Learning-from-the-Undesirable (LfU)

• Learning-from-the-Undesirable (LfU) is a paradigm that leverages negative data—such as harmful predictions or erroneous behaviors—to inform unlearning, improve safety, and enhance model robustness.
• It employs techniques like gradient ascent, negative preference optimization, and robust feature suppression to actively counteract undesirable influences in training data.
• Empirical findings suggest LfU can significantly reduce overfitting and improve privacy and safety, achieving high levels of utility retention even when forgetting up to 90% of problematic patterns.

Learning-from-the-Undesirable (LfU) refers to a class of learning paradigms, algorithms, and regularization techniques that leverage information about "undesirable" data, behaviors, or outcomes—such as harmful model predictions, negative demonstrations, or undesirable internal updates—to steer model learning. The core theme is to not simply ignore or mask such negatives, but to explicitly use them as a source of information: to drive forgetting, enhance robustness, prevent overfitting, or support safe and responsible decision-making. LfU is now a unifying principle across safe reinforcement learning, robust supervised learning, unlearning/privacy, imitation learning from mixed-quality data, and model alignment.

1. Conceptual Foundations and Scope

Learning-from-the-Undesirable encompasses objectives and workflows where undesirable elements—demonstrations, features, trajectories, internal model states, or documented real-world harms—inform how the learning process is shaped. LfU traces to multiple frontiers:

• Unlearning in deep models: Removing the influence of sensitive or harmful data from models, using negative labels, preference signals, or reward shaping—for privacy (e.g., data deletion requests), safety, or copyright compliance (Yao et al., 2023, Zhang et al., 8 Apr 2024, Yoon et al., 21 May 2025).
• Enhancing generalization and robustness: Penalizing model reliance on spurious, non-robust, or dataset-specific patterns by exposing and suppressing undesirable feature contributions, using out-of-distribution data (Lee et al., 2021), or adversarial representations (Nam et al., 17 Nov 2025, Mitchell et al., 4 Sep 2024).
• Safe/reliable RL and control: Learning from trajectories annotated as unsafe, hazardous, or policy-violating, either by modeling non-Markovian patterns of negative side effects (Low et al., 2023) or maximizing statistical distance from undesirable behaviors (Hoang et al., 10 Oct 2024).
• Offline imitation learning from mixed data: Simultaneous use of expert and explicitly undesirable demonstrations, optimizing objectives that attract policies to expert-like behavior while repelling them from negative patterns (Hoang et al., 27 May 2025).
• Retrospective analysis of real-world failures: Building catalogs of historical "undesirable consequences" to inform, constrain, and broaden design spaces in technology development (Pang et al., 10 May 2024).

The systems- and task-agnostic property of LfU is that undesirable examples are not just avoided but are used as positive information about what to unlearn, improve, or guard against.

2. LfU Paradigms in Modern Machine Learning

2.1 Model Unlearning and Alignment

In LLMs and large reasoning models (LRMs), LfU objectives are integral to scalable unlearning. Consider the general form of unlearning:

$$\min_\theta~ \mathcal{L}_\text{LfU}(\theta) = \text{Loss}_\text{retain} + \lambda\,\text{Loss}_\text{undesirable},$$

where Loss₍retain₎ maintains utility on "good" data, and Loss₍undesirable₎ explicitly suppresses undesirable content, features, or behaviors.

Gradient-based approaches perform ascent on the loss of the undesirable set (ℒ(x,θ) over a "forget set" $\mathcal{D}_f$), possibly regularized by a retain set $\mathcal{D}_r$ or model-level constraints. Preference-optimization variants structure the undesirable response space by, for instance, favoring explicit refusals (e.g., "I don’t know") with stepwise chain-of-thought masking and robust regularization (Yoon et al., 21 May 2025).

Negative Preference Optimization (NPO) introduces a bounded preference penalty to drive down the (relative) log probability of undesirable completions, effectively regularizing away catastrophic collapse and enabling massive-scale unlearning (Zhang et al., 8 Apr 2024).

