Relabeling Module in ML Systems

Updated 1 December 2025

Relabeling Module is an algorithmic component that systematically updates labels using methods like random, optimization-driven, and adversarial strategies.
It is applied in diverse areas such as model unlearning, active learning, and reinforcement learning to improve annotation, scalability, and computational efficiency.
The module provides formal guarantees—including differential privacy, structural invariance, and statistical robustness—that ensure reliable and unbiased label transformations.

A relabeling module is an algorithmic component designed to update, refine, or reassign categorical labels within a computational process. Such modules play central roles in diverse areas including data annotation, model unlearning, active learning, reinforcement learning, graph rewriting, distributed systems, and Bayesian inference. The principal function of a relabeling module is to transform the current assignment of labels—either to data points, nodes, processes, or latent variables—by a mechanism that is systematically defined, often with formal mathematical guarantees, computational efficiency, or preserving key invariances.

1. Core Mechanisms and Theoretical Principles

Relabeling modules are characterized by explicit mechanisms for label transformation—these mechanisms may be random, adversarial, optimization-driven, categorical, or structurally defined. The mathematical principles include:

Random Complementary Labeling: For efficient machine unlearning, random relabeling counteracts the memorization of a data point $(x_i,y_i)$ by generating a minibatch of $k'$ synthetic samples $(x_i,\tilde{y})$ with $\tilde{y} \in \mathcal{Y}\setminus\{y_i\}$ , updating model parameters to erase targeted influence. A single or a limited number of gradient steps with these labels achieves “unlearning” in $O(1)$ time per deletion and a statistical fidelity guarantee based on a differential-privacy-style bound (Li et al., 2023).
Optimization-driven Relabeling: In monotonic classification, relabeling solves the constrained optimization

$\min_{\hat{Y}}\ \|Y - \hat{Y}\|_0 \quad \text{subject to monotonicity constraints}$

using flow-based or graph-theoretic methods, ensuring minimal modification that enforces required label orderings (Cano et al., 2018).

Adversarial/Uncertainty-based Relabeling: In active learning, state relabeling assigns continuous “uncertainty” labels to samples according to classifier output distribution, guiding sample selection by adversarial training with a generator-discriminator architecture (Zhang et al., 2020).
Utility-based Relabeling in RL: For multi-task or meta-reinforcement learning, relabeling reassigns trajectories to alternate tasks or reward functions based on a maximized expected “utility” (usually future return after policy adaptation), inducing a posterior data-sharing scheme that matches the meta-learning objective (Wan et al., 2021).
Soft-label Generation via Teacher Models: In dataset distillation with long-tailed data, relabeling assigns to each synthetic sample a soft label computed as the output of a frozen robust teacher network, after special debiasing and statistical alignment steps to guarantee supervision is unbiased (Cui et al., 24 Nov 2025).

These modules are defined not as arbitrary label changes, but as rigorously specified map(s) $R$ (possibly stochastic or data/history dependent) that transform the label structure of model-internal or data-external entities under clear algorithmic constraints.

2. Formal Algorithms and Computational Properties

Relabeling modules are typically presented via explicit pseudocode, recurrence, or matrix operations reflecting their computational integration in broader pipelines:

Random Relabeling for Unlearning (Supervised learning):

# Given deletion request (x_i, y_i)
k_prime = k - 1
fake_labels = sample_uniform(Y \ {y_i}, k_prime)
mini_batch = [(x_i, y) for y in fake_labels]
g = (1/k_prime) * sum(grad_loss(f_theta(x), y) for (x, y) in mini_batch)
theta_new = theta - eta * g

Complexity:

O(k-1)

per deletion, where

k

is the number of classes (Li et al., 2023).

Weisfeiler-Lehman Relabeling in Graph Alignment:

Iterative dispatch of anchor labels via matrix propagation, followed by mutual-best similarity hashing between two graphs, converging in a small number of iterations; per-step complexity is $O(|E|\cdot|C_a|)$ (Liu et al., 2022).

Relabel-to-flip in Classification:

Use influence functions to estimate the gradient effect of label flips; greedily select a minimal training subset whose relabeling flips a model’s prediction on a given test point.

