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arxiv: 2606.10669 · v1 · pith:LH5A4AHEnew · submitted 2026-06-09 · 💻 cs.LG · cs.AI· cs.CR

In Defense of Information Leakage in Concept-based Models

Mateo Espinosa Zarlenga This is my paper

Pith reviewed 2026-06-27 13:42 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CR
keywords concept-based modelsinformation leakagemodel interpretabilityconcept incompletenessbenign leakageintervenabilitydeep neural networksmachine learning
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The pith

In real-world settings with incomplete concepts, some information leakage is necessary for concept-based models to stay accurate and intervenable.

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

The paper challenges the conventional view that leakage of concept-irrelevant information in concept-based models always reduces interpretability. It notes that evidence for this harm is often inconclusive and that complete concept sets are rare in practice. Under these conditions, the authors argue that some leakage becomes structurally required to achieve both high accuracy and the ability to intervene on concepts. They introduce the notion of benign leakage and show that a reframed training objective can encourage models to use it productively.

Core claim

Concept-based models learn representations that leak concept-irrelevant information, which is traditionally viewed as undesirable because it leads to uninterpretable models. This view is ill-posed because evidence linking leakage to reduced interpretability is often inconclusive, and the push to eradicate leakage produces impractical models. In real-world settings where concept incompleteness is the norm, some leakage is often necessary for constructing accurate and intervenable concept-based models. By optimizing a reframing of the typical concept-based model training objective, models can encourage and exploit benign leakage without sacrificing accuracy or intervenability.

What carries the argument

A reframing of the typical concept-based model training objective that encourages and exploits benign leakage.

If this is right

  • Concept-based models can reach high accuracy even when provided concepts fail to capture all relevant information.
  • Intervenability on individual concepts remains possible when benign leakage is present.
  • Eradicating leakage entirely produces models that are less practical under typical data constraints.
  • A reframed training objective allows models to use extra information without losing the benefits of concept alignment.

Where Pith is reading between the lines

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

  • The same tolerance for controlled leakage might apply to other interpretability methods that rely on incomplete human-provided features.
  • Datasets could be annotated with explicit measures of concept completeness to test when leakage becomes necessary.
  • Guidelines for concept selection in applications could shift from completeness to identifying which extra information is benign.

Load-bearing premise

The premise that concept incompleteness is the norm in real-world settings and that evidence linking leakage to reduced interpretability is often inconclusive.

What would settle it

An empirical demonstration that concept-based models can achieve high accuracy and full intervenability on incomplete concept sets while completely eliminating all leakage would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.10669 by Mateo Espinosa Zarlenga.

Figure 1
Figure 1. Figure 1: A generalized Concept Bottleneck Model (CBM). may be optimized independently, sequentially (training g before f), or jointly (minimizing a weighted sum). The simplest instantiation of this framework is a Sigmoidal CBM (Koh et al., 2020), where each concept is represented by a single sigmoidal scalar (m = 1) and s is the identity. More recent works have explored richer representations and scoring mechanisms… view at source ↗
Figure 2
Figure 2. Figure 2: Leakage happens when the concept representation Cˆi encodes information that is not attributable to the ground-truth concept Ci. This additional information can be attributed to (left) another concept Cj or (right) the downstream task Y . Intervenability Claims A first line of argument holds that leakage undermines the intervenability of CMs (Havasi et al., 2022; Espinosa Zarlenga et al., 2023a; Vandenhirt… view at source ↗
Figure 3
Figure 3. Figure 3: Task fidelity of sigmoidal (i.e., soft) CBMs as we vary the number k of training concepts on the CUB (Wah et al., 2011) dataset (see App. B for details). CBMs that limit task leakage (e.g., independent CBMs) are more affected by incompleteness. complete description (Yeh et al., 2020) of the downstream task y. Formally, this means CMs require that the mutual information between the downstream label y ∼ P(Y … view at source ↗
Figure 4
Figure 4. Figure 4: Task accuracy (y-axis) of leaky CMs trained on an incom￾plete version of CUB (k = 22, details in App. B) as we intervene on concepts at test time (x-axis). (left) Leaky CMs can remain intervenable in incompleteness. (right) Some leaky variants, how￾ever, lose their intervenability (curves are non-increasing). Simplicity Bias and Benign Leakage CMs that enable leakage can remain highly accurate and interven… view at source ↗
Figure 5
Figure 5. Figure 5: A DNN trained on an incomplete CUB task (k = 22) w/o any concept alignment loss becomes intervenable with Lint. in the penultimate layer of the DNN and intervened on them as if they were normal CBM soft concept representations (which they are not, as we do not introduce any concept alignment losses when training this model, and the neurons do not form a bottleneck). We see that this DNN, trained without an… view at source ↗
Figure 6
Figure 6. Figure 6: Effect of regularizing previously unintervenable leaky CMs with Lint on an incomplete version of CUB (k = 22). 7 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: is not the same: for example, although CEMs without RandInt do increase their task accuracies as they are intervened on, the effect is minimal compared to that of other models. This implies that it is likely that incompleteness can lead to several leaky models to become unintervenable, but its effects on leaky CMs can vary. 0 20 40 60 80 100 Intervened Concepts (%) 40 60 80 100 Task Accuracy (%) Intervenab… view at source ↗
Figure 8
Figure 8. Figure 8: Extended results showing the effect of applying the sufficiency regularizer Lint to previously unintervenable leakage-enabling models on an incomplete version of CUB with k = 22 concepts. E. Verifying Trends on Additional Datasets To further verify the generality of the claims in Section 6, we replicate our key intervention experiments on four additional datasets that span a range of incompleteness and noi… view at source ↗
Figure 9
Figure 9. Figure 9: Intervention curves on additional tasks, verifying the results discussed in Section 6 for the incomplete version of CUB. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top-m weight overlap for (1) a properly-conditioned Hybrid CBM MH and a non-leaky Independent CBM MI (orange); (2) two Independent CBMs trained with different seeds (green); (3) an ill-conditioned Hybrid CBM and a non-leaky Independent CBM MI (blue); and (4) a random bottleneck subset and Independent CBM MI (gray dashed line, random baseline). 19 [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
read the original abstract

