An Algorithm Board in Neural Decoding

TL;DR

This work investigates a symmetry-based phenomenon in neural decoding, showing that unsupervised decoding trajectories exhibit a central-axis symmetry with ground-truth trajectories and that a correction process using binary space encoding ($N$-level subspaces) progressively aligns predictions with ground truth. Through EM-based unsupervised decoding and a correction mechanism, the authors demonstrate that increasing $N$ yields improved fit (e.g., $R^2$ rising toward 1 and PCC approaching 1) and convergence of distributional metrics (KL/JS towards 0), while the PDFs of predicted positions evolve from a single Gaussian to a mix of $2^N$ Gaussian-like components. Qualitative analyses reveal the predicted position distributions become multi-Gaussian with more spikes in the noise PSDs as $N$ grows, and the PSDs of predictions stabilize. An algorithm board, inspired by the Galton board, is proposed as a mathematical foundation for the discovered symmetry, suggesting brain-like data processing patterns and guiding the design of future symmetry-aware decoding systems.

Abstract

Understanding the mechanisms of neural encoding and decoding has always been a highly interesting research topic in fields such as neuroscience and cognitive intelligence. In prior studies, some researchers identified a symmetry in neural data decoded by unsupervised methods in motor scenarios and constructed a cognitive learning system based on this pattern (i.e., symmetry). Nevertheless, the distribution state of the data flow that significantly influences neural decoding positions still remains a mystery within the system, which further restricts the enhancement of the system's interpretability. Based on this, this paper mainly explores changes in the distribution state within the system from the machine learning and mathematical statistics perspectives. In the experiment, we assessed the correctness of this symmetry using various tools and indicators commonly utilized in mathematics and statistics. According to the experimental results, the normal distribution (or Gaussian distribution) plays a crucial role in the decoding of prediction positions within the system. Eventually, an algorithm board similar to the Galton board was built to serve as the mathematical foundation of the discovered symmetry.

Figures (10)

• Figure 1: First, neural data $\textbf{S}_k$ are decoded through an unsupervised EM algorithm to obtain predicted location $\hat{z}^0_{1:K}$. Then, this unsupervised predicted positions and the ground-truth trajectory ($z^0_{1:K}$) are approximately symmetric about the central axis ($f^1_{mid\_0}$) in the active space. Therefore, space is encoded as 0 and 1 above and below the central axis, respectively, which means that the ground-truth positions and predicted positions entering this upper or lower region are encoded as the corresponding 0 and 1. Through analogy between predicted encoding values (0 or 1) and ground-truth encoding values (0 or 1), symmetrical correction obtains $\hat{z}^1_{1:K}$ when $N=1$. Here, $N$ is a spatial parameter to control the change from space to subspace. When $N=2$, similar unsupervised prediction and correction operations are performed in the corresponding subspace or sub-region, as in the case of $N=1$. This process is repeated successively.
• Figure 2: (a) The figure shows the visualization of the unsupervised predicted trajectory (green line), the predicted trajectory after one correction (red line), and the ground-truth trajectory (black line). (b) The figure demonstrates the enlarged and visualized observation of approximately 3000 samples extracted from Fig. (a). As can be seen, the green trajectory undergoes symmetric correction to produce the red trajectory, which tracks the black trajectory almost perfectly. These indicate that the corrected predicted trajectory has high accuracy.
• Figure 3: (a) and (b) respectively show the scatterplot between the predicted positions and the ground-truth positions from $N=0$ to $N=2$, and from $N=3$ to $N=5$. Where $X$-axis represents the ground-truth positions, and $y$-axis guarantees the unsupervised prediction positions ($N=0$) and the corrected prediction position ($N>0$).
• Figure 4: From left to right, the actual waveform, the histogram of probability density function (PDF), and power spectral density (PSD) of the ground-truth moving positions are shown in the $x$-position. Among them, its PDF does not have significant distribution characteristics, such as non-Gaussian distribution, while its PSD decreases gradually and tends to a constant.
• Figure 5: (a) and (b) illustrate the waveform, PDF and PSD of the predicted positions in the $x$-positions from $N=0$ to $N=2$ and from $N=3$ to $N=5$, respectively.