arxiv: 2604.07962 · v1 · submitted 2026-04-09 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Is your algorithm unlearning or untraining?

Eleni Triantafillou , Ahmed Imtiaz Humayun , Monica Ribero , Alexander Matt Turner , Michael C. Mozer , Georgios Kaissis

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:02 UTC · model grok-4.3

classification 💻 cs.LG

keywords machine unlearninguntrainingforget setdata removalmodel editingdistribution removalconcept erasuremachine learning

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The pith

The term machine unlearning conflates two separate goals without the literature noticing the split.

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

The paper shows that efforts to delete specific data or behaviors from trained models actually pursue two different ends. Untraining reverses only the direct effect of the chosen forget-set examples on the model's parameters. Unlearning goes further and treats those examples as samples from a larger distribution, aiming to remove the entire concept or behavior they represent. A reader should care because the lack of this separation has produced mismatched evaluation metrics, unsuitable baselines for comparisons, and overlooked research questions about how to handle each goal cleanly.

Core claim

Research on machine unlearning has proceeded under two distinct problem formulations without acknowledging the difference. Untraining seeks to reverse the influence that a given forget set exerted on the model during training. Unlearning instead uses the forget set to excise the full underlying distribution from which those examples were drawn, thereby removing the represented concept or behavior more broadly. The note supplies technical definitions for each and classifies existing work under the two headings.

What carries the argument

The distinction between untraining (reversing the training influence of a specific forget set) and unlearning (removing the broader distribution or concept sampled by that forget set).

If this is right

Algorithm comparisons become valid only when both methods address the same formulation.
Metrics and baselines must be selected to match the intended target rather than a generic unlearning score.
Separate research tracks open for efficient distribution-level removal versus precise example-level reversal.
Methods developed under one formulation cannot be assumed to solve the other.
Practitioners must declare which formulation they require before selecting an approach.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Tool selection for real deployments should begin by deciding whether specific records or an entire category of behavior needs to be erased.
Hybrid pipelines that first untrain and then extend the removal to the distribution become a natural next direction.
Related areas such as model editing or continual learning may carry similar unstated splits between point and distribution objectives.

Load-bearing premise

The two notions are distinct enough in practice that conflating them produces mismatched metrics, invalid baselines, and missed research directions.

What would settle it

A systematic review that finds every published method already states whether it targets only the forget-set examples or the full distribution they represent, or an experiment showing that standard unlearning benchmarks yield identical performance for both formulations.

read the original abstract

As models are getting larger and are trained on increasing amounts of data, there has been an explosion of interest into how we can ``delete'' specific data points or behaviours from a trained model, after the fact. This goal has been referred to as ``machine unlearning''. In this note, we argue that the term ``unlearning'' has been overloaded, with different research efforts spanning two distinct problem formulations, but without that distinction having been observed or acknowledged in the literature. This causes various issues, including ambiguity around when an algorithm is expected to work, use of inappropriate metrics and baselines when comparing different algorithms to one another, difficulty in interpreting results, as well as missed opportunities for pursuing critical research directions. In this note, we address this issue by establishing a fundamental distinction between two notions that we identify as \unlearning and \untraining, illustrated in Figure 1. In short, \untraining aims to reverse the effect of having trained on a given forget set, i.e. to remove the influence that that specific forget set examples had on the model during training. On the other hand, the goal of \unlearning is not just to remove the influence of those given examples, but to use those examples for the purpose of more broadly removing the entire underlying distribution from which those examples were sampled (e.g. the concept or behaviour that those examples represent). We discuss technical definitions of these problems and map problem settings studied in the literature to each. We hope to initiate discussions on disambiguating technical definitions and identify a set of overlooked research questions, as we believe that this a key missing step for accelerating progress in the field of ``unlearning''.

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.

