik Eichhorn, Joshua Ammermann +4

Karlsruhe Institute of Technology, Germany · Technical University of Munich, Germany

Quantum Circuit Optimization Quantum Circuit Compilation Supervised Learning

Jul 30, 2026

Rethinking Total Absorption Gamma Spectroscopy Deconvolution: Supervised Machine Learning vs Response-Matrix Methods

The extraction of

β

-feeding distributions in Total Absorption

γ

-ray Spectroscopy constitutes a challenging inverse problem, particularly in nuclei with complex decay schemes involving a large number of excited states. In such cases, the measured spectrum arises from the superposition of many detector response functions, making the determination of the individual feedings intrinsically ill-posed and highly sensitive to the methodology employed. In this work, we present a systematic comparison between supervised Machine-Learning techniques and Response-Matrix methods using realistic Monte Carlo simulations of an experimental Total Absorption Spectrometer. Supervised Machine-Learning approaches construct a non-parametric estimator that infers level feedings from the measured spectrum after a training stage, whereas Response-Matrix methods determine the feeding distribution by directly minimizing the difference between measured and reconstructed spectra. Our results show that supervised Machine-Learning techniques achieve superior accuracy in the reconstruction of individual feeding intensities, whereas Response-Matrix methods provide robust and physically consistent initial solutions. These findings support a hybrid strategy in which a Response-Matrix method is first used to obtain an initial feeding estimate, which is then refined using a supervised Machine-Learning approach to achieve improved overall accuracy.

J. Balibrea-Correa, E. N{á}cher, C. Fonseca-Vargas +1

Instituto de Física Corpuscular, CSIC - Universidad de Valencia, Spain, 46980, Valencia, Spain

Spectral Methods Supervised Learning Inverse Problems

Jun 9, 2026

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.

Ilias Diakonikolas, Daniel M. Kane, Mingchen Ma

University of Wisconsin-Madison · University of California, San Diego

ReLU Neural Networks Active Learning Statistical Learning Theory Supervised Learning Agnostic Learning

May 31, 2026

A Fiber Criterion for Representation Identifiability in Supervised Learning

Supervised learning evaluates predictors through their input-output behavior. When a predictor is implemented as a composition

f=c\circ h

, supervised evidence constrains the composite map

f

but need not determine the representation-head factorization

(h,c)

. This paper formalizes the resulting representation-level identifiability problem: for a class of admissible representation-head pairs, a representation property is identifiable from the induced predictor exactly when it is constant on the fibers of the projection

(h,c)\mapsto c\circ h

, equivalently when it descends to a well-defined property of the predictor. Predictor-preserving augmentation gives a canonical obstruction: auxiliary information can be appended to a representation while the head ignores it, leaving the predictor unchanged but altering properties such as minimality, compression, invariance, equivariance, nuisance information, or semantic accessibility. This construction separates representation identifiability from optimization and finite-sample estimation. Finite-sample diagnostics illustrate, rather than prove, the criterion: exact algebraic witnesses hold the predictor fixed while changing representation diagnostics, and matched-performance Waterbirds models show that different constraints can select different representations at similar supervised performance. The results clarify that representation-level claims require assumptions, objectives, measurements, or inductive biases beyond supervised predictive behavior alone.

Vasileios Sevetlidis

Athena Research Center, Kimmeria Campus, Xanthi, Greece · Democritus University of Thrace, Vas. Sofias Campus, Xanthi, Greece · International Hellenic University, Serres, Greece

Representation Identifiability Parameter Identifiability Supervised Learning

May 28, 2026

Universal Multiclass Transductive Online Learning

We consider the problem of universal transductive online classification with a possibly unbounded label space. This setting considers online learning, with the sequence of instances (without labels) known to the learner in advance. We say a concept class

\mathcal{H}

is learnable if there is a learning algorithm

\mathcal{A}

, such that for every realizable sequence, the number of mistakes made by

\mathcal{A}

grows at most sublinearly with the number of predictions. We characterize the learnability of this setting and show that there are only two possible optimal rates for the learnable classes: either bounded or increasing logarithmically. We introduce a new combinatorial structure, called ``Level-Constrained-Littlestone-Littlestone (LCLL) tree'', which, along with the indifference property, characterizes the learnability. We also extend the learnability result to the agnostic case and the case where only the stochastic process that generates the instance sequence is known.

