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arxiv: 2606.24586 · v1 · pith:CURRSW52new · submitted 2026-06-23 · 💻 cs.CV · cs.LG

EERLoss: A Novel Loss Function for Training Deep Biometric Models. A Case Study in Keystroke Dynamics

Nahuel Gonzalez , Marta Robledo-Moreno , Ivan DeAndres-Tame , Ruben Vera-Rodriguez , Ruben Tolosana This is my paper

Pith reviewed 2026-06-26 00:25 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords EERLossEqual Error Ratekeystroke dynamicsbiometric verificationloss functiondeep learningDET curveKVC-onGoing
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The pith

EERLoss approximates the Equal Error Rate in a subdifferentiable way to train deep biometric models directly on the target metric.

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

Biometric verification models are usually trained with objectives that do not align with the Equal Error Rate used to judge them. The paper proposes EERLoss as a subdifferentiable approximation to EER that can be used as a training loss. Tested on keystroke dynamics with a benchmark of over 185,000 subjects, it beats other losses, converges faster, and cuts EER by up to 30% relative when used to retrain a top model. It also allows targeting specific points on the DET curve. This matters because it aligns training with the actual performance goal for difficult biometric tasks.

Core claim

The paper claims that EERLoss is a subdifferentiable, arbitrarily accurate approximation to the Equal Error Rate for use as a loss in training deep biometric models. In the case study of keystroke dynamics verification on the KVC-onGoing benchmark, models trained with EERLoss achieve better results than those trained with prior losses and show up to approximately 30% relative reduction in EER compared to the previous state of the art.

What carries the argument

EERLoss, a subdifferentiable approximation to EER that enables direct gradient-based optimization of the Equal Error Rate.

If this is right

  • EERLoss outperforms state-of-the-art loss functions in ablation studies on keystroke dynamics.
  • It leads to substantially faster convergence, reducing training cost.
  • Applying it to the KVC-winning architecture produces significant EER improvements.
  • The loss framework supports optimization at any chosen operating point on the DET curve.

Where Pith is reading between the lines

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

  • The method may apply to other biometric modalities with similar variability issues.
  • Direct EER optimization could simplify system design by reducing the gap between training and deployment metrics.
  • Faster convergence might allow for more extensive hyperparameter searches or larger models within the same compute budget.
  • If the approximation holds, it could inspire similar differentiable proxies for other threshold-based metrics in machine learning.

Load-bearing premise

The approximation of EER must be close enough to the true value that gradient descent on the approximation improves the actual EER without being misled by approximation errors.

What would settle it

If a model trained using EERLoss shows a decreasing loss value but no corresponding decrease in the true Equal Error Rate computed on a separate test set, this would indicate the approximation is not guiding effective optimization.

Figures

Figures reproduced from arXiv: 2606.24586 by Ivan DeAndres-Tame, Marta Robledo-Moreno, Nahuel Gonzalez, Ruben Tolosana, Ruben Vera-Rodriguez.

Figure 1
Figure 1. Figure 1: Average per-user EER (interpolated) for different values of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effect of Batch Size. Error decreases consistently as the number of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Empirical violation of geometric priors. We illustrate the non-ideal nature of keystroke embeddings through the distribution of: (a) cluster radii, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Distribution of subject clusters in the embedding space on the 1,000- [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of subject clusters in the embedding space on the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

Deep learning approaches to biometric verification are commonly trained by optimizing indirect objectives, creating a misalignment between the optimization process and the primary evaluation metric, typically the Equal Error Rate (EER). This paper introduces EERLoss: a subdifferentiable, arbitrarily accurate approximation to EER for training deep biometric models. Furthermore, this framework has the potential to be adapted to optimize any specific operating point on the DET curve, enhancing its generalizability. To validate this approach, EERLoss is evaluated on a particularly demanding behavioral biometric modality: keystroke dynamics verification. This task is characterized by its high intra-class and low inter-class variability. Experiments are conducted on the large-scale KVC-onGoing benchmark, incorporating data from over 185,000 subjects across different scenarios. A comprehensive ablation study initially demonstrates the superiority of EERLoss in comparison to existing state-of-the-art loss functions. It also converges substantially faster compared to other losses, reducing the overall training cost. Additionally, a comparison is made between the proposed loss and the KVC-winning architecture by re-training it with EERLoss, demonstrating that the proposed approach significantly outperforms the original SoTA, achieving a relative EER reduction of up to approx. 30\%. This improvement on a challenging, large-scale benchmark validates the effectiveness of EERLoss as a task-aligned training objective specifically suited for high-variance biometric traits.

