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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Mobile face anti-spoofing through privileged multi- teacher distillation under SWAP constraints⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ostap Stets</string-name>
          <email>ostap.stets@gmail.com</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ihor Konovalenko</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andrii Bomba</string-name>
          <email>abomba@ukr.net</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oleh Shmanko</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>I. Horbachevsky Ternopil National Medical University</institution>
          ,
          <addr-line>Maidan Voli St., 1, Ternopil, 46002</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>National University of Water and Environmental Engineering</institution>
          ,
          <addr-line>11 Soborna St., Rivne, 33028</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Ternopil Ivan Puluj National Technical University</institution>
          ,
          <addr-line>Ruska str., 56, 46001, Ternopil</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>Face anti-spoofing (FAS) on mobile devices requires models that are not only accurate and robust across domains but also optimized under strict SWAP (Speed, Weight, Accuracy, Power) constraints. Current approaches often face a trade-off: strong generalization relies on additional modalities such as depth or rPPG signals, but mobile deployment can only afford lightweight RGB-only models. In this paper, we propose a privileged-information knowledge distillation (PI-KD) framework that enables multi-teacher supervision during training while keeping the deployment student efficient and mobile-friendly. Specifically, we outline how temporal teachers (rPPG-based) and geometric teachers (depth-based) can transfer complementary supervisory signals into a compact RGB-only student model. We discuss expected advantages for cross-dataset generalization, robustness to unseen attacks, and SWAP trade-offs, and we propose evaluation protocols that future empirical work should adopt. Our contribution lies in presenting a methodology that bridges privileged multimodal supervision with practical on-device constraints, opening a pathway toward more reliable and efficient mobile face anti-spoofing systems.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;face anti-spoofing (FAS)</kwd>
        <kwd>presentation attack detection (PAD)</kwd>
        <kwd>knowledge distillation (KD)</kwd>
        <kwd>CEUR-WS 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Face anti-spoofing (FAS) is a critical safeguard in mobile biometric authentication, where decisions
must be both reliable and resource-efficient. Production systems must optimize SWAP metrics:
Speed
(latency),</p>
      <sec id="sec-1-1">
        <title>Weight</title>
        <p>(model
size/memory),</p>
      </sec>
      <sec id="sec-1-2">
        <title>Accuracy</title>
        <p>
          (PAD
metrics
such
as
APCER/BPCER/ACER/RIAPAR), and Power (energy consumption per inference). The ISO/IEC
30107-3 test methodology formalizes PAD error metrics and evaluation protocols, anchoring how
operating points are compared in practice [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. Deep learning methods have substantially advanced
FAS, including pixel-wise supervision and domain-generalization strategies. Yet, models that
generalize best, often rely on sensing or capacity that mobile devices cannot afford at inference
(e.g., depth, rPPG, or heavy backbones). This tension in robustness versus deployability persists
across recent surveys reviewing cross-dataset performance and multi-modal setups [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          A principled way to bridge this gap is Learning Using Privileged Information (LUPI): during
training, a “Teacher” may access auxiliary information not available at test time, while the
deployed “Student” obeys the standard runtime contract (e.g., RGB-only). LUPI formalizes how
such additional signals can shape decision boundaries and accelerate learning without altering the
inference interface [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ]. Within FAS, two privileged cues are especially complementary: depth (3D
structure/recapture artifacts) and rPPG (physiological rhythms). Liu et al. showed that pixel-wise
depth
estimation and sequence-level rPPG
supervision
guide a network toward
more
discriminative. generalizable liveness cues, improving intra-dataset and cross-dataset robustness –
exactly the properties desired before compressing knowledge into a mobile-sized student [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ].
        </p>
        <p>
          To realize a deployable solution, we propose to adopt knowledge distillation as the compression
mechanism – transferring the behavior of one or more teachers into a compact student that
preserves accuracy while meeting mobile constraints [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ]. In our privileged multi-teacher KD
design, an rPPG-aware temporal teacher and a depth/landmark-aware geometric teacher supervise
an RGB-only student; the student alone runs on-device, enabling better SWAP trade-offs without
changing the inference inputs. This paper is a method proposal and discussion: we specify the
PIKD design choices and a SWAP-aware evaluation blueprint for future empirical validation.