Steve Hanneke, Hongao Wang

Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA

Multiclass Classification Transductive Learning Classification Statistical Learning Theory Supervised Learning

May 22, 2026

Coupled Training with Privileged Information and Unlabeled Data

In many prediction problems, we have extra information during training (for example, measurements that are expensive or slow to collect) that will not be available when the model is deployed. A common strategy is to first train a model that uses all training information, then use its predictions on unlabeled examples to train a second model that only uses the inputs available at test time. However, when the extra training-only information is weak or noisy, this Two-Stage approach can mislead the deployment model and even hurt accuracy. We propose a joint training method that learns the two models together, so the deployment model can benefit from the extra information only when it actually helps, instead of inheriting its mistakes. We provide guarantees that describe when joint training improves prediction accuracy and analyze a simple alternating training algorithm for large, high-dimensional models. Experiments on synthetic data and real-world prediction tasks show that our approach avoids these failures and robustly outperforms standard Two-Stage baselines.

Jiahao Shi, Omar Hagrass, Jason M. Klusowski

Department of Electrical and Computer Engineering, Princeton University · Department of Operations Research and Financial Engineering, Princeton University

Learning Using Privileged Information Semi-Supervised Learning Teacher-Student Learning Supervised Learning

May 21, 2026

Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines

Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that learns through subdirect decomposition of algebraic structure rather than numerical optimization, against standard baselines on image and tabular classification across varying training-set sizes. We find that AML trained only on training data without using validation or cross-validation outperforms a family of cross-validated baseline methods including CNNs on small to medium image datasets (50--2000 training examples). On tabular datasets in the same size range, XGBoost is overall the best performing method, but AML is nonetheless comparable to methods incorporating task-specific biases such as LightGBM and random forests. AML achieves this competitive performance across two very different types of datasets using a generic algebraic inductive bias, rather than the modality-specific biases built into standard baselines like CNNs for images or XGBoost for tabular data, and requires no cross validation because it has no task-dependent hyperparameters to tune.

David Mendez, Fernando Martin-Maroto, Gonzalo G. de Polavieja

Mathematics of Behavior and Intelligence Lab, Champalimaud Foundation, Lisbon

Classification Image Classification Data-Efficient Learning Supervised Learning Small-Data Learning

May 19, 2026

The New Associationism: Lessons from Deep Learning

What can the success of modern AI tell us about how humans learn? This paper argues that taking AI seriously as a model of human learning supports a modest but genuine associationism. The central finding is that supervised learning -- learning driven by evaluative feedback -- underlies a surprisingly wide range of contemporary AI systems, from large language models to game-playing agents, differing primarily in how much work is required to generate the relevant feedback signal. This vindicates associationist ideals of a uniform, gradual, error-driven learning mechanism operating across domains, and defuses the once-influential argument that associationist mechanisms are too limited to account for human cognitive capacities. At the same time, the successes of deep learning depend on computational architectures that go well beyond anything classical associationists envisaged, and supervised learning operates within these as one component rather than a complete account of learning.

Daniel Rothschild

Cognitive Modeling Supervised Learning

May 16, 2026

Soft Learning

Modern machine learning forces practitioners to choose between powerful but expensive deep networks and fast but limited classical algorithms. Here we introduce Soft Learning, a framework that maintains a library of heterogeneous specialists -- spanning linear models, tree ensembles, kernel machines, and neural networks -- and discovers provably optimal combination weights through cross-validated non-negative least squares. Soft Learning is guaranteed to match or exceed the best weighted combination of its specialists, trains over two orders of magnitude faster than deep networks on CPU alone (72-435x faster across tested configurations), provides inherent interpretability through learned weights that reveal which algorithmic paradigm best fits the data, and is future-proof: adding specialists is mathematically guaranteed to maintain or improve performance. Across 37 datasets (25 classification, 12 regression) against nine methods including CatBoost and tuned deep networks, Soft Learning ranks first on 70% of tasks, achieves the best mean rank (Friedman test, p = 1.12 x 10^-12), and is the only method to simultaneously excel at both classification and regression -- all without GPU hardware or hyperparameter tuning. These results suggest a paradigm shift from "which algorithm is best?" to "what is the provably optimal combination?" -- a question Soft Learning answers with formal guarantees for any data modality.