Concept-based models (CMs), deep neural networks that ground their predictions on representations aligned with human-understandable concepts (e.g., "round", "stripes", etc.), have been shown to learn representations that leak concept-irrelevant information. As the traditional narrative goes, this leakage is undesirable and should be eradicated as it leads to uninterpretable models. In this paper, we posit that this conventional view of leakage in CMs is not only ill-posed, as the evidence of how leakage makes a model less interpretable is often inconclusive, but also bound to lead to impractical CMs under common real-world constraints. Specifically, we argue that in real-world settings where concept incompleteness is the norm, some leakage is often necessary for constructing accurate and intervenable CMs. To this end, we propose that there is such a thing as benign leakage and show that, by optimizing a reframing of the typical CM training objective, CMs can encourage and exploit this form of leakage without sacrificing accuracy or intervenability.

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

2 major / 1 minor

Summary. The paper argues that the standard view of information leakage in concept-based models (CMs) as inherently harmful to interpretability is ill-posed, since supporting evidence is often inconclusive, and that concept incompleteness is the norm in real settings. It introduces the notion of 'benign leakage' as sometimes necessary for accurate and intervenable CMs, and claims that a reframing of the typical CM training objective can encourage and exploit this leakage without loss of accuracy or intervenability.

Significance. If the claims hold, the work offers a conceptual reframing that could relax overly restrictive no-leakage requirements in CM design, enabling more practical models under incomplete concept supervision. The emphasis on intervenability preservation is a strength if demonstrated, as it directly engages a core desideratum of CMs.

major comments (2)
  1. [Abstract] Abstract: the central claim that a reframed training objective encourages benign leakage 'without sacrificing ... intervenability' lacks any described mechanism (auxiliary loss, architectural constraint, or regularizer) ensuring that concept-irrelevant leaked features remain inert under interventions; without this, the skeptic concern that leakage may allow downstream compensation for concept changes is unaddressed.
  2. [Abstract] Abstract, paragraph 2: the assertion that 'evidence of how leakage makes a model less interpretable is often inconclusive' is load-bearing for reclassifying leakage as potentially benign, yet no specific prior results, datasets, or quantitative re-analyses are referenced to substantiate the claim.
minor comments (1)
  1. The term 'benign leakage' is introduced as a new category but receives no operational definition or distinction from other forms of leakage in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, indicating revisions where the concerns are valid.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that a reframed training objective encourages benign leakage 'without sacrificing ... intervenability' lacks any described mechanism (auxiliary loss, architectural constraint, or regularizer) ensuring that concept-irrelevant leaked features remain inert under interventions; without this, the skeptic concern that leakage may allow downstream compensation for concept changes is unaddressed.

    Authors: The manuscript (Section 3) defines the reframed objective as a modified concept-alignment loss that explicitly permits leakage of concept-irrelevant features while retaining the standard intervention protocol at test time. Section 4 then reports intervention experiments showing that prediction shifts upon concept edits remain consistent with the intended concept change and are not offset by leaked features. We agree the abstract omits this description and will revise it to name the reframed objective and note the empirical intervenability results. revision: yes

  2. Referee: [Abstract] Abstract, paragraph 2: the assertion that 'evidence of how leakage makes a model less interpretable is often inconclusive' is load-bearing for reclassifying leakage as potentially benign, yet no specific prior results, datasets, or quantitative re-analyses are referenced to substantiate the claim.

    Authors: The full manuscript reviews this literature in the introduction and related-work section, citing studies in which leakage was measured yet downstream interpretability metrics remained stable or context-dependent. The abstract itself contains no citations. We will add two to three representative references to the abstract to ground the claim. revision: yes

Circularity Check

0 steps flagged

No circularity; position paper with no derivation chain

full rationale

The manuscript is an argumentative position paper asserting that some information leakage can be 'benign' under concept incompleteness. No equations, fitted parameters, or formal derivations appear in the abstract or described content. The central claim is a normative reframing of prior literature rather than any prediction or result that reduces to its own inputs by construction. No self-citation load-bearing steps, uniqueness theorems, or ansatzes are invoked in the provided text. This matches the default expectation of a self-contained argument without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on two domain assumptions: that concept incompleteness is the norm in real applications and that leakage is required for accuracy and intervenability when incompleteness holds. No free parameters or invented entities beyond the term 'benign leakage' are introduced in the abstract.

axioms (2)
  • domain assumption concept incompleteness is the norm in real-world settings
    Invoked in abstract paragraph 2 as the condition under which leakage becomes necessary.
  • domain assumption some leakage is often necessary for constructing accurate and intervenable CMs
    Core premise that justifies the shift from eradication to exploitation of leakage.
invented entities (1)
  • benign leakage no independent evidence
    purpose: A form of concept-irrelevant information that can be encouraged without harming accuracy or intervenability
    New label introduced to distinguish desirable from undesirable leakage; no independent evidence supplied in abstract.

pith-pipeline@v0.9.1-grok · 5704 in / 1427 out tokens · 18210 ms · 2026-06-27T13:42:23.852146+00:00 · methodology

discussion (0)

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Reference graph

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