Shared-Private Prototype Matching (SPPM)

• The paper introduces SPPM, a method that combines shared prototypes with private physiological signatures to calibrate pseudo-label acceptance for improved adaptation.
• SPPM is defined by a clear shared-private split, where shared prototypes represent source global structure and private signatures capture sample-specific variations.
• The matching rule employs cosine similarity thresholds to filter pseudo-labels, leading to significant accuracy improvements in cross-domain stroke EEG adaptation.

Searching arXiv for recent and directly relevant papers on Shared-Private Prototype Matching and adjacent prototype-based methods. Shared-Private Prototype Matching (SPPM) is a prototype-centric formulation in which transferable structure is represented by shared prototypes, while subject-, domain-, modality-, or sample-specific variation is retained in private representations; learning or adaptation then depends on matching across these two sides rather than relying on confidence or global feature alignment alone. In the present literature, the term is used explicitly in cross-patient stroke MI-EEG adaptation, where SPPM appears as a pseudo-label calibration mechanism that filters target predictions by combining semantic confidence with shared-private physiological consistency (Wang et al., 11 May 2026). Closely related work in federated learning, multimodal learning, domain adaptation, privacy-preserving transfer, clustering, and event relation extraction uses the same underlying ingredients—shared semantic anchors, private local structure, and prototype matching or transport—without standardizing the exact name. This suggests that SPPM is best understood as a broader methodological pattern rather than a single canonical architecture (Wang et al., 13 May 2026, Zhou et al., 3 Jun 2026, Wang et al., 30 Apr 2026, Tanwisuth et al., 2021, Lai et al., 2023).

1. Canonical SPPM formulation

The clearest explicit instantiation of SPPM is given for cross-subject unsupervised adaptation in stroke motor-imagery EEG. The source domain contains labeled trials,

$\mathcal{D}_s=\{(X_i^s,y_i^s)\}_{i=1}^{N_s},$

and the target domain contains unlabeled trials,

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$

A trial is mapped to a latent feature and class posterior by

$$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$

Training proceeds in two stages: source-supervised initialization with prototype-memory construction, followed by adaptation in which target predictions are repeatedly recomputed, scored by SPPM, and accepted only when they satisfy both semantic and physiological criteria (Wang et al., 11 May 2026).

In that formulation, SPPM is not a generic feature-alignment layer inside the encoder. It is a calibration gate in the adaptation loop. Its stated failure mode is the existence of target trials that are semantically confident according to the classifier but physiologically inconsistent with the shared class organization learned from source patients. The operational objective is therefore not merely to align target samples with class centroids, but to decide whether a pseudo-label is trustworthy enough to participate in adaptation.

2. Shared and private representations

The “shared” component in the named SPPM formulation is a source-derived prototype memory. The “private” component is a compact, patient- or sample-specific physiological signature extracted from each EEG trial. Importantly, there is no explicit latent decomposition of the form

$h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$

Instead, sharedness is instantiated by class prototypes, and privateness by a separate signature extractor $\Psi(\cdot)$ defined on EEG input space (Wang et al., 11 May 2026).

For source samples, the private signature is

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$

For target samples, the paper specifies fixed sensorimotor channel groups $\{\mathcal G_q\}_{q=1}^Q$ and computes

$$a_{j,q}=\operatorname{Avg}_{c\in\mathcal G_q}X_{j,c},\qquad d_j=|a_{j,1}-a_{j,2}|,$$

$$\rho_j=\operatorname{Norm}_2([a_{j,1},\dots,a_{j,Q},d_j]).$$

This private signature is deliberately compact and physiologically interpretable.

Class-wise shared prototypes are built only from labeled source signatures. With

$\mathcal I_k=\{i\mid y_i^s=k\},$

the class prototype is

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$0

Each class is also assigned a tolerance envelope: $\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$1

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$2

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$3

The prototype memory is therefore

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$4

This design makes the shared-private split asymmetric. The shared side is class-level and source-global; the private side is sample-level and target-specific. A plausible implication is that SPPM, in its strictest current usage, is less a full disentangled representation model than a decision mechanism that checks whether private target evidence is compatible with shared source structure.

