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NOBLE - Neural Operator with Biologically-informed Latent Embeddings to Capture Experimental Variability in Biological Neuron Models
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Introduces NOBLE, a 1D Fourier neural operator conditioned on NeRF-style sinusoidal embeddings of interpretable neuron features (threshold current and threshold slope), trained on synthetic HoF neuron-model data to predict somatic voltage responses with trial-to-trial variability and a 4200x speedup over the numerical solver.
Problem
Bio-realistic PDE-based neuron models are deterministic, computationally expensive to build and simulate, and cannot capture the intrinsic trial-to-trial variability observed in experimental electrophysiology recordings; prior deep learning surrogates are deterministic and retrained per model.
Approach
Learn a single neural operator mapping a continuous latent embedding of interpretable neuron features (I_thr, s_thr from the F-I curve, sinusoidally encoded NeRF-style with frequencies modulated by the features) plus the current injection to somatic voltage, so that sampling and interpolating in the latent space yields an ensemble of novel bio-realistic neuron models.
Key results
- A single NOBLE model reaches a relative L2 voltage test error of 2.18% on training HoF models and 1.92% on held-out test models with embedded (I_thr, s_thr), versus 12.1% with no embedding.
- NOBLE generates 10,000 predictions in 8.59 s at batch size 1000 versus about 36,200 s for the numerical solver, a speedup of roughly 4200x.
- Fine-tuning with a sag-amplitude feature loss reduces sag amplitude relative L2 error from 19.2% to 9.6% while keeping voltage error near 0.035%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add both I_thr and s_thr biologically informed embeddings (ablation) | NOBLE · PVALB test set, HoF train models | relative L2 error (voltage): 2.73% -> 1.92% (I_thr alone); 2.83% -> 1.92% (s_thr alone) | Helped |
| Remove all feature embeddings (ablation) | NOBLE · PVALB test set, HoF train models | relative L2 error (voltage): 1.92% -> 12.1% | Hurt |
| Use only one embedded feature, I_thr or s_thr (ablation) | NOBLE · PVALB test set, HoF train models | relative L2 error (spike-related features): Spikecount: 3.1% -> 4.4% (I_thr) or 4.9% (s_thr); AP1 width: 27% -> 107% (I_thr) or 233% (s_thr) | Hurt |
| Add AHP_depth embedding (ablation) | NOBLE with I_thr and s_thr embeddings · PVALB test set, HoF train models | relative L2 error (AP1 width): 27% -> 22% | Helped |
| Add AHP_depth embedding (ablation) | NOBLE with I_thr and s_thr embeddings · PVALB test set, HoF train models | relative L2 error (voltage): 1.92% -> 2.16% | Hurt |
| Reduce training diversity from 50 to 20 HoF models (ablation) | NOBLE · PVALB held-out test models | relative L2 error (spikecount): 9.2% -> 45% | Hurt |
| Reduce training diversity from 50 to 20 HoF models (ablation) | NOBLE · PVALB held-out test models | relative L2 error (voltage): 11.7% -> 10.6% | No clear effect |
| Fine-tune on negative, subthreshold stimuli without feature-specific loss (ablation) | NOBLE · PVALB test set, sag_amplitude | relative L2 error (sag_amplitude): 69.6% -> 19.2% | Helped |
| Add sag_amplitude-specific loss with λ=25 (ablation) | Fine-tuned NOBLE · PVALB test set, sag_amplitude | relative L2 error (sag_amplitude): 19.2% -> 9.6% | Helped |
| Use batch size 1000 for inference (ablation) | NOBLE · 10,000 PVALB predictions | generation time: 157 seconds -> 8.59 seconds | Helped |
Surprising findings
- Without any feature embedding, NOBLE fails to predict any firing responses, indicating embeddings are necessary for spiking behavior.
- Direct interpolation between PDE model parameters yields traces deviating significantly from experimental data, whereas latent-space interpolation remains bio-realistic.
Limitations
- Limited to single-neuron settings with square DC step current inputs.
- AP1_width relative error is high (27% to 350%+) due to sensitivity of half-width measurement to small misalignments.
- Ensemble variability could not be directly validated against experimental trial-to-trial data, since only a single trace per amplitude is available.
Experimental setup
Datasets: synthetic HoF PVALB neuron simulations (50 train, 10 test models) VIP neuron HoF models human cortex experimental patch-clamp recordings
Metrics: relative L2 error spikecount error AP1 width error mean AP amplitude error steady state voltage error speedup over numerical solver
Baselines: numerical solver (NEURON-based PDE simulation) HoF PDE models
Builds on: Fourier Neural Operator NeRF positional encoding physics-informed neural operator
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