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arxiv: 2604.15166 · v2 · pith:T6HXDXI5new · submitted 2026-04-16 · 💻 cs.CV · cs.AI· cs.LG

Class Unlearning via Depth-Aware Removal of Forget-Specific Directions

Arman Hatami , Romina Aalishah , Ilya E. Monosov This is my paper

Pith reviewed 2026-05-21 00:04 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LG
keywords dampdirectionsforgettingclassdepth-awarelayersremovalunlearning
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The pith

DAMP removes forget-specific directions from neural networks using depth-aware projections to achieve better class unlearning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Machine unlearning seeks to erase specific knowledge from a model without retraining from scratch. The paper shows that many existing class unlearning methods leave forget-class information encoded in the internal layers. DAMP addresses this by computing prototypes for forget and retain classes at each layer and projecting out the forget directions. It scales the strength of these edits according to the layer depth to balance forgetting with retained utility. On several image classification benchmarks, this results in forgetting that is closer to that of a freshly retrained model.

Core claim

At each network stage DAMP calculates the forget direction as the residual of the forget-class prototype minus the retain-class prototype in the input space to the next learnable operator, then updates the weights by projecting away a depth-scaled portion of that direction to lower the downstream sensitivity to forget-class inputs.

What carries the argument

Depth-Aware Modulation by Projection (DAMP), a closed-form weight update that removes forget residuals with larger edits in deeper layers.

Load-bearing premise

Computing and removing residuals relative to retain-class prototypes at each layer removes the underlying forget-class information from the network rather than just suppressing it at the output.

What would settle it

Training a linear probe on the network's deep-layer features after DAMP and finding that it can classify forget classes well above chance would show that the information remains in the representations.

Figures

Figures reproduced from arXiv: 2604.15166 by Arman Hatami, Ilya E. Monosov, Romina Aalishah.

Figure 1
Figure 1. Figure 1: Comparison of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of DAMP Selectivity with the baseline re￾trained model, Gradient Ascent Unlearning (GAU), knowledge￾distillation unlearning (KDU), Data Deletion Fine-Tuning (DD￾FT), Logit Masking (LM), Random Relabeling (RandRelabel), Selective Synaptic Dampening (SSD), and Saliency Unlearn￾ing (SalUn) for a 5-layer CNN (CNN-5) on CIFAR-10; forget classes 3 (Cat) and 5 (Dog). Existing methods exhibit weak, near… view at source ↗
Figure 3
Figure 3. Figure 3: The first panel (top-left) shows the difference between the RDM of the original model that has not been subjected to unlearning [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of DAMP bias shift with the baseline, re￾trained model, Gradient Ascent Unlearning (GAU), knowledge￾distillation unlearning (KDU), Data Deletion Fine-Tuning (DD￾FT), Logit Masking (LM), Random Relabeling (RandRelabel), Selective Synaptic Dampening (SSD), and Saliency Unlearn￾ing (SalUn) for a 5-layer CNN (CNN-5) on CIFAR-10; forget class 3 (Cat). The asterisk marks the forget class. Existing unl… view at source ↗
Figure 5
Figure 5. Figure 5: Overview of the proposed DAMP. Starting from a pretrained network, we compute class prototypes in the edit space of each stage. For each forget class, its prototype is decomposed into a component explained by the retain span and a forget residual. The resulting residual directions are orthonormalized. In parallel, a layer coefficient αℓ is computed from depth and forget-retain separability. These two quant… view at source ↗
read the original abstract

Machine unlearning aims to remove targeted knowledge from a trained model without the cost of retraining from scratch. In class unlearning, however, reducing accuracy on forget classes does not necessarily imply true forgetting: forgotten information can remain encoded in internal representations, and apparent forgetting may arise from classifier-head suppression rather than representational removal. We show that existing class-unlearning methods often exhibit weak or negative selectivity, preserve forget-class structure in deep representations, or rely heavily on final-layer bias shifts. We then introduce DAMP (Depth-Aware Modulation by Projection), a one-shot, closed-form weight-surgery method that removes forget-specific directions from a pretrained network without gradient-based optimization. At each stage, DAMP computes class prototypes in the input space of the next learnable operator, extracts forget directions as residuals relative to retain-class prototypes, and applies a projection-based update to reduce downstream sensitivity to those directions. To preserve utility, DAMP uses a parameter-free depth-aware scaling rule derived from probe separability, applying smaller edits in early layers and larger edits in deeper layers. The method naturally extends to multi-class forgetting through low-rank subspace removal. Across MNIST, CIFAR-10, CIFAR-100, and Tiny ImageNet, and across convolutional and transformer architectures, DAMP more closely resembles the retraining gold standard than some of the prior methods, improving selective forgetting while better preserving retain-class performance and reducing residual forget-class structure in deep layers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces DAMP (Depth-Aware Modulation by Projection), a one-shot closed-form weight-surgery method for class unlearning. At each stage it computes class prototypes in the input space of the next learnable operator, extracts forget directions as residuals relative to retain-class prototypes, and applies a projection update; a parameter-free depth-aware scaling rule modulates edit magnitude by layer depth. The central claim is that across MNIST, CIFAR-10, CIFAR-100 and Tiny ImageNet, and across CNN and transformer backbones, DAMP more closely matches the retraining gold standard than prior methods by improving selective forgetting, preserving retain-class accuracy, and reducing residual forget-class structure in deep layers.

