Sinkclass Autoencoder for Quantum Dimensionality Reduction

• Sinkclass autoencoder is a dimensionality reduction architecture that integrates Sinkhorn divergence with label-driven regularization to yield bimodal latent embeddings for quantum applications.
• It employs a deep encoder-decoder framework with explicit noise and label branches to compress 67-dimensional Higgs boson data into a 16-dimensional, discriminative representation.
• Empirical results show that, with optimized hyperparameters, Sinkclass outperforms variational and classifier autoencoders, achieving a QSVM AUC of up to 0.74.

The Sinkclass autoencoder is a dimensionality reduction architecture designed to facilitate quantum machine learning, particularly for high-dimensional data sets outside the present reach of quantum algorithms. By integrating optimal-transport regularization (Sinkhorn divergence) with explicit label-driven latent space separation, the Sinkclass autoencoder enhances class-discriminative, low-dimensional embeddings suitable for subsequent quantum support vector machine (QSVM) classification. Developed in the context of Higgs boson detection at the LHC with 67 input features, it enables quantum classifiers to operate on compressed yet maximally informative inputs, outperforming variational and classifier autoencoders as well as conventional classical reduction techniques (Odagiu et al., 1 Dec 2025).

1. Architectural Overview

The Sinkclass autoencoder processes datasets with large feature counts, exemplified by 67-dimensional feature vectors normalized to $[0,1]$. Its network configuration is composed of four major components:

• Encoder ($\mathscr{E}_\omega$): A stack of six fully-connected layers with decreasing dimensionality $$[64 \rightarrow 52 \rightarrow 44 \rightarrow 32 \rightarrow 24 \rightarrow 16]$$, using implicit ReLU activations. The mapping $x\in\mathbb{R}^{67} \to z\in\mathbb{R}^{16}$ produces compact latent representations.
• Conditional Latent-Space Regularizer ("Noise Generator"):
  • Gaussian branch: Two layers $[64 \rightarrow 128]$, taking noise $\xi \sim \mathcal{N}(0,I_{16})$.
  • Label branch: One layer $[64]$, with the true class bit ($0$ or $1$) as input.
  • Fusion network: Concatenates outputs and propagates through three layers $[256 \rightarrow 192 \rightarrow 16]$, yielding the “target” latent vector $z_{\rm target}$.
• Decoder ($\mathscr{D}_\rho$): Six fully-connected layers, mirroring the encoder $$[16 \rightarrow 24 \rightarrow 32 \rightarrow 44 \rightarrow 52 \rightarrow 64 \rightarrow 67]$$, reconstructing $\hat x$ from $z$.
• Classifier ($\mathscr{C}_\upsilon$): A conventional feed-forward module attached to $z$, predicting signal versus background with a sigmoid output, structurally analogous to that in a “Classifier AE”.

2. Loss Function Composition

The Sinkclass objective incorporates three contributions:

• Reconstruction error ($\mathcal{L}_{\rm MSE}$):

$$\mathcal{L}_{\rm MSE} = \frac{1}{N}\sum_i \bigl\|x^{(i)} - \hat x^{(i)}\bigr\|_2^2$$

• Binary cross-entropy classifier loss ($\mathcal{L}_{\rm BCE}$):

$$\mathcal{L}_{\rm BCE} = -\frac{1}{N}\sum_i \Bigl[y^{(i)}\log p^{(i)} + (1-y^{(i)})\log(1-p^{(i)})\Bigr]$$

• Sinkhorn divergence ($\mathcal{L}_{\rm SH}$):

Entropically regularized optimal-transport divergence calculated between the batch of encoded latent vectors $\{z^{(i)}\}$ and the batch of generator outputs $\{z_{\rm target}^{(i)}\}$ (see Patrini et al. 2020 for mathematical detail).

The total loss minimized is:

$$\mathcal{L}_{\rm SCAE} = \alpha\,\mathcal{L}_{\rm SH} + \beta\,\mathcal{L}_{\rm BCE} + \mathcal{L}_{\rm MSE}$$

The hyperparameters $\alpha$ and $\beta$ determine the regularization/classification trade-off.

