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QiMLP: Quantum-inspired Multilayer Perceptron with Strong Correlation Mining and Parameter Compression
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Proposes QiMLP, an MLP whose layers use Kronecker-product weight and bias matrices inspired by multi-body quantum systems, claiming strong feature-correlation mining and hundreds-fold parameter compression on MNIST, CIFAR-10, IMDb and 20NewsGroups.
Problem
Standard MLP neurons use weighted summation that struggles to capture strong correlations among features and carries heavy parameter over-configuration.
Approach
Replace the dense weight matrix and bias of a neuron layer with Kronecker products of small learnable matrices (multi-body quantum system operators), giving a product-form parameterization that is claimed to model strong correlations and compress parameters; strong correlation is quantified via von Neumann entropy-based measure.
Key results
- On MNIST, the two-body QiMLP outperforms the classic MLP in accuracy while using far fewer parameters; three- and four-body variants lose accuracy due to over-compression.
- Paper claims QiMLP reduces parameter count by more than 200 times versus a same-structure classic MLP (reported as hundreds of times).
- On IMDb and 20NewsGroups, two-body QiMLP is reported to beat classic MLP, while three-body is similar to MLP; strong-correlation proportion grows in deeper layers.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace classic MLP layers with two-body QiMLP layers (ablation) | QiMLP · MNIST test | accuracy | Helped |
| Replace classic MLP layers with three-body QiMLP layers (ablation) | QiMLP · MNIST test | accuracy | No clear effect |
| Replace classic MLP layers with four-body QiMLP layers (ablation) | QiMLP · MNIST test | accuracy | Hurt |
| Increase the number of repeated reconstructed weight matrices (k) (ablation) | QiMLP · MNIST | accuracy | Helped |
| Increase the number of repeated reconstructed weight matrices (k) (ablation) | Four-body QiMLP · MNIST | accuracy | Mixed |
| Replace classic MLP layers with two-body QiMLP layers (ablation) | QiMLP · CIFAR-10 test | accuracy | Helped |
| Increase the number of repeated reconstructed weight matrices (k) (ablation) | QiMLP · CIFAR-10 | accuracy | No clear effect |
| Replace classic MLP layers with two-body QiMLP layers (ablation) | QiMLP · IMDb test | accuracy | Helped |
| Replace classic MLP layers with three-body QiMLP layers (ablation) | QiMLP · IMDb test | accuracy | No clear effect |
| Replace classic MLP layers with two-body QiMLP layers (ablation) | QiMLP · NewsGroups test | accuracy | Helped |
| Replace classic MLP layers with three-body QiMLP layers (ablation) | QiMLP · NewsGroups test | accuracy | No clear effect |
| Use Kronecker-product parameterization instead of classic MLP weights | QiMLP · Real models | parameter count: more than 200 times | Helped |
Surprising findings
- Three- and four-body QiMLP variants underperform the classic MLP because the parameter count becomes too small, showing over-compression limits accuracy.
- Increasing the repetition parameter k did not improve CIFAR-10 accuracy, which the authors attribute to over-compression.
Limitations
- Strong-correlation measurement for multi-body systems is only analyzed for two-body QiMLP because mutual information is hard to compute for multi-body systems.
- Smaller-body variants compress parameters too aggressively and lose accuracy, so the compression/accuracy trade-off is not resolved.
- Strong correlation is defined statistically and measured via a trained approximation of the Kronecker-product form, which is an indirect proxy.
Experimental setup
Datasets: MNIST CIFAR-10 IMDb 20NewsGroups
Benchmarks: MNIST CIFAR-10 IMDb 20NewsGroups
Metrics: accuracy number of parameters strong correlation proportion
Baselines: classic MLP BERT+MLP
Builds on: multilayer perceptron tensor decomposition beta-VAE BERT
Closest papers by meaning
- Winning Lottery Tickets in Neural Networks via a Quantum-Inspired Classical Algorithm (NeurIPS 2026 · similarity 0.84)
- On the Relation between Trainability and Dequantization of Variational Quantum Learning Models (ICLR 2025 · similarity 0.84)
- Circuit Design and Efficient Simulation of Quantum Inner Product and Empirical Studies of Its Effect on Near-Term Hybrid Quantum-Classic Machine Learning (CVPR 2024 · similarity 0.84)
- Generating Universal Adversarial Perturbations for Quantum Classifiers (AAAI 2024 · similarity 0.83)
- Rethink the Role of Deep Learning towards Large-scale Quantum Systems (ICML 2025 · similarity 0.83)
- Quantum Implicit Neural Representations (ICML 2024 · similarity 0.83)
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