Desk Editor's Note private letter to a colleague

This note splits unlearning into reversing specific example influence versus excising the full distribution behind them, and the split is new, but the paper does not show that the mix-up has produced the claimed practical problems.

read the letter

The main point is that papers using the term machine unlearning actually target two different things. Untraining means undoing the effect that particular forget-set examples had on the model weights. Unlearning means using those examples to remove the wider distribution or concept they represent. The authors treat this as an unacknowledged split in the existing work and give definitions plus a literature mapping to each bucket. That mapping is the clearest part of the note and it does line up with separate use cases like pointwise privacy deletion versus distributional safety removal. The paper is short and stays conceptual, so it does not add new algorithms or experiments. The definitions themselves are stated plainly enough to be usable as a reference. The soft spot is the jump from the split to the list of problems. The note says the overload creates ambiguity in metrics, baselines, and missed research directions, yet it does not walk through any concrete paper or result where mixing the two goals produced a wrong evaluation or blocked progress. Without those examples the claim stays plausible rather than demonstrated. The argument does not contain circular reasoning or unsupported math, and the stress-test note is right that the distinction is operational in principle. This is for people already working in machine unlearning who want to be precise about what their method is supposed to achieve. A reader looking for new techniques or large-scale tests will not find them here. I would send it for peer review because the field is expanding quickly and a clean terminological distinction can help future work even if the current note needs more case studies to land its stronger claims.

Referee Report

3 major / 2 minor

Summary. The paper claims that the term 'machine unlearning' is overloaded in the literature, conflating two distinct problem formulations without prior acknowledgment: 'untraining,' which aims to reverse the influence of specific examples in a forget set on the model, and 'unlearning,' which uses those examples to remove the broader underlying distribution or concept they represent. It supplies qualitative technical definitions, maps literature problem settings to each category, and argues that the conflation leads to ambiguity in algorithm expectations, inappropriate metrics/baselines, interpretation difficulties, and missed research directions.

Significance. If the distinction holds and is adopted, it would sharpen evaluation practices in the rapidly growing machine unlearning field for large models, enabling metrics and baselines matched to pointwise privacy-style deletion versus distributional safety-style erasure. This conceptual clarification could surface overlooked directions and reduce wasted effort on mismatched comparisons, providing a timely organizing framework even without new empirical results.

major comments (3)

[Definitions paragraph and Figure 1 caption] Main text, definitions of untraining and unlearning: The notions are introduced only qualitatively (reversing specific-example influence versus excising the full distribution/concept) with no formal mathematical statements, such as optimization objectives, loss functions, or measurable criteria (e.g., no use of influence functions, KL divergence, or membership-inference proxies). This leaves the central distinction non-operational and prevents direct application to existing algorithms or verification of the claimed metric mismatches.
[Literature mapping section] Literature mapping discussion: The assertion that the overload 'has not been observed or acknowledged' and produces concrete problems (inappropriate metrics, missed directions) is stated without a detailed mapping, table, or even a handful of cited examples showing specific papers that conflate the two and suffer the listed issues. A load-bearing claim of widespread impact requires at least illustrative case studies.
[Issues paragraph] Discussion of practical consequences: The paper lists issues such as 'use of inappropriate metrics and baselines' and 'difficulty in interpreting results' but provides no concrete illustration (hypothetical or drawn from literature) of how conflating the two notions produces a wrong conclusion or suboptimal algorithm choice.

minor comments (2)

[Abstract] The abstract and main text use LaTeX macros (e.g., unlearning, untraining) without defining them on first use for readers unfamiliar with the notation.
[Figure 1] Figure 1 is referenced as illustrating the distinction but its caption and surrounding text do not explicitly label the two panels or arrows with the new terminology, reducing clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful and constructive review. We appreciate the recognition that clarifying the distinction between untraining and unlearning could benefit the field. We agree that the manuscript would be strengthened by more formal definitions, explicit literature examples, and concrete illustrations of the issues. We will revise accordingly to address these points.

read point-by-point responses

Referee: [Definitions paragraph and Figure 1 caption] Main text, definitions of untraining and unlearning: The notions are introduced only qualitatively (reversing specific-example influence versus excising the full distribution/concept) with no formal mathematical statements, such as optimization objectives, loss functions, or measurable criteria (e.g., no use of influence functions, KL divergence, or membership-inference proxies). This leaves the central distinction non-operational and prevents direct application to existing algorithms or verification of the claimed metric mismatches.

