Common population codes produce extremely nonlinear neural manifolds

TRACKING THE TOPOLOGY OF NEURAL MANIFOLDS ACROSS POPULATIONS

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

Random compressed coding with neurons

Classical models of efficient coding in neurons assume simple mean responses-"tuning curves"- such as bell-shaped or monotonic functions of a stimulus feature. Real neurons, however, can be more complex: grid cells, for example, exhibit periodic responses that impart the neural population code with high accuracy. But do highly accurate codes require fine-tuning of the response properties? We address this question with the use of a simple model: a population of neurons with random, spatially extended, and irregular tuning curves. Irregularity enhances the local resolution of the code but gives rise to catastrophic, global errors. For optimal smoothness of the tuning curves, when local and global errors balance out, the neural population compresses information about a continuous stimulus into a low-dimensional representation, and the resulting distributed code achieves exponential accuracy. An analysis of recordings from monkey motor cortex points to such "compressed efficient coding." Efficient codes do not require a finely tuned design-they emerge robustly from irregularity or randomness.

Unsupervised, piecewise linear decoding enables an accurate prediction of muscle activity in a multi-task brain computer interface

Objective.Creating an intracortical brain computer interface (iBCI) capable of seamless transitions between tasks and contexts would greatly enhance user experience. However, the nonlinearity in neural activity presents challenges to computing a global iBCI decoder. We aimed to develop a method that differs from a globally optimized decoder to address this issue.Approach.We devised an unsupervised approach that relies on the structure of a low-dimensional neural manifold to implement a piecewise linear decoder. We created a distinctive dataset in which monkeys performed a diverse set of tasks, some trained, others innate, while we recorded neural signals from the motor cortex (M1) and electromyographs (EMGs) from upper limb muscles. We used both linear and nonlinear dimensionality reduction techniques to discover neural manifolds and applied unsupervised algorithms to identify clusters within those spaces. Finally, we fit a linear decoder of EMG for each cluster. A specific decoder was activated corresponding to the cluster each new neural data point belonged to.Main results.We found clusters in the neural manifolds corresponding with the different tasks or task sub-phases. The performance of piecewise decoding improved as the number of clusters increased and plateaued gradually. With only two clusters it already outperformed a global linear decoder, and unexpectedly, it outperformed even a global recurrent neural network decoder with 10-12 clusters.Significance.This study introduced a computationally lightweight solution for creating iBCI decoders that can function effectively across a broad range of tasks. EMG decoding is particularly challenging, as muscle activity is used, under varying contexts, to control interaction forces and limb stiffness, as well as motion. The results suggest that a piecewise linear decoder can provide a good approximation to the nonlinearity between neural activity and motor outputs, a result of our increased understanding of the structure of neural manifolds in motor cortex.

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

Measuring Stimulus Information Transfer Between Neural Populations through the Communication Subspace

Sensory processing arises from the communication between neural populations across multiple brain areas. While the widespread presence of neural response variability shared throughout a neural population limits the amount of stimulus-related information those populations can accurately represent, how this variability affects the interareal communication of sensory information is unknown. We propose a mathematical framework to understand the impact of neural population response variability on sensory information transmission. We combine linear Fisher information, a metric connecting stimulus representation and variability, with the framework of communication subspaces, which suggests that functional mappings between cortical populations are low-dimensional relative to the space of population activity patterns. From this, we partition Fisher information depending on the alignment between the population covariance and the mean tuning direction projected onto the communication subspace or its orthogonal complement. We provide mathematical and numerical analyses of our proposed decomposition of Fisher information and examine theoretical scenarios that demonstrate how to leverage communication subspaces for flexible routing and gating of stimulus information. This work will provide researchers investigating interareal communication with a theoretical lens through which to understand sensory information transmission and guide experimental design.

Unsupervised, piecewise linear decoding enables an accurate prediction of muscle activity in a multi-task brain computer interface

Objective

Creating an intracortical brain-computer interface (iBCI) capable of seamless transitions between tasks and contexts would greatly enhance user experience. However, the nonlinearity in neural activity presents challenges to computing a global iBCI decoder. We aimed to develop a method that differs from a globally optimized decoder to address this issue.

Approach

We devised an unsupervised approach that relies on the structure of a low-dimensional neural manifold to implement a piecewise linear decoder. We created a distinctive dataset in which monkeys performed a diverse set of tasks, some trained, others innate, while we recorded neural signals from the motor cortex (M1) and electromyographs (EMGs) from upper limb muscles. We used both linear and nonlinear dimensionality reduction techniques to discover neural manifolds and applied unsupervised algorithms to identify clusters within those spaces. Finally, we fit a linear decoder of EMG for each cluster. A specific decoder was activated corresponding to the cluster each new neural data point belonged to.

Main results

We found clusters in the neural manifolds corresponding with the different tasks or task sub-phases. The performance of piecewise decoding improved as the number of clusters increased and plateaued gradually. With only two clusters it already outperformed a global linear decoder, and unexpectedly, it outperformed even a global recurrent neural network (RNN) decoder with 10-12 clusters.

Significance

This study introduced a computationally lightweight solution for creating iBCI decoders that can function effectively across a broad range of tasks. EMG decoding is particularly challenging, as muscle activity is used, under varying contexts, to control interaction forces and limb stiffness, as well as motion. The results suggest that a piecewise linear decoder can provide a good approximation to the nonlinearity between neural activity and motor outputs, a result of our increased understanding of the structure of neural manifolds in motor cortex.

Preliminary Evidence for Global Properties in Human Listeners During Natural Auditory Scene Perception

Theories of auditory and visual scene analysis suggest the perception of scenes relies on the identification and segregation of objects within it, resembling a detail-oriented processing style. However, a more global process may occur while analyzing scenes, which has been evidenced in the visual domain. It is our understanding that a similar line of research has not been explored in the auditory domain; therefore, we evaluated the contributions of high-level global and low-level acoustic information to auditory scene perception. An additional aim was to increase the field's ecological validity by using and making available a new collection of high-quality auditory scenes. Participants rated scenes on 8 global properties (e.g., open vs. enclosed) and an acoustic analysis evaluated which low-level features predicted the ratings. We submitted the acoustic measures and average ratings of the global properties to separate exploratory factor analyses (EFAs). The EFA of the acoustic measures revealed a seven-factor structure explaining 57% of the variance in the data, while the EFA of the global property measures revealed a two-factor structure explaining 64% of the variance in the data. Regression analyses revealed each global property was predicted by at least one acoustic variable (R2 = 0.33-0.87). These findings were extended using deep neural network models where we examined correlations between human ratings of global properties and deep embeddings of two computational models: an object-based model and a scene-based model. The results support that participants' ratings are more strongly explained by a global analysis of the scene setting, though the relationship between scene perception and auditory perception is multifaceted, with differing correlation patterns evident between the two models. Taken together, our results provide evidence for the ability to perceive auditory scenes from a global perspective. Some of the acoustic measures predicted ratings of global scene perception, suggesting representations of auditory objects may be transformed through many stages of processing in the ventral auditory stream, similar to what has been proposed in the ventral visual stream. These findings and the open availability of our scene collection will make future studies on perception, attention, and memory for natural auditory scenes possible.

Phantom oscillations in principal component analysis

Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this simple interpretation fails for timeseries, spatial maps, and other continuous data. In these cases, nonoscillatory data may have oscillatory principal components. Here, we show that two common properties of data cause oscillatory principal components: smoothness and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations produced by PCA, which we call "phantom oscillations," impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.