$\text{For }i = 1, \ldots, N:\quad s_i = -\frac{1}{N}\,g_t^\top H^{-1}\delta\ell_i$

Sort $s_i$ and accumulate until the prediction changes (Yang et al., 2023). Per-test complexity $O(p^3 + Np^2)$ .

Process Relabeling for Distributed Shuffle/Transpose:

Find a permutation $\sigma \in S_n$ —via maximum-weight bipartite matching—so as to minimize communication volume in data shuffling; the relabeling gain matrix $W_{ij}$ quantifies the cost-benefit of reassigning process ranks (Kabić et al., 2021). Complexity: $O(n^3)$ for matching; practical for moderate $n$ .

Prompt Relabeling for Diffusion Alignment:

On each batch, inspector modules compare object/relationship extraction between text and sampled images; if inconsistent, prompts are formally relabeled to the detected contents and the model is fine-tuned using rescaled loss for consistent and relabeled samples, controlling learning signal strength (Chen et al., 2023).

3. Integration Patterns and Application Contexts

Relabeling modules appear across numerous subfields, each with domain-adapted mechanisms:

Data Privacy and Model Unlearning: Efficiently erasing specific data influence by local (constant-time) parameter updates rather than global retraining (Li et al., 2023).
Active and Semi-supervised Learning: Enhancing sample selection by uncertainty relabeling, refining divisions between labeled and unlabeled data (Zhang et al., 2020).
Policy Learning and Reinforcement Learning: Generating new training instructions, tasks, or subgoals—either from successful/failed behaviors (LLM-guided relabeling, hindsight/foresight utility), or via sequence summarization/chaining (as with SPRINT), to densify supervisory signals and accelerate curriculum learning (Zhang et al., 24 Jun 2025, Zhang et al., 2023, Wan et al., 2021, Singh et al., 2023).
Graph-based Learning: Weisfeiler–Lehman relabeling for node/graph alignment, propagating anchor-derived fingerprints to create shared hash labels for cross-graph regularization (Liu et al., 2022); lattice-based relabeling for categorical graph rewriting with PBPO+ (Overbeek et al., 2020).
Dataset Construction/Distillation: Soft relabeling using robust teacher outputs for distilled images to correct for distributional skew, especially under extreme class imbalance (Cui et al., 24 Nov 2025).
Mixture Models (Bayesian Inference): Relabeling of latent variables to overcome label-switching, most simply via pivotal units that anchor clusters for coherent posterior summarization (Egidi et al., 2015).
Pseudo-label Refinement in Large-scale Supervision: Dynamic offline refinement and merging of tracker-based pseudo-labels in person re-identification, removing, hard-relabelling, or merging identity assignments for noise suppression at scale (Mamedov et al., 24 Nov 2025).
Annotation Systems: Human-in-the-loop relabeling modules that enable experts to efficiently enact batch, subgroup, or per-record modifications, with formal operational logging, as in LabelVizier for technical text (Zhang et al., 2023).
Monotonic Classification: Relabeling as a key preprocessing step to enforce monotonicity constraints via minimal label modifications, implemented as graph algorithms or consensus-driven iterative noise filtering (Cano et al., 2018).

4. Guarantees, Invariances, and Theoretical Insights

Relabeling modules often formalize and guarantee:

Fidelity to Target Constraints: Differential-privacy-style closeness bounds to the naively “correct” retrained system (Li et al., 2023), task-reachable utility maximization (Wan et al., 2021), or monotonicity enforcement (Cano et al., 2018).
Computational and Communication Optimality: Achieved or approximated via mapping optimality (process relabeling), minimal-deletion sets (influence-based flipping), or matching-based assignments (Kabić et al., 2021, Yang et al., 2023).
Statistical Robustness & Unbiasedness: E.g., unbiased soft relabeling in dataset distillation leverages a debiased teacher and BN-aligned recovery to avoid head-class collapse (Cui et al., 24 Nov 2025), or soft relabeling via generative models in mixup for manifold-intrusion resolution (Sohn et al., 2022).
Structural Preservation: Lattice-based relabeling in graph rewriting guarantees monotonic meets/joins and order-preservation, ensuring that application of a rule is well-posed for all morphisms (Overbeek et al., 2020).
Convergence Properties: Control over the effect of relabeling (e.g., variance reduction in mixing times, as in card shuffling (Jonasson, 2015)), convergence to label-consistent posteriors in MCMC (Egidi et al., 2015), or monotonicity/accuracy tradeoffs in noisy ordinal classification (Cano et al., 2018).

