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 \emph{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 \emph{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.
We introduce Bernstein-Vazirani Networks (BVNs), a non-variational quantum machine learning framework that leverages quantum interference for supervised learning, demonstrated on vision and representation learning tasks. In their standard form, BVNs follow the principle of quantum Fourier sampling: labelled data are placed in superposition and interfered in the Fourier basis to extract globally informative features. We then define generalised BVNs that enable interference in problem-adapted bases, yielding more expressive models under the same measurement budget as in the standard setting. BVNs achieve universal function approximation through (over)complete interference bases, while training of BVNs is gradient-free. Experiments on synthetic and real-world classification tasks, as well as implicit image representation, show strong generalisation capabilities and competitive performance with classical and quantum baselines.
Objectives: To determine whether zero-shot prompting of a large language model (LLM) is sufficient to detect shared decision-making (SDM) behaviors in real clinical encounters, and whether supervised learning adds value under patient-grouped, nested evaluation. Methods: We analyzed 21 audio-recorded outpatient surgical decision encounters (19 unique patients; 7,566 utterance segments; ~6.1 hours) between families of children with multiple long-term conditions and their surgical providers. Trained coders labeled segments for 12 SDM behaviors (human-human macro Cohen's kappa = 0.695). We compared a zero-shot local LLM (Qwen 2.5 32B), a supervised classifier over frozen sentence embeddings, and their logistic stack, under patient-grouped outer folds with inner cross-fitted thresholds and patient-resampled confidence intervals. Results: The zero-shot LLM reached macro kappa = 0.139 (95% CI 0.111-0.164). The supervised classifier reached kappa = 0.227 (0.186-0.262), a paired improvement of 0.088 (0.051-0.119). A logistic stack of the two reached kappa = 0.242 (0.198-0.284). We identified multiple corpus-specific leakage paths, including grouping sibling recordings separately and allowing labels from an outer held-out patient to enter few-shot exemplars used while fitting downstream models. Conclusion: Zero-shot prompting alone is not sufficient to measure SDM behavior as reliably as a small supervised model, and patient-level grouping alone does not prevent leakage when labeled prompt exemplars are precomputed outside the outer evaluation loop. Reported performance is sensitive to the unit of data splitting and to where labeled exemplars enter the pipeline. External validation is needed before these findings generalize beyond this population, model, prompt, and codebook.
Fiber tractography's ability to reconstruct the brain's structural pathways, has made it a crucial component of modern neuroimaging, enabling detailed, non-invasive mapping of structural connectivity and supporting a wide range of neurological research and clinical applications. However, despite its importance, tractography remains a challenging task due to the inherent complexity of white matter structure and its susceptibility to false positives, which can lead to the misrepresentation of critical pathways. To overcome these limitations, in this thesis, we propose a hybrid framework that integrates reinforcement learning with supervised learning for refining RL policies, specifically tailored for tract-specific tractography. Notably, our framework does not rely on ground-truth fibers for training. Moreover, the tract-specific formulation bypasses the need for an explicit segmentation process, simplifying the overall pipeline. Our work includes two main contributions, each building upon the previous. First, we introduce a hybrid approach that combines reinforcement learning with supervised learning (specifically, GPT-based policy learning) to refine policies in a tract-specific context. Second, we propose a scalable framework for data-driven multi-policy fusion, which leverages the complementary strengths of multiple RL policies to improve tractography performance and robustness. We demonstrate the effectiveness of our framework through extensive validation on benchmark public datasets including TractoInferno, HCP, and ISMRM-2015, highlighting its ability to generalize across data sources and accurately reconstruct brain white matter tracts. We believe that these contributions represent significant advancements in the field of tractography, improving robustness, reliability, and accuracy while reducing dependence on ground-truth annotations.
Harmful chat dialogues are ever-shifting through type-shifting and lexical evasion, yet we find they share invariant principles, i.e., an Ordered Reasoning Chain (ORC) of recurring topics, harm language indicators, severity hierarchies, and type characteristics, which can help us capture the key information in the frequently changing lexical expressions. We propose BRACE, which encodes the ORC as four differentiable stages (Topic -> Indicator -> Severity -> Type) with intermediate supervision, serving as a structured regularizer blended with direct heads, and supported by prototype-based feature augmentation and feature path disentanglement. The evaluation results show that, across 4 domains and 5 harm categories, BRACE achieves harm-type macro F1 of 0.934 (RoBERTa-wwm-ext, 3-seed mean), with decoder backbones (Qwen3-1.7B LoRA) reaching 0.949. Ablation studies show that all components contribute to BRACE, and the structural decomposition of ORC enables BRACE to distinguish harmful types with semantic ambiguity. Disclaimer: This paper may contain content that is disturbing to some readers.
