Everyone's psychological world is a reconstruction of the physical world—exquisitely detailed, vibrant, and deeply personal. It is not merely a reflection of the physical world but a projection and interpretation of our inner selves. As Carl Jung once noted, "The world we see is, in fact, a reflection of our own inner world". In this process of reconstruction, our perceptions, experiences, emotions, and memories intertwine into a unique psychological landscape, guiding us toward an understanding of life, others, and the universe. Therefore, researching the intersection of Sensation (the representation of the physical world) and Perception (the psychological reconstruction) is key to understanding the fusion of these two worlds.
On December 10, the research group of Professor Jia Liu from the Department of Psychological and Cognitive Science at Tsinghua University published a research paper titled "From sensory to perceptual manifolds: The twist of neural geometry" in Science Advances, a sub-journal of Science. By studying population firing activity in the secondary visual cortex (V2) of macaques during a motion-induced illusory contour recognition task, the study elucidates how the brain uses a "Twist Operation" to expand the dimensionality of neural representation space. This process converts stimuli that are linearly inseparable in the physical world into perceptual categories that are linearly distinguishable in the psychological world.
Research Design and the "Linearly Inseparable" Task
Based on the phenomenon of motion-induced illusory contours, the team designed a classic "linearly inseparable" visual classification task. The stimulus consists of a circle of random dots moving toward or away from each other, creating an inclined "Illusory Contour" (a "virtual boundary") that does not exist physically but is clearly perceived by the observer.
By controlling three features—the movement axis (Horizontal or Vertical, HV), the movement direction (Outward or Inward, OI), and the spatial arrangement (Clockwise or Anticlockwise, CA)—the team constructed a three-dimensional stimulus space. In this space, virtual boundaries of different inclinations are highly interlaced, forming a classic linearly inseparable problem referred to in this study as the "cube XOR problem".
From Sensory to Perceptual Manifolds
Under the framework of Neural Geometry, the study distinguishes between two types of manifolds:
Sensory Manifold: Represents the features of physical stimuli, reflecting the direct embedding of external input in neural space.
Perceptual Manifold: Corresponds to the representation after the brain integrates and interprets sensory information—essentially, "understanding"—which supports subsequent decision-making.
The results show that early V2 neural population activity is mainly distributed in a 3D subspace, highly aligned with the three movement features (HV, OI, CA). However, over time, the neural state undergoes a series of geometric "twists" to achieve dimensionality expansion, eventually forming a seven-dimensional perceptual manifold. In this expanded space, a new task-related axis can linearly separate contours of different orientations.
Key Mechanisms: NMS and Heterogeneity
To uncover the mechanism behind this geometric twist, the team compared real neurons with synthesized single-feature selective neurons. The findings include:
Neurons with only Pure Selectivity can only solve linear problems in stimulus space.
Real neurons possess Nonlinear Mixed Selectivity (NMS), which allows them to linearize originally inseparable problems.
Artificial neural network simulations further revealed that NMS alone is not enough; only when connection weights are highly heterogeneous does a 7D perceptual manifold and twist structure similar to the experimental results form.
This suggests that NMS and neuronal heterogeneity are the critical mechanisms for achieving dimensionality expansion and geometric twisting.
Significance
This work provides a concrete mechanical example of how "sensation generates perception" from a geometric perspective, bridging visual illusions, neural population coding, and high-dimensional geometry.
Biological Insight: It proves that biological neural systems can solve linearly inseparable problems through internal dimensionality expansion, offering a new perspective on how abstract features and high-level cognitive functions emerge in cortical networks.
AI Inspiration: The "geometric twist" framework provides inspiration for designing artificial neural networks with higher discriminative power and robustness.
Authors and Publication Information
Joint First Authors: Heng Ma (Postdoc), Lingsheng Jiang (Assistant Researcher), and Tao Liu (PhD Student).
Corresponding Author: Professor Jia Liu.
Funding: Supported by the Beijing Municipal Science & Technology Commission, the National Natural Science Foundation of China, the Tsinghua University Guoqiang Institute, and the Beijing Academy of Artificial Intelligence.
Paper Link: https://www.science.org/doi/10.1126/sciadv.adv0431
Faculty Profile:
Jia Liu
Title: Head of the Department of Psychological and Cognitive Science, Professor, and Doctoral Supervisor; Tsinghua University Basic Science Chair Professor.
Research Direction: Cognitive Neural Foundations of AI, Visual Intelligence.