2.2 Robust Representation Learning and Feature Suppression

LfU undergirds representation-level augmentation and regularization, particularly in low-resource and adversarially fragile regimes. The LfU regularization for SFT (supervised fine-tuning) aligns internal representations between a standard model and one exposed to an "undesirable" update (e.g., a one-step gradient-ascent induced overfitting direction), promoting flatness and robustness in feature space (Nam et al., 17 Nov 2025). This approach yields significant gains in generalization and robustness to prompt or domain shifts.

In the context of out-of-distribution (OOD)-augmented training, undesirable features—shared between in-domain and OOD samples but weakly correlated with ground truth—are penalized by casting the OOD examples (with uniform labels) as negative anchors. This pushes decision boundaries away from non-robust, spurious directions, securing both standard and adversarial generalization (Lee et al., 2021).

2.3 Safe RL and Temporal Negative Patterns

In RL, LfU methods leverage trajectory-level classification of undesirable side effects. Rather than per-step cost signals, a trajectory classifier (often a recurrent model) is trained to estimate the presence and class of negative outcomes. A constrained RL agent then maximizes reward subject to probabilistic bounds on different classes of negative side effects, implemented via Lagrangian primal-dual optimization and backpropagation through the classifier (Low et al., 2023).

3. Algorithmic Formulations and Workflows

3.1 LfU Objective Design

Across the literature, the choice and balance of objective terms are central. Example objectives include:

Paradigm	LfU Loss Structure	Key Elements
LLM Unlearning (Yao et al., 2023, Yoon et al., 21 May 2025)	$$-\text{CE}_{\mathcal{D}_f} + \text{KL}_{\mathcal{D}_r} + \text{template}$$	Negative log-likelihood on negatives; regularization
NPO (Zhang et al., 8 Apr 2024)	$$-(2/\beta) \mathbb{E}_{\mathcal{D}_{\text{bad}}}[\log(1+(\hat{p}_\theta/\hat{p}_{\text{ref}})^\beta)]$$	Bounded preference, adaptive weighting
RL from negative demonstrations (Hoang et al., 10 Oct 2024)	$\max_\pi D(\mu_\pi,\mu_u)$ via f-divergence	Distance from undesirable occupancy
Imitation from positive/negative (Hoang et al., 27 May 2025)	$$\min_{d^\pi} D_{\text{KL}}(d^\pi || d^G) - \alpha D_{\text{KL}}(d^\pi || d^B)$$	Convex, non-adversarial mixture
OOD-penalty feature suppression (Lee et al., 2021)	$$\mathbb{E}_{\text{OOD}}[\text{CE}(\hat{y}, \text{Uniform})]$$	Places OOD on decision boundary

3.2 Evaluation Metrics and Robustness

LfU frameworks introduce metrics to quantify both forgetting efficacy and retention of model utility. In reasoning models, this includes stepwise similarity (ROUGE, cosine, LLM-as-judge) at the chain-of-thought level and their harmonic mean (Chain-of-Thought Forget Efficacy, CFE) (Yoon et al., 21 May 2025). LLM unlearning work employs harmful/leak rate, diversity, fluency (PPL), and utility-reward/entailment on held-out data (Yao et al., 2023).

Robustness must be validated under alternative inference protocols, such as prompt manipulations or decoding suppression (ZeroThink, LessThink), as residual knowledge may leak under non-default generation (Yoon et al., 21 May 2025, Nam et al., 17 Nov 2025).

4. Empirical Insights and Key Results

LfU methods have demonstrated strong empirical performance and distinct failure modes:

• Preservation-utility trade-off: NPO and preference-optimization penalties achieve higher levels of forgetting without catastrophic collapse, surpassing standard gradient ascent-unlearning (Zhang et al., 8 Apr 2024, Yoon et al., 21 May 2025). For example, NPO+RT maintains >60% model utility even after forgetting up to 90% of data (Zhang et al., 8 Apr 2024).
• Enhanced generalization in low-data SFT: LfU regularization for representation consistency improves math accuracy by +16.8% over vanilla SFT, also reducing robustness variance to prompt templates by 92.1% (Nam et al., 17 Nov 2025).
• Group robustness without explicit labels: Parallel student-teacher models leveraging negative saliency transfer ("unlearning from experience") achieve worst-group accuracy comparable to or exceeding group-aware methods (Mitchell et al., 4 Sep 2024).
• Offline RL and imitation from mixed-quality data: Convex LfU objectives, such as the difference-of-KL (ContraDICE), stably outperform adversarial and discriminator-weighted baselines, particularly when a small number of high-quality positives and informative negatives are given (Hoang et al., 27 May 2025).