        </p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Problem formulation</title>
      <p>This work proposes a privileged-information, multi-teacher distillation scheme that trains on
multi-modal supervision (available only during training) while deploying a single RGB-only
student optimized under SWAP constraints. We formalize the task, models, objective, and
constraints below.</p>
      <sec id="sec-2-1">
        <title>2.1. Task and data</title>
        <p>Let x ∈ X RGB denote an RGB video clip (or short sequence of frames) captured by a mobile camera,
and y ∈{0 , 1 } the PAD label (0: attack, 1: bona fide). During training (only), we assume access to
privileged signals tied to the same clip:
zrPPG – temporal/physiological cues (e.g., rPPG traces or features)
zgeom – geometric cues (e.g., depth/landmarks)</p>
        <p>
          Training data thus form Dtrain=( xi , yi , zirPPG , zigeom , si)iN=1, where si indicates the source domain
(sensor, PAI type, capture condition). At deployment, only x is available, meaning that the target
domain may be unseen. Performance is evaluated with PAD metrics (APCER, BPCER, ACER) as
formalized in ISO/IEC 30107-3 [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ].
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Models</title>
        <p>



</p>
        <p>
          Student f θ : X RGB →[
          <xref ref-type="bibr" rid="ref1">0 , 1</xref>
          ] outputs a liveness score pθ ( y =1|x ). The backbone is
mobileefficient (e.g., MobileNetV3/EfficientFormer/MobileViT) to enable SWAP-constrained
deployment
Temporal teacher T ω is trained with/for rPPG-aware supervision on ( x , zrPPG), producing
logits t ω( x ) or intermediate features ϕω( x )
A geometric teacher Gψ is trained with/for depth/landmark supervision on ( x , zgeom),
producing logits gψ ( x ) or features ϕψ ( x )
        </p>
        <p>
          This setting follows Learning Using Privileged Information (LUPI) – auxiliary signals guide
learning but are absent at test time [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ] – and uses knowledge distillation (KD) to transfer teacher
behavior into the deployable student [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ]. Prior PAD work shows that depth and rPPG provide
complementary liveness cues that improve generalization [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ].
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Training objective</title>
        <p>The student is trained with standard classification on hard labels with binary cross-entropy to
establish a strong baseline decision surface. Let σ (· / T ) denote softmax at temperature T . Then,
classification loss can be described using formula 1:</p>
        <p>Lcls= 1 ∑N BCE ( yi , f θ ( xi)) (1)</p>
        <p>N i=1
where xi is the RGB input sample; yi∈{1,0 } (1 = bona fide, 0 = attack); f θ ( xi) is the student’s
predicted probability for bona fide; N is the number of training samples; BCE is Binary Cross
Entropy.</p>
        <p>We align the student’s softened outputs with both temporal (rPPG) and geometric
(depth/landmark) teachers using KL divergence; the temperature T &gt;0 and weights α , β control
the strength of each signal.</p>
        <p>Llogit= 1 ∑N (α KL(σ (t ω( xi)/ T )∥σ ( f θ ( xi)/ T ))+ β KL(σ ( gψ ( xi)/ T )∥σ ( f θ ( xi)/ T ))) (2)</p>
        <p>N i=1
where t ω( xi) and gψ ( xi) are logits from the temporal (rPPG) and geometric (depth/landmark)
teachers; C is the number of classes (for PAD, C =2); α , β ≥ 0 are distillation weights; T &gt;0 is the
temperature.</p>
        <p>To further transfer inductive biases, we could match intermediate representations: student
features may be projected and pulled toward each teacher’s features with squared L2 penalties
weighted by γ , δ:</p>
        <p>Lfeat= 1 ∑N ( γ‖Pθ ϕθ ( xi)− Pω ϕω( xi)‖22+ δ‖Pθ ϕθ ( xi)− Pψ ϕψ ( xi)‖22) (3)</p>
        <p>N i=1
where ϕθ , ϕω , ϕψ are student/teacher feature vectors; Pθ , Pω , Pψ are linear projections to a
shared feature space; ‖u‖22 denotes the squared L2 norm; γ , δ ≥ 0 are feature-distillation weights.</p>
        <p>The final objective sums the classification term, dual logit-distillation, and (optionally)
featuredistillation; only the student is deployed at inference.</p>
        <p>
          minθ L= Lcls+ Llogit + Lfeat with hyperparameters : α , β , γ , δ , T (4)
This formulation supports domain-generalization by (1) leveraging complementary privileged
cues during training [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ], and (2) allowing standard regularizers (e.g., style/augmentation schedules)
without altering the runtime model.
