Using distance on the Riemannian manifold to compare representations in brain and in models

Brain Representation in Conscious and Unconscious Vision

The development of robust frameworks to understand how the human brain represents conscious and unconscious perceptual contents is paramount to make progress in the neuroscience of consciousness. Recent functional MRI studies using multi-voxel pattern classification analyses showed that unconscious contents could be decoded from brain activity patterns. However, decoding does not imply a full understanding of neural representations. Here we re-analysed data from a high-precision fMRI study coupled with representational similarity analysis based on convolutional neural network models to provide a detailed information-based approach to neural representations of both unconscious and conscious perceptual content. The results showed that computer vision model representations strongly predicted brain responses in ventral visual cortex and in fronto-parietal regions to both conscious and unconscious contents. Moreover, this pattern of results generalised when the models were trained and tested with different participants. Remarkably, these observations results held even when the analysis was restricted to observers that showed null perceptual sensitivity. In light of the highly distributed brain representation of unconscious information, we suggest that the functional role of fronto-parietal cortex in conscious perception is unlikely to be related to the broadcasting of information, as proposed by the global neuronal workspace theory, and may instead relate to the generation of meta-representations as proposed by higher-order theories.

Transecting and contrasting the feeding designs of the astigmatan community from bird nests

The chelal moveable digit patterns of seventeen free-living astigmatan mites commonly found in bird nests is decomposed (for the first time) into functional groups using standardised profiles. Contrasts along the mastication surface are used to detect trophic features so as to explain the coexistence of different species in that community. Variation in profiles in general track geometric similarity changes in chelicerae and chelae, except in the moveable digit design transition between Thyreophagus entomophagus TH3 and Lepidoglyphus destructor G6. Full-kerf (Aleuroglyphus ovatus AL2 and Chortoglyphus arcuatus CH1) and particularly thin-kerf (Acarus farris A17) species are found. Both the moveable 'digit tip angle' and the angular bluntness of the anterior region (on which the tip sits, denoted the 'distal digit angle'), mirror digit robustification.Ventral surface intrinsic curvature of the moveable digit appears common across species. Acarus gracilis A4, Glycyphagus domesticus G5 and Lepidoglyphus destructor G6 have more than expected strengthened digit tips compared to other taxa. Rates of this strengthening with chelal occlusive force varies across species. With respect to the whole moveable digit profile a design transition from glycyphagids through acarids to pyroglyphids is found, along with an evolutionary path amongst pest species (Rhizoglyphus robini R1, through Tyrophagus longior T40, to Tyrophagus putrescentiae T13). Acarus gracilis A4 appears unique. In particular Tyrophagus palmarum T17 & T32 and Tyrophagus similis T21 & T44 are indistinguishable from replicates of each other and typify a basal form Tyrophagus longior T40, Tyrophagus putrescentiae T13, Acarus immobilis A1, Tyrolichus casei T62 and Acarus farris A17 are only mildly different from the observed scale of sampling variation of the basal overall profile form in this study Two design groups of ever increasing post-horizontal ramus investment are clear, with the basal rami of Chortoglyphus arcuatus CH1, Thyreophagus entomophagus TH3, Rhizoglyphus robini R1, Glycometrus hugheseae G3 and Dermatophagoides pteronyssinus D3 being taller and sometimes more rounded than those of the distinct group Acarus gracilis A4, Suidasia pontifica S5, Glycyphagus domesticus G5, Lepidoglyphus destructor G6 and Aleuroglyphus ovatus AL2. The bulk of the bird nest astigmatan species have a common profile pattern of apparent asperities on their mastication surface. Although, two species, Rhizoglyphus robini R1 and Chortoglyphus arcuatus CH1, have somewhat exaggerated features on this common 'Bauplan' (perhaps scaled for greater adductive force). Certain species: Acarus immobilis A1, Dermatophagoides pteronyssinus D3, Glycometrus hugheseae G3, Glycyphagus domesticus G5, Lepidoglyphus destructor G6 and Tyrophagus putrescentiae T13, have an individualised distinctly featured mastication surface. These species must each feed differently or on different material in bird nests. Basal ramus and chelal leverage differences are discussed. More work on the ascending ramus and specific dentition in future work is needed to explain certain remaining mite coexistences in this habitat.

A Task-Related EEG Microstate Clustering Algorithm Based on Spatial Patterns, Riemannian Distance, and a Deep Autoencoder

BACKGROUND

The segmentation of electroencephalography (EEG) signals into a limited number of microstates is of significant importance in the field of cognitive neuroscience. Currently, the microstate analysis algorithm based on global field power has demonstrated its efficacy in clustering resting-state EEG. The task-related EEG was extensively analyzed in the field of brain-computer interfaces (BCIs); however, its primary objective is classification rather than segmentation.

METHODS

We propose an innovative algorithm for analyzing task-related EEG microstates based on spatial patterns, Riemannian distance, and a modified deep autoencoder. The objective of this algorithm is to achieve unsupervised segmentation and clustering of task-related EEG signals.