Mohammed Aledhari, Ali Aledhari, Fatimah Aledhari +1

Department of Data Science & Department of Computer Science and Engineering, University of North Texas, Denton, TX 76207, USA · Department of Computer and Information Science, Fordham University, New York, NY 10458, USA

Ensemble Learning Supervised Learning

Apr 27, 2026

Learning to Think from Multiple Thinkers

We study learning with Chain-of-Thought (CoT) supervision from multiple thinkers, all of whom provide correct but possibly systematically different solutions, e.g., step-by-step solutions to math problems written by different thinkers, or step-by-step execution traces of different programs solving the same problem. We consider classes that are computationally easy to learn using CoT supervision from a single thinker, but hard to learn with only end-result supervision, i.e., without CoT (Joshi et al. 2025). We establish that, under cryptographic assumptions, learning can be hard from CoT supervision provided by two or a few different thinkers, in passive data-collection settings. On the other hand, we provide a generic computationally efficient active learning algorithm that learns with a small amount of CoT data per thinker that is completely independent of the target accuracy

\varepsilon

, a moderate number of thinkers that scales as

\log \frac{1}{\varepsilon}\log \log \frac{1}{\varepsilon}

, and sufficient passive end-result data that scales as

\frac{1}{\varepsilon}\cdot poly\log\frac{1}{\varepsilon}

.

Nirmit Joshi, Roey Magen, Nathan Srebro +2

Toyota Technological Institute at Chicago. · Weizmann Institute of Science. · New York University.

CoT Supervision Active Learning Supervised Learning

Apr 8, 2026

Learning to Query History: Nonstationary Classification via Learned Retrieval

Nonstationarity is ubiquitous in practical classification settings, leading deployed models to perform poorly even when they generalize well to holdout sets available at training time. We address this by reframing nonstationary classification as time series prediction: rather than predicting from the current input alone, we condition the classifier on a sequence of historical labeled examples that extends beyond the training cutoff. To scale to large sequences, we introduce a learned discrete retrieval mechanism that samples relevant historical examples via input-dependent queries, trained end-to-end with the classifier using a score-based gradient estimator. This enables the full corpus of historical data to remain on an arbitrary filesystem during training and deployment. Experiments on synthetic benchmarks and Amazon Reviews '23 (electronics category) show improved robustness to distribution shift compared to standard classifiers, with VRAM scaling predictably as the length of the historical data sequence increases.

Jimmy Gammell, Bishal Thapaliya, Yoon Jung +3

Purdue University, Elmore Family School of Electrical and Computer Engineering. · Amazon. · Georgia Institute of Technology.

Classification Retrieval-Augmented Classification OOD Generalization Supervised Learning

Mar 23, 2026

Stable but Wrong: When Learning Stabilizes Away from the Truth

Stable training is often treated as evidence that learning is succeeding, but stability characterizes optimization behavior rather than correctness relative to an external objective. We study what happens when the signal being optimized remains persistently biased. We define Stable but Wrong (SBW) as a learning state in which the learning process remains stable under a task-appropriate operational criterion while the learned outcome remains systematically displaced from an independently defined objective. A minimal strongly convex model shows that a persistent bias in the update direction can shift the unique convergence point away from the true optimum. Controlled experiments in reinforcement learning, supervised learning, and continual fine-tuning of a large language model reveal a recurring separation between apparently normal optimization and correctness under static and feedback-coupled biases. Recovery-stage clean-data access and exploration interventions further show that subsequent trajectories can remain modifiable, although the interventions differ in protocol and do not imply a shared mechanism. The results expose a basic limit of optimization stability as a reliability signal in persistent and feedback-coupled learning systems.

Zhipeng Zhang

China Mobile Research Institute, Beijing 100053, China · China Mobile GBA (Greater Bay Area) Innovation Institute, Guangzhou 510656, China

Supervised Learning

Mar 15, 2026

Learning in Function Spaces: An Unified Functional Analytic View of Supervised and Unsupervised Learning

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational optimization over function spaces induced by the data distribution. Within this framework the data distribution defines operators that capture structural properties of the data, such as similarity relations or statistical dependencies. Learning algorithms can then be viewed as estimating functions expressed in bases determined by these operators. This perspective provides a unified way to interpret several learning paradigms. In supervised learning the objective functional is defined using labeled data and typically corresponds to minimizing prediction risk, whereas unsupervised learning relies on structural properties of the input distribution and leads to objectives based on similarity or smoothness constraints. From this viewpoint, the distinction between learning paradigms arises primarily from the choice of the functional being optimized rather than from the underlying function space. We illustrate this framework by discussing connections with kernel methods, spectral clustering, and manifold learning, highlighting how operators induced by data distributions naturally define function representations used by learning algorithms. The goal of this work is not to introduce a new algorithm but to provide a conceptual framework that clarifies the role of function spaces and operators in modern machine learning.

