Knowledge distillation trains a small student model to reproduce the outputs of a large teacher model, and its progress is typically monitored through the teacher--student discrepancy. The quantity of ultimate interest, however, is the student's error with respect to the true task. We study the relation between these two objectives in a minimal three-party model, a true teacher (generative model), a teacher, and a student, all soft committee machines, in which the true teacher contains a shared latent factor that the teacher cannot represent, with mismatch strength controlled by a single scalar $\dmiss$. Within an order-parameter description of online distillation, and exploiting closed-form (arcsine-type) expressions for all errors under error-function activations, we prove that the learning dynamics and the distillation error $\Ets$ are exactly invariant to $\dmiss$, whereas the true error $\Etzs$ and the gap $Δ=\Etzs-\Ets$ are strictly increasing in $\dmiss$, with a rate that is amplified linearly by the complexity $M_0$ of the true teacher. Numerical phase diagrams over the plane spanned by true-teacher complexity and student capacity confirm the predicted deformation: the contours of $\Ets$ do not move while the landscape of $\Etzs$ rises systematically, and a teacher-miss regime, where mimicry succeeds but the task fails, expands with $\dmiss$. The results give a quantitative warning against evaluating distillation solely through teacher-mimicry metrics and identify the gap $Δ$ as a minimal diagnostic for distinguishing teacher-miss from capacity-limited failure.
Qi Qin, Jiajie Zhu, Dali Chen +6cs.LG stat.ME stat.ML
Tabular foundation models (TFMs) achieve strong performance through in-context learning, but context-dependent inference imposes substantial latency and memory costs, hindering large-scale deployment. We propose GEAR (\emph{Generative Expansion and Real Anchoring}), a modular two-stage framework that distills TFMs into lightweight MLP or tree-based predictors that can be deployed on commodity CPUs. Stage 1 uses synthetic covariates solely as teacher-query locations and trains the student on soft TFM targets, expanding coverage beyond observed rows. Stage 2 re-anchors the student to the target distribution using real labels and out-of-fold teacher predictions, whitch avoids self-labeling leakage. We further derive a risk certificate characterizing the trade-off between generated-query volume and generator fidelity. Experiments on TALENT and TabArena demonstrate the broad applicability of GEAR. Two-stage MLPs outperform supervised MLPs by 1.81--2.00 AUC points on binary tasks and 1.19--1.35 points on multiclass tasks, with additional gains over real-data-only distillation of 1.76--2.19 and 2.09--2.40 points, respectively. On binary tasks, the gains also transfer to LightGBM and XGBoost, and all three student families outperform CatBoost, the strongest non-TFM baseline, in mean AUC. Ablations show gains beyond longer training or alternative warm starts, greater stability from staged than mixed optimization, and generator-dependent diminishing returns as query volume increases. Finally, GEAR reduces median inference time by 57--2866 times and peak prediction memory by 1.9--3.3 times, while retaining higher AUC than matched supervised baselines.
Federated learning (FL) enables collaborative learning over decentralized data silos without centralizing raw data. However, heterogeneous local architectures often induce non-aligned representation spaces, making it difficult to transfer global knowledge across silos. Existing paradigms share this knowledge as model parameters, distilled predictions, or class prototypes, yet all encode it in an absolute space that must be aligned across clients. Heterogeneous backbones break this alignment, so the shared knowledge becomes unreliable and misleads local training. We propose FedTopo, a relation-level framework that encodes global knowledge as class relation topology, capturing how classes relate within each client rather than where they lie in feature space. Each client builds its relation topology from local prototypes and uploads it with class statistics. The server then aggregates these relations in a reliability-aware manner that down-weights weakly supported ones, and broadcasts the global topology to clients. The global topology guides local training by emphasizing topology-similar negative classes. Experiments on three datasets under eight heterogeneous backbones show that FedTopo consistently outperforms parameter-, distillation-, and prototype-sharing baselines, with low communication and no inference overhead. Our code is available at https://github.com/Zhaoyang-Ma/FedTopo.
