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pith:MU5Q3RHH

pith:2026:MU5Q3RHHUXYZLVLL4VNLVB6TJM

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$\alpha$-TCAV: A Unified Framework for Testing with Concept Activation Vectors

Alexander Jung, Ekkehard Schnoor, Jawher Said, Malik Tiomoko, Wojciech Samek

The standard TCAV score has non-decaying variance from its discontinuous indicator, which α-TCAV fixes by substituting a parameterized smooth function for a unified probabilistic framework.

arxiv:2605.15688 v1 · 2026-05-15 · stat.ML · cs.AI · cs.LG · math.PR

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Claims

C1strongest claim

We identify a fundamental flaw in the standard TCAV score: its reliance on a discontinuous indicator function induces non-decaying variance in critical regimes. To address this, we introduce α-TCAV, a generalized framework that replaces the indicator with a parameterized smooth function, yielding a unified probabilistic formulation that subsumes both TCAV and Multi-TCAV.

C2weakest assumption

The derivations of the distributions for PatternCAV, FastCAV, and ridge-regression CAVs are analytically tractable and that the smooth function in α-TCAV can be tuned to achieve either imitation of Multi-TCAV or a calibrated Bayes-optimal measure without introducing new bias. This premise enters in the stochastic analysis section and the guidance on tuning the parameter.

C3one line summary

α-TCAV replaces TCAV's hard indicator with a tunable smooth function to create a unified probabilistic framework with lower variance and guidance for parameter choice or Bayes-optimal scoring.

References

151 extracted · 151 resolved · 4 Pith anchors

[1] Zur Elektrodynamik bewegter Körper 1905

[2] The Annals of Applied Probability , volume= 2018

[3] The Thirteenth International Conference on Learning Representations , year=

[4] Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization · arXiv:2604.03146

[5] The \ Companion 1993

Receipt and verification

First computed	2026-05-20T00:01:12.526593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

653b0dc4e7a5f195d56be55aba87d34b128ff42f9a21de9e1c32d6a9a41f87db

Aliases

arxiv: 2605.15688 · arxiv_version: 2605.15688v1 · doi: 10.48550/arxiv.2605.15688 · pith_short_12: MU5Q3RHHUXYZ · pith_short_16: MU5Q3RHHUXYZLVLL · pith_short_8: MU5Q3RHH

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/MU5Q3RHHUXYZLVLL4VNLVB6TJM \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 653b0dc4e7a5f195d56be55aba87d34b128ff42f9a21de9e1c32d6a9a41f87db

Canonical record JSON

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      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-15T07:22:59Z",
    "title_canon_sha256": "8d586ce140c497c4ae3bba821a7b9172e1272da09adfe3fcac59fdfce40bfc74"
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