5. Empirical and Application-driven Performance

Empirical assessment of relabeling modules often includes:

Online/Incremental Efficiency: Random relabeling for unlearning processes hundreds of deletions on MNIST in less than $1\%$ the time of naively retraining, with nearly identical accuracy for small $m$ and $>96\%$ for $m=600$ (Li et al., 2023).
Improved Robustness and Accuracy: Generative relabeling in mixup (GenLabel) boosts accuracy across openML tasks and increases adversarial robustness against FGSM (Sohn et al., 2022); state relabeling improves active-learning sample efficiency and segmentation mIoU over VAAL (Zhang et al., 2020).
Annotation Quality and Scalability: Expert-in-the-loop relabeling workflows process thousands of text annotation errors interactively, with industry-scale throughput (Zhang et al., 2023).
Label Noise and Structure Correction: Dynamic relabeling and PID consolidation in person re-ID refines vast pseudo-labeled datasets, removing up to $7.4\%$ of images and $16\%$ of IDs per epoch for downstream performance gain (Mamedov et al., 24 Nov 2025).
Cross-domain and Cross-graph Alignment: WL relabeling enables exact matching in graph alignment, propagating anchor connectivity for combinatorial supervision across domains (Liu et al., 2022).
Datasets with Extreme Imbalance: Soft relabeling, in concert with unbiased recovery, lifts performance on low-IPC long-tailed distillation tasks by 10–20 points compared to hard labeling (Cui et al., 24 Nov 2025).

6. Limitations, Assumptions, and Extensions

Relabeling modules, despite their advantages, may be constrained by:

Statistical Assumptions: Efficacy depends on the accuracy of generative models (for posterior-based or density-based relabeling in mixup), the existence of well-separated pivotal units (Bayesian mixtures), or the monotonicity of class/feature relationships (Egidi et al., 2015, Sohn et al., 2022, Cano et al., 2018).
Potential for Overcorrection: Aggressive relabeling (e.g., in monotonic classification) may compromise predictive accuracy if too much data is altered to enforce labeling structure (Cano et al., 2018).
Algorithmic Simplicity vs. Optimality: Heuristic or greedy relabeling (e.g., minimal subset flip) typically does not guarantee global optimal solutions but achieves practical tractability (Yang et al., 2023).
Computational Overheads: Graph-theoretic or matching-based modules can be cubic in the problem size, although sparsity or mini-batch techniques often mitigate this (Kabić et al., 2021, Liu et al., 2022).
Coverage and Diversity: Coverage-based relabeling in RL and distillation (e.g., SPRINT, long-tailed distillation) needs careful hyperparameter tuning to achieve optimal expansion without semantic drift (Zhang et al., 2023, Cui et al., 24 Nov 2025).
Dependence on Exogenous Models: Some approaches require strong teacher or detector models (as in BN-recalibrated distillation or classifier-feedback-based relabeling in diffusion) to generate meaningful targets, possibly introducing bottlenecks or bias if teacher reliability is compromised (Chen et al., 2023, Cui et al., 24 Nov 2025).

In sum, relabeling modules provide mathematically rigorous, computationally practical, and empirically validated operations for the re-assignment of labels in a wide array of machine learning, statistical, and systems settings. They are central primitives in privacy-preserving updates, active learning, data annotation, representation refinement, and post-processing for both supervised and unsupervised regimes. Contemporary research directions focus on adaptive, context-aware, and theoretically certified relabeling mechanisms that ensure scalability, fairness, and robust out-of-distribution generalization.