Hien Dang, Pratik Patil, Alessandro Rinaldomath.ST cs.LG stat.ML
Self-distillation (SD) is typically studied when the student is retrained on the teacher's original training inputs. In many practical deployments, however, the labeled training data are no longer available, and one has access only to the trained predictor and fresh unlabeled covariates. We study SD in this prediction-only regime through a fresh-X prediction-mixed scheme: a pure-distilled student is trained on fresh covariates pseudo-labeled by the teacher, and the final predictor is an affine combination of the teacher and student predictions. For ridge regression under proportional asymptotics, we derive deterministic equivalents for the optimally mixed prediction risk under general anisotropic covariance and deterministic signal. We show that this risk is strictly smaller than the teacher risk for almost every pair of teacher and student regularization levels, including when the fresh covariates are out-of-distribution and even when their covariance is isotropic. We further show that the optimal mixing weight cannot be identified from unlabeled data alone, but can be consistently estimated in a single post-training step using a small independent labeled calibration set, without additional model fitting. Finally, for binary logistic regression, we show that prediction mixing can outperform both the teacher and the pure-distilled classifier.
As machine learning models and datasets continue to grow, developing complex models has become increasingly computationally demanding. Knowledge distillation reduces deployment cost by compressing a large, well-trained teacher model into a compact student model, but it does not address settings where constructing the teacher itself is the bottleneck. Motivated by this challenge, we introduce Knowledge Cascade (KCas), a reverse knowledge distillation framework that uses information from a small, inexpensive student model to guide the development of a more complex teacher model. Although this direction is counterintuitive because the teacher typically has greater representational capacity, we show that student-to-teacher transfer can be principled when supported by statistical scaling relationships. We first develop KCas for nonparametric multivariate functional estimation in reproducing kernel Hilbert spaces via smoothing splines, where selecting multiple smoothing parameters is a major computational bottleneck. KCas transfers student-selected smoothing parameters to the full-sample regime through asymptotic scaling laws, substantially reducing computational cost for high-dimensional and large-scale datasets while retaining theoretical guarantees. Beyond smoothing splines, we illustrate the same principle through kernel density estimation and deep learning hyperparameter transfer. Simulations and real-data experiments show that KCas achieves substantial computational savings while maintaining strong statistical performance, and can sometimes outperform the corresponding full-sample procedure.
Knowledge Distillation (KD) is a powerful tool for model compression, yet the precise mechanisms by which student models acquire feature representations remain underexplored. In this work, we analyze student feature learning using the Interaction Tensor framework. Our analysis reveals that effective KD acts as a regularizer that prunes low-frequency, sample-specific features, encouraging the student to rely on a compact set of highly reusable features. Crucially, we observe that the dataset-level confusion matrix contains structural information analogous to the teacher's "Dark Knowledge." Leveraging this insight, we propose Confusion Distillation (CD), a teacher-free self-distillation method that utilizes the model's own evolving )confusion patterns as dynamic soft targets. CD achieves competitive performance on ResNet-34 and ResNet-50 for CIFAR-100, outperforming existing self-distillation methods like CS-KD and PS-KD by 1.2% while offering a computationally efficient alternative to standard KD.
Mohammad Jafari Jozani, Bahram Moeinianfarstat.ML cs.LG math.ST stat.ME
Support vector machines (SVMs) are a standard tool for binary classification, but their classical formulations are purely data-driven and offer no direct way to encode trusted benchmark models or structured preferences on selected subsets of the data. We propose Elite-Driven Support Vector Machines (EDSVM), a general framework that augments regularized empirical risk minimization by guiding the slack variables for a curated set of elite observations (typically the union of support vectors from one or more reference SVMs). EDSVM combines the usual slack loss with a deviation penalty that shrinks new slacks toward benchmark slack values, defining a localized, margin-aligned notion of proximity to reference models, unlike global function penalties in knowledge distillation or teacher-student methods, and without requiring privileged features as in SVM+/LUPI. Within this framework we develop two concrete models, C-EDSVM and LS-EDSVM, based respectively on hinge-type and squared-slack losses. For both variants we derive dual quadratic programs that can be implemented with modest modifications of standard SVM solvers, and we give simple sufficient conditions under which the induced margin losses are classification calibrated. Simulation studies and experiments on several UCI benchmarks show that EDSVMs closely track the behaviour induced by reference SVMs while achieving predictive performance that is competitive with, and sometimes better than, C-SVM, LINEX-SVM, and LS-SVM.