Failure modes identified include:

• Residual reasoning traces: Answer-only unlearning leaves chain-of-thought traces that can leak forgotten knowledge.
• Decoding circumvention: Suppressing chain-of-thought in decoding can reinstate previously "forgotten" facts, indicating that local modifications may not persist across generation modes (Yoon et al., 21 May 2025).
• Instability in unconstrained unlearning: Pure gradient ascent can drive models into trivial or unstable regions unless preference constraints or regularization are imposed (Zhang et al., 8 Apr 2024).

5. Representative Applications

Data Privacy and Right-to-be-Forgotten

Ticketed learning–unlearning schemes provide a practical LfU solution: each data example is endowed with a space-efficient cryptographic "ticket" at training, and a small central state suffices for exact ERM recalculation with deleted subsets, ensuring privacy and compliance without retraining or data retention (Ghazi et al., 2023).

Responsible Technology and Societal Impact

BLIP exemplifies LfU in system design: it curates summaries of real-world undesirable consequences, categorizes them via LLMs, and presents them at decision points in design, review, and ethics workflows. The process significantly increases the diversity and originality of identified negative consequences in user studies, operationalizing LfU as a cyclical feedback for technology development (Pang et al., 10 May 2024).

Safe Autonomous Control and RL

Temporal classifiers for negative side effects, margin-constrained RL, and Q-learning with negative demonstration avoidance instantiate LfU for policy learning, especially in risk- or safety-critical environments (Low et al., 2023, Hoang et al., 10 Oct 2024).

6. Limitations and Open Challenges

• Evaluation definitions: Unlearning success and LfU efficacy are task- and context-dependent; unified metrics are needed, especially to assess deep or non-local influence in complex models (Yao et al., 2023, Yoon et al., 21 May 2025).
• Stability and scalability: Naive or unconstrained negative updating (e.g., pure gradient ascent) risks catastrophic collapse; sophisticated bounding, preference penalties, or alternate formulations are necessary (Zhang et al., 8 Apr 2024).
• Dependence on negative data quality: LfU methods presume clean and relevant negative data (explicitly bad demonstrations, undesirable outcomes). Handling mislabeled or ambiguous negatives remains open (Hoang et al., 27 May 2025, Hoang et al., 10 Oct 2024).
• Generalizing to weak supervision: LfU in settings without exact negatives—either through OOD data with uncertain relation, or incomplete group labels—necessitates further mechanism design and theoretical guarantees (Lee et al., 2021, Mitchell et al., 4 Sep 2024).
• Computational overhead: LfU-based regularizations (especially with auxiliary parameter or feature perturbations) induce extra computation and memory cost, though variants can reduce this (Nam et al., 17 Nov 2025).

7. Theoretical and Practical Implications

Learning-from-the-Undesirable is now a key principle in the drive for robust, safe, and ethical machine learning:

• It offers a systematic methodology for both corrective action (unlearning, negative imitation) and proactive robustness (feature suppression, representation stability).
• Convex and cooperative algorithmic instantiations ensure the scalability and stability of LfU even in high-dimensional or nonconvex settings (Hoang et al., 27 May 2025, Hoang et al., 10 Oct 2024).
• In operational settings—privacy enforcement, safety assurance, broader-impact documentation—LfU translates theoretical rigor into deployable pipelines (Pang et al., 10 May 2024, Ghazi et al., 2023).
• Future research will likely focus on expanding LfU to partially observed negatives, compositional and multi-agent environments, and tighter theoretical connections between undesirable input spectra and feature induction.

In summary, LfU provides a broad and theoretically grounded paradigm for integrating negative information into the learning loop, transforming undesirable datapoints, behaviors, or histories into actionable, model-improving signals that underpin safe, robust, and ethically-aligned AI.