Significance. If the method genuinely erases forget-class information from internal representations rather than merely shifting decision boundaries at the output head, it would offer an efficient, optimization-free alternative to retraining or gradient-based unlearning while addressing the documented failure mode of residual structure in deep layers. The closed-form derivation and explicit handling of multi-class forgetting via low-rank subspaces are notable strengths.

major comments (3)
  1. [Abstract] Abstract: the claim that DAMP 'more closely resembles the retraining gold standard' and 'reduc[es] residual forget-class structure in deep layers' is asserted without any quantitative tables, error bars, ablation studies, or numerical comparisons to retraining or baselines, so the central empirical claim cannot be evaluated from the manuscript.
  2. [Method] Method (depth-aware scaling paragraph): the assertion that the scaling rule is 'parameter-free' and 'derived from probe separability' is not accompanied by an explicit equation or derivation showing how separability measurements translate into per-layer multipliers without introducing fitted quantities or hidden hyperparameters.
  3. [Method] Central assumption (prototype-residual step): the claim that residuals relative to retain-class prototypes isolate forget-specific directions that are both linear and sufficient to capture all encoded forget-class information is load-bearing for the 'true forgetting' versus 'head suppression' distinction, yet the manuscript provides no direct test (e.g., linear probing of internal activations before/after DAMP) to rule out non-linear entanglement or redundant pathways.
minor comments (2)
  1. [Abstract] Notation for 'forget-specific directions' and 'probe separability' is introduced without a formal definition or reference to prior usage.
  2. [Method] The extension to multi-class forgetting via low-rank subspace removal is mentioned but lacks a concrete algorithmic description or complexity statement.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address each major comment point by point below, clarifying the empirical support and methodological details while committing to revisions where the presentation can be strengthened.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that DAMP 'more closely resembles the retraining gold standard' and 'reduc[es] residual forget-class structure in deep layers' is asserted without any quantitative tables, error bars, ablation studies, or numerical comparisons to retraining or baselines, so the central empirical claim cannot be evaluated from the manuscript.

    Authors: We acknowledge that the abstract's central claims would benefit from more immediate quantitative support. The full manuscript reports results across MNIST, CIFAR-10, CIFAR-100, and Tiny ImageNet for both CNN and transformer backbones, with comparisons to prior methods and retraining from scratch on metrics including forget-class accuracy, retain-class accuracy, and measures of residual structure. To address the concern directly, we will revise the abstract and add a consolidated summary table (with error bars from repeated runs) that explicitly quantifies how DAMP aligns with the retraining baseline relative to other methods. revision: yes

  2. Referee: [Method] Method (depth-aware scaling paragraph): the assertion that the scaling rule is 'parameter-free' and 'derived from probe separability' is not accompanied by an explicit equation or derivation showing how separability measurements translate into per-layer multipliers without introducing fitted quantities or hidden hyperparameters.

    Authors: We agree that the depth-aware scaling rule requires an explicit derivation to substantiate the 'parameter-free' claim. In the revised method section we will insert the full equation for the per-layer multiplier together with a step-by-step derivation that shows how separability statistics (computed once from probe activations) are mapped to scaling factors. No fitted quantities or hidden hyperparameters are introduced; the rule uses only the observed separability values at each depth. revision: yes

  3. Referee: [Method] Central assumption (prototype-residual step): the claim that residuals relative to retain-class prototypes isolate forget-specific directions that are both linear and sufficient to capture all encoded forget-class information is load-bearing for the 'true forgetting' versus 'head suppression' distinction, yet the manuscript provides no direct test (e.g., linear probing of internal activations before/after DAMP) to rule out non-linear entanglement or redundant pathways.

    Authors: This is a substantive point about the strength of evidence for representational rather than merely head-level forgetting. Our experiments already demonstrate reduced residual forget-class structure in deep layers through representation-level metrics and closer alignment with retraining performance. We will add a direct linear-probing analysis of internal activations before and after DAMP to quantify the removal of linear forget directions. Regarding possible non-linear entanglement or redundant pathways, we note that the method explicitly targets linear subspaces; any remaining non-linear components would constitute a limitation that we will discuss explicitly in the revision. revision: partial

Circularity Check

0 steps flagged

DAMP derivation is self-contained closed-form without circular reduction

full rationale

The paper presents DAMP as a one-shot closed-form weight-surgery procedure that computes prototypes in per-operator input space, extracts residuals, and applies projection updates with a parameter-free depth-aware scaling rule derived from probe separability. No load-bearing step reduces by construction to a fitted quantity defined inside the paper, nor does any central claim rest on a self-citation chain or imported uniqueness theorem. Empirical comparisons to retraining across datasets and architectures provide external validation, so the derivation chain remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumption that forget-class information is linearly separable in the input space to each layer and that removing the residual direction will not destroy retain-class utility. No explicit free parameters are introduced; the scaling rule is stated to be parameter-free. No new physical entities are postulated.

axioms (2)
  • domain assumption Class prototypes computed in the input space of each learnable operator capture the relevant forget-specific directions.
    Invoked when the method extracts residuals relative to retain-class prototypes at each stage.
  • domain assumption Projection-based weight updates at each layer remove downstream sensitivity without requiring gradient optimization.
    Core premise of the one-shot closed-form surgery.
invented entities (1)
  • forget-specific directions no independent evidence
    purpose: Residual vectors in layer input space used as targets for projection removal.
    Newly defined construct extracted from class prototypes; no independent evidence outside the method itself is provided.

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Forward citations

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