Authors: We agree that formalizing the distinction would make it more operational. Although the note is primarily conceptual, we will revise the definitions section to include mathematical characterizations. Untraining can be defined as finding parameters theta' such that the model approximates one trained without the forget set D_f, e.g., via influence function approximation: theta' ≈ theta - H^{-1} * grad_{D_f} or by minimizing the expected loss difference on D_f. Unlearning can be formalized as minimizing a divergence (e.g., KL) between the model's output distribution and the target distribution excluding the concept represented by D_f. We will also link these to appropriate metrics, such as membership inference success for untraining versus concept-level erasure measures for unlearning. This will enable direct application to algorithms. revision: yes
Referee: [Literature mapping section] Literature mapping discussion: The assertion that the overload 'has not been observed or acknowledged' and produces concrete problems (inappropriate metrics, missed directions) is stated without a detailed mapping, table, or even a handful of cited examples showing specific papers that conflate the two and suffer the listed issues. A load-bearing claim of widespread impact requires at least illustrative case studies.

Authors: We acknowledge that an explicit mapping with examples would better support the claim. While the manuscript discusses mapping problem settings, we will add a table in the revision that categorizes representative papers (e.g., from recent unlearning surveys and key works on exact unlearning, approximate methods, and concept erasure) into untraining, unlearning, or ambiguous categories, with justifications. This will include specific citations showing how goals, metrics, and baselines align or mismatch with each formulation, providing the requested illustrative case studies. revision: yes
Referee: [Issues paragraph] Discussion of practical consequences: The paper lists issues such as 'use of inappropriate metrics and baselines' and 'difficulty in interpreting results' but provides no concrete illustration (hypothetical or drawn from literature) of how conflating the two notions produces a wrong conclusion or suboptimal algorithm choice.

Authors: We agree that concrete illustrations would clarify the practical impact. We will add a dedicated paragraph with both hypothetical scenarios and literature-based examples. For example, an algorithm using gradient ascent on a forget set (suited to untraining) evaluated via broad concept-removal accuracy (an unlearning metric) could lead to false negatives on effectiveness. We will also reference cases where papers state privacy-style deletion goals but employ distributional metrics, resulting in ambiguous interpretations, and discuss how this conflation may have caused missed opportunities for targeted baselines. revision: yes

Circularity Check

0 steps flagged

No significant circularity; terminological distinction is self-contained

full rationale

The paper contains no derivations, equations, fitted parameters, or load-bearing self-citations. Its central claim is a direct observation that the term 'unlearning' has been applied to two distinct problem formulations (reversing specific example influence vs. excising the underlying distribution), with no internal reduction of any result to its own inputs by construction. The argument maps literature settings to the two notions without invoking uniqueness theorems, ansatzes, or renamed empirical patterns from prior self-work. This is a standard non-circular conceptual clarification.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The paper rests on the domain assumption that the literature has conflated two distinct goals and that this conflation creates practical problems; no free parameters or invented physical entities are introduced.

axioms (1)

domain assumption Different research efforts in machine unlearning address two distinct problem formulations that have not been distinguished in the literature.
This is the core premise stated in the abstract.

invented entities (2)

untraining no independent evidence
purpose: Label for the goal of reversing the training effect of a specific forget set.
New term coined to separate it from the broader goal.
unlearning no independent evidence
purpose: Refined label for the goal of removing the entire underlying distribution or concept.
Narrowed definition of the existing term.

pith-pipeline@v0.9.0 · 5624 in / 1235 out tokens · 33108 ms · 2026-05-10T18:02:19.423823+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Untraining aims to reverse the effect of having trained on a given forget set... Unlearning... to use those examples for the purpose of more broadly removing the entire underlying distribution
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Definition 4.1. (ε,δ)-unlearning (Neel et al., 2021)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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