Sagnik Nandy, Samriddha Lahiry, Pragya Sur +1stat.ME cs.LG math.ST stat.ML
Multimodal supervised learning seeks to leverage multiple heterogeneous data sources to improve predictive performance. A central challenge is determining the fusion granularity across modalities: over-integration may amplify noise while under-integration fails to exploit cross-modal dependence. Existing approaches rely on pre-specified fusion architectures, from early to late fusion, that may not adapt to the underlying dependence structure among modalities. We propose DAIF, a data adaptive intermediate fusion framework that combines random matrix theory and non-parametric dependence measures to learn fusion structure directly from data. We operate under a Bayesian multimodal factor model where the prior on the latent factors determines the cross-modal dependence. Our method clusters modalities based on estimated intermodal dependence, then performs clusterwise empirical Bayes estimation of the priors. These estimated priors are used to construct denoisers within an approximate message passing (AMP) framework, yielding denoised low-dimensional features that borrow strength across related modalities while preserving modality-specific signal. The resulting embeddings are used for downstream supervised prediction. We evaluate the framework through simulations under varying dependence structures and signal regimes, comparing against several benchmark methods, and demonstrate its practical utility on two multimodal datasets, namely a trimodal TEA-seq dataset (Swanson et al., 2021) and TCGA-BRCA dataset (Goldman et al., 2020). In the first example, we predict the expression level of a T-cell differentiation marker protein and in the second case we analyze patient survival prediction based on multimodal information. Our method competes with or outperforms the state-of-the-art techniques in both prediction problems, demonstrating its versatility across diverse supervised learning tasks.
Humans often find good solutions to combinatorial optimization problems that are computationally hard even for advanced computer algorithms. In the Euclidean traveling salesman problems (TSP), people rapidly produce tours that are near-optimal, despite severe limits on time and computation. What makes a tour human-like, and how might such solutions be learned? Here we address these questions through a large-scale behavioral and computational investigation of human performance in Euclidean TSP. We sampled a broad space of TSP instances, collected human solutions, and compared them with neural policies based on Pointer Networks, which are recurrent neural networks with an attention-based pointing mechanism that define probability distributions over valid tours. We trained these networks under multiple objectives, including reinforcement learning (RL), supervised learning from optimal tours, supervised learning from human tours, and RL fine-tuning after optimal-supervised pretraining. Human tours were not identical to optimal tours, but occupied a near-optimal geometric basin: they shared many structural properties with optimal solutions while preserving systematic human-specific deviations. The best account of human tours was not direct imitation of optimal tours, but a model pretrained on optimal tours, fine-tuned by RL, and decoded through $\text{Best-of-}N$ sampling. These findings suggest that human-like solutions may emerge from a combination of structured supervised learning, RL, and test-time search, echoing computational principles underlying many modern artificial intelligence systems.
Financial sentiment extraction has largely relied on news text and supervised extraction against return labels alone, leaving 10-K filings -- and volatility, the target risk disclosure is arguably best suited to informing -- comparatively unexplored. We extend a supervised lexicon-learning approach to 10-K filings and their Item 1A risk-factor sections, training sentiment scores against both return and volatility labels at three levels of aggregation: sector, portfolio, and individual firm. Across 1,383 filings from 94 Nasdaq-100 technology constituents (2006--2023), we evaluate the resulting twelve sentiment metrics on classification accuracy, correlation with realised market outcomes, and qualitative lexical content. Full-filing text produces more accurate sentiment at the sector and portfolio level for both targets, but this reverses at the individual-firm level, where the narrower Item 1A section performs better -- an effect we attribute to the interaction between document volume and the amount of independent training signal available at each level of aggregation. A Loughran-McDonald dictionary baseline is consistently, strongly negatively correlated with price at every level tested, underscoring the value of a supervised approach for regulatory disclosure text. These findings, and the design choices they motivate, establish the sentiment-generation methodology underlying a subsequent, larger-scale, multi-source system.
Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.