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 / 0 minor

Summary. The paper introduces EERLoss, a subdifferentiable and arbitrarily accurate approximation to the Equal Error Rate (EER) intended as a training objective for deep biometric verification models. It evaluates the approach on keystroke dynamics verification using the large-scale KVC-onGoing benchmark (185k+ subjects), reporting ablation superiority over existing losses, faster convergence, and up to ~30% relative EER reduction when re-training the prior KVC-winning architecture.

Significance. If the approximation's gradients reliably improve the true (non-differentiable) EER without exploiting surrogate artifacts, the result would be significant for biometric model training by closing the gap between optimization objective and evaluation metric. The large subject count and cross-scenario evaluation on a high-variance modality provide a strong empirical test bed; explicit credit is due for the scale of the benchmark and the direct comparison against the prior winning architecture.

major comments (2)
  1. [Abstract] Abstract: the central claim that EERLoss yields gradients that improve true EER (rather than approximation artifacts) rests on experimental outcomes whose controls are not visible; no ablation on the accuracy hyperparameter, no surrogate-true alignment analysis, and no verification that the reported EER protocol matches the loss definition are provided, which is load-bearing for the 30% relative improvement assertion.
  2. [Abstract] Abstract: the assertion of an 'arbitrarily accurate' subdifferentiable approximation is presented without derivation details, error bounds, or analysis of bias growth with model capacity/training steps, leaving open whether optimization drives the surrogate down while true EER plateaus.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of the presentation and validation of EERLoss. We address each major comment below and will revise the manuscript to provide the requested controls, derivations, and analyses.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that EERLoss yields gradients that improve true EER (rather than approximation artifacts) rests on experimental outcomes whose controls are not visible; no ablation on the accuracy hyperparameter, no surrogate-true alignment analysis, and no verification that the reported EER protocol matches the loss definition are provided, which is load-bearing for the 30% relative improvement assertion.

    Authors: We agree that explicit controls are needed to support the claim that gradients improve the true EER. In the revised version we will add an ablation on the accuracy hyperparameter, include a surrogate-true EER alignment plot over training, and explicitly document that the loss definition matches the EER protocol used in the KVC-onGoing benchmark (standard threshold sweep on the DET curve). These additions will be placed in the experimental section and will directly address the load-bearing nature of the 30% relative improvement result. revision: yes

  2. Referee: [Abstract] Abstract: the assertion of an 'arbitrarily accurate' subdifferentiable approximation is presented without derivation details, error bounds, or analysis of bias growth with model capacity/training steps, leaving open whether optimization drives the surrogate down while true EER plateaus.

    Authors: The current manuscript states the subdifferentiable approximation property but does not supply the requested supporting material. We will revise the method section to include the full derivation, analytic error bounds on the approximation, and an empirical study of bias as a function of model capacity and training steps. This analysis will also examine whether the surrogate and true EER remain aligned throughout optimization. revision: yes

Circularity Check

0 steps flagged

EERLoss derivation is self-contained; no circular reductions to inputs or self-citations.

full rationale

The paper defines EERLoss as a subdifferentiable approximation to the non-differentiable EER metric and validates it via ablation and re-training experiments on the external KVC-onGoing benchmark (185k+ subjects). No equations, parameters, or claims in the provided text reduce the reported EER gains to quantities fitted from the same runs or to self-citations. The central claim rests on independent experimental comparison rather than definitional equivalence or load-bearing self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the subdifferentiability claim implies an unstated smoothing or approximation technique whose details are absent.

pith-pipeline@v0.9.1-grok · 5804 in / 1015 out tokens · 37107 ms · 2026-06-26T00:25:24.813363+00:00 · methodology

discussion (0)

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Reference graph

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