        </p>
      </sec>
      <sec id="sec-2-4">
        <title>2.4. SWAP constraints and optimization goal</title>
        <p>Let the measured deployment characteristics on a target device be:



</p>
        <p>L(θ) – latency (ms/inference)
W (θ) – model size or peak memory (MB)
E (θ) – energy (mJ/inference)</p>
        <p>
          Err (θ , τ ) – PAD error at operating point τ (e.g., ACER computed per [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]).
        </p>
        <p>
          Then we get the optimization view:
minθ ,τ Err (θ , τ )+ λL L(θ)/ Lmax + λW W (θ)/ W max + λE E (θ)/ Emax
(5)
where Lmax , W max , Emax encode the deployment constraints, which are device and app-specific;
the operating point τ is the decision threshold which should be selected according to [
          <xref ref-type="bibr" rid="ref1 ref6">1, 6</xref>
          ] to meet
application requirements (e.g., fixed BPCER); KD terms α , β , γ , δ act as training-time levers that
can shift the Pareto frontier toward lower error without increasing runtime cost, consistent with
the LUPI/KD paradigm [
          <xref ref-type="bibr" rid="ref3 ref5">3,5</xref>
          ]
        </p>
      </sec>
      <sec id="sec-2-5">
        <title>2.5. Evaluation targets (for future empirical work)</title>
        <p>Although this paper is a method proposal, a future study validating the approach should report:




</p>
        <p>
          Accuracy: APCER/BPCER/ACER or other metrics at specified τ per [
          <xref ref-type="bibr" rid="ref1 ref6">1, 6</xref>
          ], including
crossdataset and unseen-attack splits.
        </p>
        <p>Speed &amp; Weight: on-device latency and model size of the student.</p>
        <p>Power: energy per inference of the student (mJ/inference).</p>
        <p>Ablations: effect of each teacher (set α =0 or β =0); effect of feature-level vs. logit-level
distillation.</p>
        <p>Pareto analysis: Accuracy over Latency and Accuracy over Energy curves to illustrate
SWAP trade-offs.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Comparative analysis of known solutions</title>
      <sec id="sec-3-1">
        <title>3.1. RGB-only classifiers vs. auxiliary or privileged supervision</title>
        <p>
          Early deep FAS systems commonly treat spoof detection as binary RGB classification, which is
attractive for mobile deployment but fragile under cross-dataset shift. Surveys consistently report
that purely RGB, label-only training tends to overfit to capture artifacts and backgrounds,
degrading robustness when the camera, illumination, or PAI species changes [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          A major step forward was auxiliary/privileged supervision: Liu et al. [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] showed that training
with pixel-wise depth and sequence-level rPPG targets guides the network toward liveness cues
tied to 3D structure and physiological rhythms, boosting both intra-dataset and cross-dataset
accuracy. The catch is that these signals are not available on consumer phones at inference time.
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Multi-modal at training vs. deployment reality (LUPI)</title>
        <p>
          The Learning Using Privileged Information (LUPI) paradigm formalizes exactly this situation:
richer signals may be used during training to shape the student’s decision boundary, while the
deployed interface remains RGB-only [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ]. LUPI provides the theoretical justification for separating
training-time supervision from test-time inputs and for using teachers to accelerate and regularize
learning.
        </p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Knowledge distillation for FAS</title>
        <p>
          Knowledge distillation (KD) is the practical mechanism to compress teacher behavior into a small
student with little or no runtime overhead. Classic KD uses temperature-softened targets to
transfer “dark knowledge”, improving the accuracy of compact models. Recent FAS work applies
KD explicitly to efficiency: a head-aware Transformer KD compresses to ~5 MB while remaining
competitive, combining logit-level and feature-level terms. However, existing KD for FAS typically
relies on single-teacher RGB supervision, leaving rPPG and depth advantages on the table [
          <xref ref-type="bibr" rid="ref4 ref7">4, 7</xref>
          ].
        </p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Mobile backbones and SWAP considerations</title>
        <p>
          For on-device use, students should be instantiated with mobile-efficient backbones. MobileNetV3
[
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] is hardware-aware and widely used in production; EfficientFormer [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] demonstrates
transformer-level accuracy at MobileNet-class latency on iPhone; MobileViT [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] is a light hybrid
that brings global context with modest cost. These neural network architectures form strong, fair
baselines for SWAP-aware comparisons (latency/size/energy vs. accuracy).