We introduce Intrinsic Green's Learning (IGL), a framework that models a target function on a manifold as the solution to a linear PDE whose source term is learned from data. Rather than approximating the target directly, IGL learns a source and integrates it against a Green's kernel. An encoder discovers a low-dimensional coordinate chart on the manifold where both the source and the kernel decompose as low-rank tensors, collapsing a high-dimensional integral into independent one-dimensional integrals with cost linear in the intrinsic dimension. A two-stage algorithm separates coordinate discovery from source fitting, a near-convex linear solve, preventing the dimensional collapse of joint training. Learnable gates on each coordinate automatically discover the intrinsic dimension of the manifold. We validate IGL on synthetic manifolds and on MNIST, where it simultaneously achieves near-optimal classification and automatic recovery of the intrinsic dimension.
Quantum computing has emerged as a promising computational paradigm for machine learning (ML), with the potential to offer computational advantages over classical approaches. At this stage, the evidence supporting the performance and advantages of quantum machine learning (QML) models relative to classical models is insufficient.To address this gap, this paper presents an empirical study on the performance of QML models and their classical counterparts. We compare seven model pairs spanning supervised learning and reinforcement learning. Our results indicate that the evaluated quantum machine learning models do not yet surpass the classical baselines in overall prediction performance, policy stability, or training time. Nevertheless, QML remains a promising approach for filtering noise and controlling false positives. Our research findings summarize the challenges facing quantum machine learning across hardware environments, training efficiency, and convergence stability, providing a foundation for research into the robustness and parameter optimization of QML. This work is publicly available at https://github.com/Z-537-437/QML.
In this paper, we formulate a new vehicle dispatch optimization problem, called Nursing Care Taxi Dispatch, as a variant of the Vehicle Routing Problem, considering constraints related to wheelchair use, user compatibility, pick-up and drop-off times, and vehicle limitations. Previous neural-based methods for Vehicle Routing Problems have typically addressed a few simple constraints, while our new problem involves multiple complex constraints, resulting in having fewer destinations to select. This complexity makes it more difficult to obtain solutions that allow all nodes to be visited with a limited number of vehicles. To balance low violation rate, computational efficiency, and solution quality, we propose a supervised machine learning approach based on the Transformer architecture. We first obtain a set of high-quality solutions using an integer linear programming solver for given inputs and then train our learning model through supervised learning. Additionally, we introduce the post-processing of the paths generated by the learning model, ensuring that all constraints are satisfied. We compared each instance's objective function value (operating time), execution time, and constraint violation rate across different methods: our proposed method and some existing methods including integer linear programming and machine learning-based methods, using real-world facility data. Our method successfully produced balanced solutions regarding operating time, execution time, and constraint violation rate. Notably, we observed a decrease in the operating time for all problem sizes and regions, while keeping constraint violations to a minimum compared to existing methods. Especially, the decrease reached up to 8% for problem sizes with fewer than 30 users.
Julio González-Díaz, Beatriz Pateiro-López, Iria Rodríguez-Acevedocs.LG stat.ME stat.ML
Minimum Spanning Trees have been used in unsupervised learning, particularly in clustering tasks, due to their ability to recognize clusters by removing edges that are considered inconsistent in defining those clusters. This paper aims to study the use of Minimum Spanning Trees in supervised learning. Specifically, we propose a classification algorithm based on Minimum Spanning Trees. To improve its performance, we introduce a robust version of the method that is also computationally more efficient. We evaluate the effectiveness of our proposed method through an extensive simulation study. We also apply the proposed methodology to a real-world case study involving aircraft trajectories.
Representation learning is often described as preserving the information in an input that is relevant for prediction. This work asks what relevance means for a fixed supervised decision problem. A representation is defined to be Bayes-sufficient for a joint distribution and loss if some prediction head can use it to implement a Bayes-optimal action rule. This makes the target information loss-dependent. In the almost-surely unique Bayes-action case, the relevant object is a Bayes quotient, which identifies inputs that require the same Bayes-optimal action. A representation is sufficient when it refines this quotient, and Bayes-minimal when it is informationally equivalent to it. The framework connects naturally to property elicitation: zero-one loss requires the Bayes class, squared loss the conditional mean, Brier loss the conditional probability in binary prediction, and log loss or strictly proper scoring rules the predictive distribution. Controlled finite experiments, learned neural bottleneck experiments, and a real-data iNaturalist taxonomic refinement experiment illustrate the distinction between sufficiency, minimality, and retained non-required information. For a fixed supervised problem, the distribution and the loss determine the Bayes action, the Bayes action determines the quotient, and the quotient determines the minimal information required for Bayes-optimal prediction.