3. Comparison with Alternative Representations

Ablation studies and direct architectural comparisons reveal the differentiating theoretical and empirical features of Sinkclass AE:

• Standard AE involves only $\mathcal{L}_{\rm MSE}$, resulting in unstructured latent space.
• Variational AE substitutes $\mathcal{L}_{\rm SH}$ with a Kullback-Leibler regularizer, enforcing strict unimodal (Gaussian) latent space, which can lead to signal/background overlap.
• Classifier AE includes $\mathcal{L}_{\rm BCE}$, promoting class-separation in the latent encoding but at the expense of substantial reconstruction quality loss due to absent distributional regularization.
• Sinkclass AE applies Sinkhorn divergence to softly guide the encoder’s output toward the learned, label-conditioned generator manifold ($z_{\rm target}$), and jointly employs $\mathcal{L}_{\rm BCE}$ to assure class separation. This mechanism yields a bimodal, disentangled latent representation that maintains both discriminativity and reconstruction fidelity.

4. Training Protocol and Hyperparameterization

• Dataset partitioning: 1.15 million samples for training, 0.144 million each for validation and test (all normalized).
• Pre-filtering: Physics-driven event selection based on $p_T$, $\eta$, and object multiplicity.
• Optimization: Adam optimizer with a learning rate of $0.001$, batch size $128$, and early stopping on validation loss.
• Hyperparameter selection:
  • Step 1: Set $\alpha=\beta=1$ to optimize learning rate and batch size, yielding $(0.001,128)$.
  • Step 2: Fix learning rate and batch, perform grid search on $(\alpha, \beta)$ for optimal unweighted MSE or BCE.

5. Empirical Evaluation and Benchmarking

The performance of the Sinkclass autoencoder is assessed via downstream QSVM AUC on the $16$D reduced representations. Results across five test splits ($3600$ events per split) are summarized:

Model variant	$\alpha, \beta$	QSVM AUC
Sinkclass (MSE-opt)	0.0008, 0.90	0.50 ± 0.01
Sinkclass (BCE-opt)	0.20, 0.02	0.74 ± 0.01
Classifier AE (BCE-opt)	0.60 (only $\mathcal{L}_{\rm BCE}$ weighted)	0.72 ± 0.01
RBM (classical baseline)	—	0.65 ± 0.016
PCA / ICA / …	—	0.53–0.60

• Best QSVM AUC: $0.74 \pm 0.01$ is achieved by Sinkclass AE tuned for BCE minimization.
• Hyperparameter sensitivity:
  • $(\alpha=0.0008,\,\beta=0.90)$ yields minimal reconstruction error (MSE), but QSVM AUC collapses to $0.50$.
  • $(\alpha=0.20,\,\beta=0.02)$ produces a maximal separation in latent space and optimal QSVM AUC, with a slight increase in reconstruction error.

6. Theoretical Underpinnings and Latent Structure

The Sinkhorn regularization ($\mathcal{L}_{\rm SH}$) ensures that the encoder’s latent distribution aligns via a learnable, non-linear transport from a simple base (Gaussian plus label information), as opposed to strictly matching a fixed Gaussian prior. This approach enables preservation of class-conditioned multimodal structure in latent space, mitigating the mode-collapse or overlap observed in variational autoencoders. The BCE classifier term ($\mathcal{L}_{\rm BCE}$) further drives the system toward a bimodal latent embedding, mapping signal and background events into spatially disjoint clusters. This structured latent space is well suited for quantum embeddings, particularly the $16$-qubit regime, thereby translating to improved downstream QSVM discrimination.

7. Applications and Broader Significance

The Sinkclass autoencoder’s design relaxes constraints that often limit variational and classifier autoencoders in quantum-classifier settings. By delivering strong class separation and information retention during dimensionality reduction, it opens quantum machine learning workflows to a wider class of high-dimensional scientific datasets, exemplified in LHC signal-versus-background searches. The recipe provided for effective regularization and hyperparameter balancing directly extends the reach of quantum classifiers and suggests potential utility in broader scientific and industrial applications where quantum resources are bottlenecked by feature dimensionality (Odagiu et al., 1 Dec 2025).