Dual-Path Unlearning Mechanisms

• Dual-pathway unlearning mechanisms are methods designed to selectively retain desired model behavior while actively suppressing targeted, forget-set information.
• They utilize frameworks like free energy minimization and PAC-Bayesian formulations to balance empirical accuracy with controlled data removal using dual optimizer strategies.
• Practical implementations address privacy compliance, adversarial robustness, and scalability, ensuring that erased data remains unrecoverable without degrading overall performance.

Dual-pathway unlearning mechanisms refer to methods in machine learning that explicitly separate or coordinate two distinct objectives: retaining desired information (or performance) on designated data, while actively removing or suppressing the influence of targeted “forget” data. This paradigm arises in response to the growing demand for efficient, certifiable, and robust removal of data or knowledge from trained models, with applications ranging from privacy compliance to AI safety and fairness. Dual-pathway designs systematically combine accuracy preservation and directed forgetting, often embedding this tradeoff in a common mathematical or algorithmic structure.

1. Theoretical Foundations: Free Energy and Information Risk Minimization

The canonical framework for dual-pathway unlearning is established by the PAC-Bayesian information risk minimization (IRM) formulation (Jose et al., 2021). Here, the unlearning process is governed by a free energy metric:

$$\mathcal{F} = \mathbb{E}_{W\sim P}[L(W|D_r)] + \frac{1}{\beta} D_{\mathrm{KL}}(P\,\|\,\text{Reference}),$$

where:

• $\mathbb{E}_{W\sim P}[L(W|D_r)]$ is the empirical loss on the retained data $D_r$ (“accuracy pathway”),
• $D_{\mathrm{KL}}(P\,\|\,\text{Reference})$ quantifies the divergence from a reference distribution representing full retraining without the forget-set (“forgetting pathway”),
• $\beta$ is a temperature parameter moderating the tradeoff.

The PAC-Bayesian upper bound certifies that the expected test loss of an unlearned model is controlled by this free energy. Minimizing $\mathcal{F}$ naturally yields dual objectives: maximizing test accuracy on retained data while minimizing retained information from the forget set via regularization toward the retrained reference.

Variational unlearning and the forgetting Lagrangian (Jose et al., 2021) arise as special cases within this IRM/free energy framework, where one term targets alignment with "unlearned" data and the other enforces similarity to the original model.

2. Methodological Instantiations

Dual-pathway unlearning appears in various methodological guises, all united by the explicit separation of the forgetting and retention objectives.

a. Free Energy Minimization

The IRM principle is the foundation for principled unlearning algorithms, including:

• Variational Unlearning: Minimization of an evidence upper bound that enforces low log-likelihood on the forget set while simultaneously minimizing the KL divergence from the original model (“closeness” to retraining).
• Forgetting Lagrangian: Introduction of a Lagrange multiplier to penalize divergence from the reference, recovering a PAC-Bayesian bound.

b. Discrete Representational Dual Paths

In architectures with discrete, sparse bottlenecks (Shah et al., 2023), dual-pathway behavior emerges in the operation of a Discrete Key–Value Bottleneck (DKVB). There:

• The “remember” pathway consists of all unmasked key–value pairs supporting generalization.
• The “forget” pathway is implemented by directly masking keys associated with the forget set, physically breaking the route from input to forgotten representation without retraining.

c. Dynamic Dual Optimizer Strategies

Dual optimizer strategies (Zhong et al., 22 Apr 2025) independently steer the forgetting and retention objectives using optimizers tailored to the specific gradient statistics of each objective, e.g., adaptive optimizers (Adam) for forgetting, and SGD for retention. Momentum decoupling further reduces interference, increasing stability.

d. Adversarial and Defense Pathways

Recent adversarially robust unlearning (Yuan et al., 20 Aug 2024) introduces an explicit duality: one pathway probes the vulnerability of unlearned models (adversarial suffixes, latent perturbations), while a second pathway is trained adversarially in the latent space to resist such targeted attacks, leading to robust unlearning.

