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Quantum-Inspired Hybrid Neural Networks for Neural Decoding: A Controlled Ablation Study of Learnable Quantum Sidecar Integration
Diana Legziel Levy, Menachem Finkelstein, Peter Chin, Eilon Vaadia, Sarel Cohen
TL;DR
The paper asks whether a shallow PQC sidecar can reproducibly improve representation geometry in neural decoding beyond accuracy alone. It evaluates a controlled 4-qubit hybrid ResNet-50 system and finds structural reorganization, reproducible geometry improvements, and a capacity-limited quantum contribution.
Problem
Neural decoders can achieve high accuracy while learning geometrically suboptimal representations, motivating tests of whether PQC sidecars improve representation geometry.
Method
The study integrates a 4-qubit residual PQC sidecar into ResNet-50 for 31-class imagined-handwriting decoding and compares controlled variants using fixed splits, initializations, and optimizers.
Results
Backbone-gradient training reduces Linear CKA similarity to baseline features by Δ = −0.025 in 4/4 seeds and improves accuracy in 3/4 seeds, while geometry-aware training yields reproducible geometry gains.
Takeaways & Limitations
The hybrid sidecar measurably reorganizes representations, but the reproducible geometry attractor and topology-independent outcome indicate that the shallow circuit’s contribution is capacity-constrained.
Takeaways & Limitations
The conclusions are bounded by noiseless statevector simulation with 4 qubits and a shallow sidecar whose restricted representational capacity limits its contribution relative to the 23M-parameter backbone.
Abstract
from arXiv · showhide
We study parameterized quantum circuits (PQCs) integrated as residual sidecar modules within a ResNet-50 backbone for 31-class neural population decoding---imagined handwriting classification from multi-neuron spike rasters. Under strictly controlled conditions (fixed data splits, seeds, and optimizer), we compare four model variants: baseline, quantum sidecar with frozen input projection, quantum sidecar with backbone-gradient-trained projection, and a measurement-guided variant that aligns angle encodings with circuit measurement outcomes. The backbone-gradient variant improves accuracy in 3/4 seeds (+0.19% mean, 95% CI [-1.10%, +1.48%]) and consistently reduces Linear CKA similarity to baseline features ($Δ=-0.025$, 4/4 seeds), indicating genuine structural reorganization of representations. A nine-variant ablation identifies simple shallow architectures as the most effective and reproducible configuration. Measurement-guided training consistently improves representation geometry without reducing accuracy. All results use noiseless statevector simulation on 4 qubits, a regime chosen to reflect the practical constraints of current near-term superconducting hardware; no quantum computational advantage over classical methods is claimed.
1 Introduction
The paper asks whether a shallow PQC sidecar can reproducibly alter representation geometry in neural decoding while operating alongside a strong classical backbone. It evaluates this under controlled conditions and finds consistent geometric changes despite only marginal aggregate accuracy improvements.
- Brain-machine-interface decoders need geometrically strong representations in addition to high accuracy for cross-session robustness.
- PQC sidecars provide topology-constrained global feature mixing through quantum entanglement, distinct from learned MLP correlations.
- A 4-qubit residual sidecar is evaluated on 31-class imagined-handwriting neural decoding with fixed splits, initialization, and optimizer across variants.
- The hybrid sidecar consistently changes representation geometry while producing only marginal aggregate accuracy improvements.
2 Related Work
Prior work covers deep-learning neural decoding, PQCs as structured function classes, and hybrid quantum-classical pipelines. This paper focuses on residual sidecars and controlled ablations of geometric effects and gradient connectivity.
- Deep-learning BMI decoders treat neural population activity as spatiotemporal signals, but geometric representation quality is rarely evaluated.
- PQC research studies structured function classes and quantum feature maps, while barren-plateau concerns motivate shallow 4-qubit designs.
- Prior hybrid architectures embed PQCs as feature-map or kernel layers; this work studies differentiable residual sidecars within deep neural networks.
- The controlled ablations examine geometric effects and gradient connectivity beyond aggregate accuracy.
3 Methods
The method inserts a topology-mixed quantum residual transform into ResNet-50 features, projects pooled features into two 4-angle vectors, and maps circuit measurements back to the backbone. Experiments compare placement, topology, projection training, and simulation constraints.
- Hybrid Architecture: The quantum sidecar is attached as a residual transform at ResNet-50 layer3, where subsequent backbone layers process its output.Layer3 outperformed layer4 and final pooled-feature placement in this dataset and model.
- Hybrid Architecture: Layer3 placement permits indirect influence on final representations through later backbone processing, unlike later placements that restrict correction.
- Circuit Topologies and Mixing: A learned soft mixture combines chain and star circuit topologies through logits α.
- Quantum Encoding: Global average pooling produces a 1024-dimensional feature vector, which two learned projections map to 4-dimensional circuit angle vectors.
- Quantum Encoding: Each angle vector drives a fixed-topology 4-qubit circuit, whose qubit-wise Z expectations are projected back to 1024 dimensions.
- Gradient Connectivity: Frozen projections remain at random initialization, whereas BackboneGrad updates them only through the classical backbone pathway because the quantum simulation is non-differentiable.
- Experimental Scope: All experiments use noiseless statevector simulation and make no claim of quantum advantage.
4 Experimental Setup
The study uses fixed neural-decoding data, a standardized ResNet-50 training protocol, four independent seeds, and metrics spanning accuracy, representation geometry, similarity, and topology preference.
- Dataset: The dataset contains 31-class imagined-handwriting neural decoding from multi-neuron spike rasters for subject T5.Fixed stratified splits contain 30,524 training, 3,816 validation, and 3,816 test samples.