3. Matching rule and pseudo-label calibration

The matching stage uses cosine similarity between the target private signature and the shared prototype of the predicted class. For each target sample,

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$5

and

$\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$6

Here $\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$7 is semantic confidence and $\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$8 is prototype consistency. A pseudo-label is accepted only when both pass thresholding: $\mathcal{D}_t=\{X_j^t\}_{j=1}^{N_t}.$9 The accepted pseudo-label is

$$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$0

The accepted index set is

$$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$1

This is a hard conjunction, not a soft fusion score, and the target loss is simply masked by $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$2: $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$3 Together with the source loss,

$$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$4

the total objective is

$$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$5

The reported $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$6 is $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$7, while $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$8 on XW-Stroke and $$z=f_\theta(X),\qquad p(X)=\operatorname{softmax}(g_\phi(z)),\qquad \hat y=\arg\max_k p_k(X).$$9 on 2019-Stroke (Wang et al., 11 May 2026).

Empirically, removing SPPM reduces accuracy from $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$0 to $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$1 on 2019-Stroke and from $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$2 to $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$3 on XW-Stroke. Removing dynamic pseudo-label updating causes larger drops, $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$4 and $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$5 points, respectively. These results support the intended interpretation: SPPM is primarily a calibrated pseudo-label acceptance boundary, not merely a prototype regularizer.

4. Hybrid and adjacent SPPM designs

Only one paper in the present set uses the exact label SPPM, but several others instantiate closely related shared-private prototype reasoning.

Framework	Shared side	Private side and matching role
CFSPMNet	Source class prototypes $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$6	Target private signatures $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$7; pseudo-labels accepted only if confidence and prototype consistency both hold
FedHPro	Server hyper-prototypes $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$8	Client embeddings, local prototypes, and class-wise gradients; alignment by gradient matching, HPCL, and HPAL
DFPL	Shared prototypes $h=h^{\mathrm{shared}}+h^{\mathrm{private}}.$9	Modality-specific prototypes $\Psi(\cdot)$0; prototype-level disentanglement and OT-based alignment

FedHPro replaces ordinary global prototypes with learnable server-side hyper-prototypes,

$\Psi(\cdot)$1

and learns them by matching class-wise client gradients from real samples to virtual gradients of the hyper-prototypes: $\Psi(\cdot)$2 Local embeddings are then aligned to the shared anchors through HPCL and HPAL. In SPPM language, this is a hybrid scheme: shared $\Psi(\cdot)$3 server hyper-prototypes, private $\Psi(\cdot)$4 client embeddings, local prototypes, and class-specific gradients; matching occurs both indirectly through gradient behavior and directly through contrastive and consistency losses (Wang et al., 13 May 2026).

DFPL is even closer to an explicit shared/private prototype construction. For each modality $\Psi(\cdot)$5, it learns token-level shared and specific features,

$\Psi(\cdot)$6

and extracts compact prototype sets

$\Psi(\cdot)$7

using query-based attention. Prototype diversity is enforced by

$\Psi(\cdot)$8

and cross-modal matching is performed with entropic OT: $\Psi(\cdot)$9 The paper also lightly aligns specific prototypes and adds class-semantic consistency. This is not shared-to-private matching in the narrow sense, but it is an explicit shared/private prototype learning framework with prototype-level alignment across modalities (Zhou et al., 3 Jun 2026).