3. Implementation and Evaluation Metrics

In practice, dual-pathway unlearning mechanisms are evaluated by their ability to balance multiple, often conflicting, metrics:

Objective	Metric/Term	Desired Effect
Forgetting (Target removal)	KL divergence, forget loss	Raise loss or suppress memory
Retaining (Generalization/utility)	Empirical/test loss, accuracy	Maintain or improve accuracy
Robustness (vs. adversarial attacks)	Utility under attack, jailbreak margin	Minimize exploitation by adversaries
Stability	Variance gap, regret bounds	Consistent performance

For generalized adoption, mechanisms are required to:

• Certify that removed data cannot be reconstructed or reactivated, even under adversarial queries (robustness to jailbreak and relearning (Yuan et al., 20 Aug 2024, Yan et al., 27 Sep 2025)).
• Preserve utility beyond just achieving successful forgetting, often formalized as utility-preserving constraints, e.g., Pareto-optimal tradeoffs (Yang et al., 21 Aug 2025).
• Provide efficient, scalable, and data-efficient updates (through masking, sparse activation, or dynamic parameter selection).

4. Robustness, Security, and Advanced Designs

Dual-pathway concepts underpin several recent advances to harden unlearning against edge cases:

• Adversarial robustness: Designs such as PRISM (Yan et al., 27 Sep 2025) introduce smoothness in both representation and parameter space, creating wide margins against adversarial perturbations and reducing gradient conflicts through orthogonal projections.
• Layered (Sequential) Unlearning: Layered Unlearning (LU) (Qian et al., 14 May 2025) implements multiple “inhibitors” in sequence, so that adversarial relearning in one pathway does not reactivate previously forgotten data, thus creating distributed defense-in-depth.
• Backdoor Attack Mitigation: Analysis of backdoor attacks (Arazzi et al., 14 Jun 2025) shows that dual-phase (training + unlearning pathway) exploits can be particularly stealthy, underscoring the importance of integrating defense strategies over both pathways.
• Evaluation Criteria: Robustness is measured not just by dropout accuracy on the forget set, but also by the Zero Retrain Forgetting (ZRF) score (how close unlearned behavior is to retrained-from-scratch), resilience to adversarial extraction, and locality/generalizability of knowledge deletion (Barez et al., 9 Jan 2025).

5. Broader Implications and Application Domains

Dual-pathway unlearning is foundational for:

• Privacy Compliance: Mechanisms must guarantee statistical indistinguishability post-deletion (e.g., via calibrated noise (Hu et al., 13 May 2025)), as mandated in the “right to be forgotten.”
• AI Safety: Especially in dual-use knowledge environments, balancing safety (by forgetting dangerous patterns) with utility (retaining benign capabilities) is essential. This requires careful tradeoff and may necessitate hybrid verification strategies (Barez et al., 9 Jan 2025).
• Model Editing and Fairness: Approaches like BiasUnlearn (Liu et al., 30 Sep 2025) leverage dual-pathway learning—negatively optimizing stereotypes while positively retaining anti-stereotype knowledge—ensuring debiasing does not cause collapse or bias reversal.

6. Challenges and Open Problems

Despite progress, open problems persist:

• Measuring Complete Erasure: Current approaches often “mask” rather than fully erase, making models vulnerable to relearning or recovery (Barez et al., 9 Jan 2025, Qian et al., 14 May 2025).
• Complex, Distributed Representations: Removing dangerous knowledge without disrupting beneficial functions is difficult when knowledge is entangled across parameters (Barez et al., 9 Jan 2025).
• Hyperparameter Sensitivity and Stability: Empirical results show high sensitivity to loss weighting, optimizer choice, and regularization; dual-optimizer mechanisms and adaptive penalization strategies address, but do not eliminate, these challenges (Zhong et al., 22 Apr 2025).
• Scalability and Efficiency: Achieving performant tradeoffs without full retraining or excessive computation remains a focal concern, addressed by methods such as sparse masking (Shah et al., 2023) and parameter selection (2505.10859).
• Setting-Specific Constraints: Continual learning, session-based recommender systems, and LLMs introduce setting-specific requirements—data-free operation, curriculum-based forgetting, inference-time mechanisms, etc.—that influence the implementation of dual-pathway strategies (Adhikari et al., 22 Sep 2025, Yang et al., 21 Aug 2025, Suriyakumar et al., 12 Jun 2025).

7. Future Directions

The field is moving toward:

• Unified frameworks capable of balancing, certifying, and adapting multiple objectives, often via modular dual-pathway architectures.
• Robust, automated, and data-efficient designs, integrating interpretability, parameter masking, and token-based interventions.
• Compositional and layered strategies that resist attack, support repeated/sequential unlearning, and maintain performance under distributional shift.
• Expanded theoretical analysis of lower bounds, geometry of loss landscapes, and explicit tradeoff frontiers.

Dual-pathway unlearning thus represents both a foundational principle and a practical blueprint for principled, robust, and efficient forgetting in modern AI systems, underpinning advances in privacy, security, safety, and fairness.