K. Lakshmanan

Department of Computer Science and Engineering, Indian Insititute of Technology (BHU), Varanasi 221005.

Supervised Learning Statistical Learning Theory

Mar 2, 2026

Relatively Smart: A New Approach for Instance-Optimal Learning

We revisit the framework of Smart PAC learning, which seeks supervised learners which compete with semi-supervised learners that are provided full knowledge of the marginal distribution on unlabeled data. Prior work has shown that such marginal-by-marginal guarantees are possible for "most" marginals, with respect to an arbitrary fixed and known measure, but not more generally. We discover that this failure can be attributed to an "indistinguishability" phenomenon: There are marginals which cannot be statistically distinguished from other marginals that require different learning approaches. In such settings, semi-supervised learning cannot certify its guarantees from unlabeled data, rendering them arguably non-actionable. We propose relatively smart learning, a new framework which demands that a supervised learner compete only with the best "certifiable" semi-supervised guarantee. We show that such modest relaxation suffices to bypass the impossibility results from prior work. In the distribution-free setting, we show that the One-Inclusion Graph learner is relatively smart up to squaring the sample complexity, and show that no supervised learning algorithm can do better. For distribution-family settings, we show that relatively smart learning can be impossible or can require idiosyncratic learning approaches, and its difficulty can be non-monotone in the inclusion order on distribution families.

Shaddin Dughmi, Alireza F. Pour

University of Southern California · University of Waterloo

PAC Learning Semi-Supervised Learning Statistical Learning Theory Supervised Learning

Feb 20, 2026

Predicting Contextual Informativeness for Vocabulary Learning using Deep Learning

We describe a modern deep learning system that automatically identifies informative contextual examples (\qu{contexts}) for first language vocabulary instruction for high school student. Our paper compares three modeling approaches: (i) an unsupervised similarity-based strategy using MPNet's uniformly contextualized embeddings, (ii) a supervised framework built on instruction-aware, fine-tuned Qwen3 embeddings with a nonlinear regression head and (iii) model (ii) plus handcrafted context features. We introduce a novel metric called the Retention Competency Curve to visualize trade-offs between the discarded proportion of good contexts and the \qu{good-to-bad} contexts ratio providing a compact, unified lens on model performance. Model (iii) delivers the most dramatic gains with performance of a good-to-bad ratio of 440 all while only throwing out 70% of the good contexts. In summary, we demonstrate that a modern embedding model on neural network architecture, when guided by human supervision, results in a low-cost large supply of near-perfect contexts for teaching vocabulary for a variety of target words.

Tao Wu, Adam Kapelner

Supervised Learning In-Context Example Selection Text Embedding Models

Feb 20, 2026

Learning Without Training

Machine learning is at the heart of managing the real-world problems associated with massive data. With the success of neural networks on such large-scale problems, more research in machine learning is being conducted now than ever before. This dissertation focuses on three different projects rooted in mathematical theory for machine learning applications. The first project deals with supervised learning and manifold learning. In theory, one of the main problems in supervised learning is that of function approximation: that is, given some data set

\mathcal{D}=\{(x_j,f(x_j))\}_{j=1}^M

, can one build a model

F\approx f

? We introduce a method which aims to remedy several of the theoretical shortcomings of the current paradigm for supervised learning. The second project deals with transfer learning, which is the study of how an approximation process or model learned on one domain can be leveraged to improve the approximation on another domain. We study such liftings of functions when the data is assumed to be known only on a part of the whole domain. We are interested in determining subsets of the target data space on which the lifting can be defined, and how the local smoothness of the function and its lifting are related. The third project is concerned with the classification task in machine learning, particularly in the active learning paradigm. Classification has often been treated as an approximation problem as well, but we propose an alternative approach leveraging techniques originally introduced for signal separation problems. We introduce theory to unify signal separation with classification and a new algorithm which yields competitive accuracy to other recent active learning algorithms while providing results much faster.