5. Privacy, shared channels, and prototype quality

A major theme in adjacent SPPM literature is that the shared prototype pathway itself can be corrupted by privacy mechanisms, non-IID bias, or coarse aggregation. This is especially visible in personalized federated learning. VPDR does not define an explicit shared/private prototype decomposition or a matching loss between shared and private prototypes, but it directly targets the shared prototype communication channel under Local Differential Privacy. In its ProtoPFL abstraction, clients compute class-wise prototype sets and the server generates global prototypes that act as “global anchors in existing contrastive or classification objectives for multi-domain alignment.” The baseline releases prototypes with isotropic Gaussian noise after per-example $\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$0 clipping; VPDR instead introduces VPP and DCR so that discriminative dimensions receive less perturbation and feature norms concentrate near the clipping threshold (Wang et al., 30 Apr 2026).

The central VPP calibration condition is

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$1

under which the groupwise anisotropic mechanism is “no weaker than” the isotropic reference. With the paper’s weight construction, if

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$2

the informative subspace can be guaranteed to receive no more noise than the isotropic $\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$3-LDP baseline. DCR further regularizes clipped versus unclipped predictions through EMA teacher-student distillation. Relative to SPPM, VPDR is best read as a complementary privacy-preserving release module for the shared side, not as a full SPPM method.

Differentially Private Prototype Learning reaches a similar conclusion from a different direction. It uses a publicly pre-trained encoder as a shared embedding space and constructs private class representatives either as DP class means,

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$4

or as DP-selected public examples matched to private class embeddings. This yields private class prototypes in a shared public space, but not a jointly learned shared-private prototype bank. For SPPM, the methodological lesson is that prototype release and prototype matching can be privatized directly, without privatizing full iterative fine-tuning (Wahdany et al., 2024).

6. Broader prototype literature, misconceptions, and plausible directions

Prototype matching alone is not equivalent to SPPM. Prototype-oriented Conditional Transport assumes closed-category unsupervised domain adaptation with a single prototype set $\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$5, where classifier weights serve as prototypes and target features are aligned by bidirectional transport,

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$6

The paper explicitly notes that “source-private” there means raw source data are unavailable during adaptation, not that source-private classes are modeled. It is therefore a prototype-matching precursor, not an explicit shared/private prototype method (Tanwisuth et al., 2021).

The same caution applies to source-private clustering and universal DA. PCD learns shared global prototypes with domain-specific cluster proportions

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$7

and transfers knowledge by cluster-label distillation rather than explicit prototype-to-prototype alignment. MemSPM, by contrast, argues that the shared side should itself be decomposed into multiple sub-prototypes, represented by a learnable memory

$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$8

with cosine-similarity addressing and sparse top-$\rho_i^s=\Psi(X_i^s),\qquad \|\rho_i^s\|_2=1.$9-style retrieval. It improves UniDA, OSDA, and PDA, but it still does not learn a dedicated target-private prototype bank (Tanwisuth et al., 2023, Lai et al., 2023).

ProtoEM shows that prototype matching can be highly effective even outside adaptation. It builds one prototype per event-relation label, refines inter-prototype dependencies with a GCN, and classifies new event pairs by negative Euclidean distance to the prototypes. Yet it does not factor prototypes into shared and private components. This supports a useful misconception check: not every prototype matcher is an SPPM method, even when prototypes interact or when multiple relation families are jointly modeled (Hu et al., 2023).

Taken together, the literature points toward a more general synthesis. A plausible next-generation SPPM system would combine explicit shared/private prototype decomposition, multi-anchor shared sub-prototypes rather than one centroid per class, transport- or contrastive-style matching, and privacy-aware shared prototype release. The current record already separates these ingredients across papers: CFSPMNet contributes calibrated shared-private pseudo-label gating, FedHPro stabilizes the shared anchors, DFPL makes the shared/specific prototype decomposition explicit, VPDR protects the shared release path, and MemSPM shows that coarse shared prototypes are often insufficient under severe concept shift (Wang et al., 11 May 2026, Wang et al., 13 May 2026, Zhou et al., 3 Jun 2026, Wang et al., 30 Apr 2026, Lai et al., 2023).