- Training Protocol: ResNet-50 is ImageNet-pretrained and trained with AdamW, OneCycleLR, weighted cross-entropy, label smoothing, batch size 128, and 100 epochs.All model variants use identical hyperparameters.
- Training Protocol: Four independent seeds—42, 333, 777, and 123—are used under fixed experimental settings.
- Metrics: Evaluation includes top-1 accuracy, macro-F1, Linear CKA, the inter/intra cosine centroid ratio R, and topology mixing weight πstar.
5 Results
Across controlled comparisons and ablations, the quantum sidecar most consistently changed representation geometry rather than aggregate accuracy. Results also identify a 4-qubit capacity ceiling, optimization sensitivity, and measurement-guided training as a geometry-improving alternative without an accuracy reduction.
- Four-Variant Comparison Across Seeds: +0.19% mean accuracy improvement occurred in 3 of 4 seeds, but the 95% CI spanned zero, so differences were not statistically significant at n = 4.Seed 123 was the exception, reflecting an uncooperative coupled-optimization equilibrium.
- Four-Variant Comparison Across Seeds: −0.025 mean ΔCKA (95% CI [−0.035, −0.013]) separated BackboneGrad from Frozen in all four seeds, indicating consistent structural reorganization.Lower Linear CKA indicates greater structural reorganization.
- Four-Variant Comparison Across Seeds: πstar = 0.579±0.021 for BackboneGrad across all four seeds, whereas Frozen remained near chance at πstar ≈0.504.The star-topology preference emerged when the projection co-adapted with the backbone.
- Four-Variant Comparison Across Seeds: 1.66× higher cross-seed accuracy variance for BackboneGrad than baseline accompanied joint optimization of the backbone and sidecar.Variance was 0.552% for BackboneGrad versus 0.332% for baseline; Frozen variance was 0.344%.
- Identifying the Bottleneck: >99.7% cosine similarity between qubit inputs persisted across projection architectures, and orthogonalized angle inputs produced no improvement.Richer projections, attention, and full XYZ Pauli readout did not overcome the observed limitation.
- Identifying the Bottleneck: R = 3.799 ± 0.082 under geometry-aware training, with a 95% CI excluding the BackboneGrad reference of 3.00, but explicit angle-space optimization incurred an accuracy cost.The 4D kissing-number bound allows only approximately 24 mutually separated directions, fewer than the 31 classes.
- Identifying the Bottleneck: Measurement-guided training improved R consistently across four seeds while accuracy remained unchanged, with mean +0.04% and a 95% CI spanning zero.Its alignment loss decreased during training, unlike the geometry angle loss, and it consistently favored chain over star entanglement.
- Identifying the Bottleneck: +0.57% accuracy from the U-Net sidecar left geometry nearly identical to the classical baseline, but additional multi-seed evaluation is needed.The U-Net and BackboneGrad reference used batch = 64 and were not directly comparable to other rows.
6 Discussion
The ablation identifies circuit capacity as the binding constraint, while backbone-coupled training reorganizes representations and consistently favors a star topology.
- Circuit capacity as the binding constraint: γ = 0.003 shows that the optimizer uses the 4-qubit circuit as a nearly negligible residual contribution to the 23M-parameter ResNet.Exact parameter-shift gradients indicate the limitation is representational capacity rather than optimization instability or gradient disconnection alone.
- Topology preference and neural population coding: πstar = 0.579 ± 0.021 across 4/4 unfrozen seeds reveals a reproducible star-topology preference under backbone-coupled training.The preference aligns with a hub-and-spoke organization associated with dominant coordinating neurons in the decoded population.
- Representation geometry and neural drift: ΔCKA = −0.025 across 4/4 seeds provides consistent evidence of structural reorganization despite marginal accuracy differences.The geometry-aware ablation further separates representation changes from topology preference: geometry improves reliably while the star preference becomes effectively random.
- Representation geometry and neural drift: The 4-dimensional angle space cannot provide mutually separated directions for all 31 classes, establishing a hard capacity ceiling for geometry optimization.The kissing-number bound allows approximately 24 mutually separated directions in 4D, fewer than the task’s 31 classes.
7 Conclusion
Under strict controls, a nine-variant ablation shows that backbone-gradient coupling reorganizes representations and reveals a reproducible topology preference, while shallow 4-qubit capacity limits the sidecar’s contribution.
- Main findings: ΔCKA = −0.025 across 4/4 seeds shows structural reorganization, while accuracy improves directionally in 3/4 seeds with a confidence interval spanning zero.The backbone-gradient variant also has 1.66× higher cross-seed variance than baseline.
- Main findings: πstar = 0.579 ± 0.021 under backbone-coupled training versus 0.504 ± 0.000 with frozen weights reveals an emergent star-topology preference.The preference is consistent across four seeds and is linked to the hub-and-spoke coalition structure of the decoded neural population.
- Limitations and implications: γ = 0.003 and the failure to separate 31 classes in 4-dimensional angle space identify circuit capacity as the binding limitation.The paper places this ceiling in the specific shallow 4-qubit sidecar and present architectural regime, not in hybrid architectures generally.
- Main findings: R = 3.799 ± 0.082 and CKA = 0.598 ± 0.014 form a reproducible geometry attractor while topology preference is erased.Both reported 4-seed confidence intervals exclude the BackboneGrad reference.
- Limitations and implications: The shallow 4-qubit sidecar reaches its contribution ceiling relative to the strong 23M-parameter backbone, motivating larger circuits and tighter quantum-classical coupling.The proposed next steps include co-optimizing projection and circuit angles and rewarding non-redundant quantum structure.