Ryan O'Dowd

Claremont Graduate University

Function Approximation Supervised Learning Transfer Learning Active Learning Manifold Learning

Feb 18, 2026

Machine Learning in Epidemiology

In the age of digital epidemiology, epidemiologists are faced by an increasing amount of data of growing complexity and dimensionality. Machine learning is a set of powerful tools that can help to analyze such enormous amounts of data. This chapter lays the methodological foundations for successfully applying machine learning in epidemiology. It covers the principles of supervised and unsupervised learning and discusses the most important machine learning methods. Strategies for model evaluation and hyperparameter optimization are developed and interpretable machine learning is introduced. All these theoretical parts are accompanied by code examples in R, where an example dataset on heart disease is used throughout the chapter.

Marvin N. Wright, Lukas Burk, Pegah Golchian +3

Leibniz Institute for Prevention Research and Epidemiology - BIPS, Bremen, Germany · University of Bremen, Germany · University of Copenhagen, Denmark

Supervised Learning

Dec 15, 2025

Machine learning Majorana topology using unsupervised and supervised learning

In unsupervised learning, the training data for deep learning does not come with any labels, thus forcing the algorithm to discover hidden patterns in the data for discerning useful information. This, in principle, could be a powerful tool in identifying topological order since topology does not always manifest in obvious physical ways (e.g., topological superconductivity) for its decisive confirmation. The problem, however, is that unsupervised learning is a difficult challenge, necessitating huge computing resources, which may not always work. In the current work, we combine unsupervised and supervised learning to establish that unlabeled (simulated) data in the Majorana splitting in realistic short disordered nanowires may enable not only a distinction between topological' and trivial', but also where their crossover happens in the relevant parameter space. This may be a useful tool in identifying topology in experimental Majorana nanowires.

Jacob Taylor, Haining Pan, Sankar Das Sarma

Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA · Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, NJ 08854, USA

Unsupervised Learning Supervised Learning

Jun 28, 2024

Pairwise Difference Learning for Classification

Pairwise difference learning (PDL) has recently been introduced as a new meta-learning technique for regression. Instead of learning a mapping from instances to outcomes in the standard way, the key idea is to learn a function that takes two instances as input and predicts the difference between the respective outcomes. Given a function of this kind, predictions for a query instance are derived from every training example and then averaged. This paper extends PDL toward the task of classification and proposes a meta-learning technique for inducing a PDL classifier by solving a suitably defined (binary) classification problem on a paired version of the original training data. We analyze the performance of the PDL classifier in a large-scale empirical study and find that it outperforms state-of-the-art methods in terms of prediction performance. Last but not least, we provide an easy-to-use and publicly available implementation of PDL in a Python package.

Mohamed Karim Belaid, Maximilian Rabus, Eyke Hüllermeier

IDIADA Fahrzeugtechnik GmbH, Munich, Germany · Dr. Ing. h.c. F. Porsche AG Stuttgart, Germany · Ludwig-Maximilians-Universität Munich, Germany

Classification Meta-Learning Supervised Learning Binary Classification

Jun 24, 2022

How many labelers do you have? A closer look at gold-standard labels

The construction of most supervised learning datasets revolves around collecting multiple labels for each instance, then aggregating the labels to form a type of "true" label. We question the wisdom of this pipeline by developing a (stylized) theoretical model of this process and analyzing its statistical consequences, showing how access to non-aggregated label information can make training well-calibrated models more feasible than it is with cleaned labels. The entire story, however, is subtle, and the contrasts between aggregated and fuller label information depend on the particulars of the problem, where estimators that use aggregated information exhibit robust but slower rates of convergence, while estimators that can effectively leverage all labels converge more quickly if they have fidelity to (or can learn) the true labeling process. The theory makes several predictions for real-world datasets, including when non-aggregate labels should improve learning performance, which we test to corroborate the validity of our predictions.

Chen Cheng, Hilal Asi, John Duchi

Department of Statistics, Stanford University · Department of Electrical Engineering, Stanford University · Departments of Statistics and Electrical Engineering, Stanford University

Model Calibration Noisy-Label Learning Dataset Aggregation Statistical Learning Theory Supervised Learning