        </p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Metrics and operating points</title>
        <p>
          When comparing systems, ISO/IEC 30107-3 requires reporting APCER, BPCER, ACER, and RIAPAR
at defined operating points [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. Many efficiency papers under-report operating-point specifics and
almost never report energy per inference, complicating appropriate SWAP comparisons across
models and devices. A standards-aligned, SWAP-aware protocol is therefore essential for credible
claims.
4. Suggested improvements
1. Dual-teacher, privileged KD rather than single-teacher RGB KD. Use an rPPG-aware
temporal teacher and a depth and landmark-aware geometric teacher to transfer
complementary liveness signals into an RGB-only student. This leverages the robustness
gains of auxiliary supervision (depth/rPPG) while keeping mobile inference unchanged [
          <xref ref-type="bibr" rid="ref3 ref4">3,
4</xref>
          ].
2. SWAP-aware student selection and reporting. Ground the study in one of mobile-focused
architecture based students (MobileNetV3, EfficientFormer, MobileViT) [
          <xref ref-type="bibr" rid="ref10 ref8 ref9">8, 9, 10</xref>
          ], and report
accuracy and device-measured latency, size, energy alongside ISO 30107-3 metrics [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ] at
clearly stated operating points, closing the common reporting gap.
3. Logit and feature KD with minimal overhead. Follow evidence from FAS-specific KD by
combining temperature-softened logit matching with one light feature-matching head
(single mid or high-level tap), then ablate to show the smallest configuration that still
moves the Pareto frontier [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ].
4. LUPI-consistent training schedule. Warm up on hard labels, enable KD with moderate
temperature, optionally add a small feature loss; this aligns with LUPI’s goal of accelerating
learning while preserving a simple RGB runtime interface [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ].
5. Comparative baselines that reflect deployment reality. Compare against: RGB-only students
trained with labels; RGB single-teacher KD (as in head-aware KD) [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]; and the proposed
dual-teacher privileged KD – reported under identical, ISO-aligned protocols [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ].
        </p>
        <p>Net effect: relative to RGB-only or single-teacher KD baselines, the proposed PI-KD aims to shift
the SWAP Pareto front, achieving lower accuracy metrics at fixed latency, size, and energy by
distilling temporal (rPPG) and geometric (depth) knowledge into a single deployable student. This
directly reconciles the robustness of auxiliary supervision with the constraints of mobile inference.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>5. Results &amp; discussion</title>
      <p>This paper proposed a privileged-information, dual-teacher knowledge distillation (PI-KD)
framework for mobile face anti-spoofing that explicitly targets SWAP constraints – Speed, Weight,
Accuracy, and Power. The key idea is to learn from temporal (rPPG-aware) and geometric (depth
and landmark-aware) teachers during training, while deploying only a compact RGB-only student
on the device. We detailed the training objective (hard-label BCE and two logit-KD terms, with
optional feature-KD), articulated a SWAP-aware optimization view, and outlined a
standardsaligned evaluation blueprint (ISO/IEC 30107-3 operating points; cross-dataset and unseen-attack
protocols; on-device latency, size, and energy with Pareto analysis).</p>
      <p>If proved out experimentally, PI-KD should shift the Pareto frontier, delivering lower accuracy
metrics at fixed latency, size, and energy, i.e., improved robustness without increasing deployment
cost. By decoupling rich training-time supervision from test-time simplicity, the approach
reconciles laboratory gains with real-world mobile constraints.</p>
      <p>There are some limitations, as the approach assumes access to privileged signals (or credible
surrogates) for teacher training, and introduces teacher-pretraining cost. Domain mismatch
between teachers and target environments, as well as privacy considerations for physiological and
depth data, must be managed.</p>
      <p>Immediate next steps include empirical validation on OULU-NPU, SiW-M, CASIA-FASD, and
CelebA-Spoof datasets under unified SWAP reporting; SWAP-U extensions that integrate
calibrated uncertainty/abstention for operating-point control; test-time domain handling for
training-free normalization or light adapters compatible with on-device budgets; data-centric
boosts (e.g., diffusion-generated hard negatives) to widen coverage of unseen PAIs; fairness audits
across demographics and cosmetics; and standardized energy-measurement protocols across
Android/iOS toolchains. Together, these directions aim to turn the proposed blueprint into a
deployable, reproducible, SWAP-centric path for reliable mobile PAD.</p>
    </sec>
    <sec id="sec-5">
      <title>Declaration on Generative AI</title>
      <sec id="sec-5-1">
        <title>The authors have not employed any Generative AI tools.</title>
      </sec>
    </sec>
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