blueqat Inc., in collaboration with the Marketing Technology Center, the R&D division of Hakuhodo DY Holdings Inc. (Minato-ku, Tokyo; President and CEO: Masayuki Mizushima), and the laboratory of Professor Keigo Arai at Tokyo University of Science, which has extensive experience in the field of quantum sensing, has developed a novel quantum-inspired algorithm capable of accurately estimating the brain’s electrical activity from magnetoencephalography (MEG) data. The effectiveness of this algorithm has been successfully demonstrated.
1 Introduction
Magnetoencephalography (MEG) is a non-invasive neuroimaging technique that captures magnetic
fields generated by electrical neural currents in the brain. The inverse problem involves estimating
the location, orientation, and strength of these electrical current dipoles—point sources representing
localized neural activity—from these measurements. Although the forward problem (computing
magnetic fields from known electrical current sources governed by Biot-Savart law) is well-posed and
straight foward, however the inverse is ill-posed, since multiple source configurations can produce
similar measurements, especially with limited data and noise. (Figure 1) Some source estimation methods, particularly
those involving high-dimensional source spaces or iterative optimization, are computationally
demanding[PA21]. This can limit real-time applications. Deep learning methods offers a solution with
computation times reduced to milliseconds, highlighting the traditional methods’ limitations. We also
utilise tensor network decomposition to make the model size smaller and faster without any drop in
accuracy.
2 Methods
2.1 Dataset Creation
For the initial work, we started from the 2-dimensional distribution of current dipoles in a grid (Ex,Ey).
Magnetic field values (Bx,By,Bz) were measured on a 2-D plane parallel to the plane of current dipoles,
fixed at a certain offset. Up to a maximum of 10 current dipoles were randomly placed in the 64 × 64
square grid. We used a dataset size of 50,000 samples.
2.2 Model Architecture
A U-Net based model architecture was used for training. Using tanh activation layers resulted in better
normalization and the required range of dipole strength. The model used 34M trainiable parameters,
which were reduced to 25M parameters after tensorisation. The measured magnetic field is used as
input and the outputs are the current dipole predictions. (Figure 2)
2.3 Tensor Decomposition
Tensor networks, originally developed for quantum physics and mathematics, have emerged as a promising
framework in machine learning, particularly for handling high-dimensional data efficiently. CP
decomposition especially compresses convolutional layers by approximating weight tensors with lowerrank[
YL24]. (Figure 3) This reduces the model size, enabling deployment on resource-constrained devices like
mobile phones or embedded systems. In our case, this will help in real-time current dipole source
localization using less compute resources than previous methods.
2.4 Results
Our model is able to reproduce the positions of current dipoles exactly and the magnitude within
tolerable error limits shown in Fig. 4.
We performed CP-decomposition on the least sensitive convolution layer and were able to reduce
the parameters from 34M to 25M, providing a reduction of 27.32% parameters. This also leads to an increase in inference speed ranging from 7-8%. The difference in Froebnius norm between the predicted Magnetic Fields of the normal model and the tensorised model was < 10−5, with sometimes the tensorised model having better accuracy.
3 Conclusion and Future Work
In this work we explored the validation of using Machine Learning and Tensor Network decomposition
as a tool to achieve low-cost and real-time localization of current dipoles from MEG data. In the
current demonstration, the effectiveness of the developed model was confirmed using a 2D model,
with future plans to expand and validate it using more complex 3D models. This technology marks an
important step toward the realization of brain-machine interfaces (BMI). Non-invasive measurement of
brain activity and high-precision analysis of those signals are critical components for BMI development,
and this research contributes to that goal from a software perspective.
References
[LGR+15] Vadim Lebedev, Yaroslav Ganin, Maksim Rakhuba, Ivan Oseledets, and Victor Lempitsky. Speeding-up convolutional neural networks using fine-tuned cp-decomposition, 2015.
[PA21] Dimitrios Pantazis and Amir Adler. Meg source localization via deep learning. Sensors, 21(13), 2021.
[YL24] Chenbin Yang and Huiyi Liu. Stable low-rank cp decomposition for compression of convolutional neural networks based on sensitivity. Applied Sciences, 14(4), 2024.
More results
Figures 5 to 7 present supplementary data supporting the effectiveness of this model.