RESULTS

The proposed algorithm was validated through experiments conducted on simulated EEG data and two publicly available cognitive task datasets. The evaluation results and statistical tests demonstrate its robustness and efficiency in clustering task-related EEG microstates.

CONCLUSIONS

The proposed unsupervised algorithm can autonomously discretize EEG signals into a finite number of microstates, thereby facilitating investigations into the temporal structures underlying cognitive processes.

An Explainable Geometric-Weighted Graph Attention Network for Identifying Functional Networks Associated with Gait Impairment

One of the hallmark symptoms of Parkinson's Disease (PD) is the progressive loss of postural reflexes, which eventually leads to gait difficulties and balance problems. Identifying disruptions in brain function associated with gait impairment could be crucial in better understanding PD motor progression, thus advancing the development of more effective and personalized therapeutics. In this work, we present an explainable, geometric, weighted-graph attention neural network (xGW-GAT) to identify functional networks predictive of the progression of gait difficulties in individuals with PD. xGW-GAT predicts the multi-class gait impairment on the MDS-Unified PD Rating Scale (MDS-UPDRS). Our computational- and data-efficient model represents functional connectomes as symmetric positive definite (SPD) matrices on a Riemannian manifold to explicitly encode pairwise interactions of entire connectomes, based on which we learn an attention mask yielding individual- and group-level explainability. Applied to our resting-state functional MRI (rs-fMRI) dataset of individuals with PD, xGW-GAT identifies functional connectivity patterns associated with gait impairment in PD and offers interpretable explanations of functional subnetworks associated with motor impairment. Our model successfully outperforms several existing methods while simultaneously revealing clinically-relevant connectivity patterns. The source code is available at https://github.com/favour-nerrise/xGW-GAT.

Multitask representations in the human cortex transform along a sensory-to-motor hierarchy

Human cognition recruits distributed neural processes, yet the organizing computational and functional architectures remain unclear. Here, we characterized the geometry and topography of multitask representations across the human cortex using functional magnetic resonance imaging during 26 cognitive tasks in the same individuals. We measured the representational similarity across tasks within a region and the alignment of representations between regions. Representational alignment varied in a graded manner along the sensory-association-motor axis. Multitask dimensionality exhibited compression then expansion along this gradient. To investigate computational principles of multitask representations, we trained multilayer neural network models to transform empirical visual-to-motor representations. Compression-then-expansion organization in models emerged exclusively in a rich training regime, which is associated with learning optimized representations that are robust to noise. This regime produces hierarchically structured representations similar to empirical cortical patterns. Together, these results reveal computational principles that organize multitask representations across the human cortex to support multitask cognition.

3M_BANTOR: A regression framework for multitask and multisession brain network distance metrics

Brain network analyses have exploded in recent years and hold great potential in helping us understand normal and abnormal brain function. Network science approaches have facilitated these analyses and our understanding of how the brain is structurally and functionally organized. However, the development of statistical methods that allow relating this organization to phenotypic traits has lagged behind. Our previous work developed a novel analytic framework to assess the relationship between brain network architecture and phenotypic differences while controlling for confounding variables. More specifically, this innovative regression framework related distances (or similarities) between brain network features from a single task to functions of absolute differences in continuous covariates and indicators of difference for categorical variables. Here we extend that work to the multitask and multisession context to allow for multiple brain networks per individual. We explore several similarity metrics for comparing distances between connection matrices and adapt several standard methods for estimation and inference within our framework: standard F test, F test with scan-level effects (SLE), and our proposed mixed model for multitask (and multisession) BrAin NeTwOrk Regression (3M_BANTOR). A novel strategy is implemented to simulate symmetric positive-definite (SPD) connection matrices, allowing for the testing of metrics on the Riemannian manifold. Via simulation studies, we assess all approaches for estimation and inference while comparing them with existing multivariate distance matrix regression (MDMR) methods. We then illustrate the utility of our framework by analyzing the relationship between fluid intelligence and brain network distances in Human Connectome Project (HCP) data.

Revisiting Riemannian geometry-based EEG decoding through approximate joint diagonalization

Objective.The wider adoption of Riemannian geometry in electroencephalography (EEG) processing is hindered by two factors: (a) it involves the manipulation of complex mathematical formulations and, (b) it leads to computationally demanding tasks. The main scope of this work is to simplify particular notions of Riemannian geometry and provide an efficient and comprehensible scheme for neuroscientific explorations.Approach.To overcome the aforementioned shortcomings, we exploit the concept of approximate joint diagonalization in order to reconstruct the spatial covariance matrices assuming the existence of (and identifying) a common eigenspace in which the application of Riemannian geometry is significantly simplified.Main results.The employed reconstruction process abides to physiologically plausible assumptions, reduces the computational complexity in Riemannian geometry schemes and bridges the gap between rigorous mathematical procedures and computational neuroscience. Our approach is both formally established and experimentally validated by employing real and synthetic EEG data.Significance.The implications of the introduced reconstruction process are highlighted by reformulating and re-introducing two signal processing methodologies, namely the 'Symmetric Positive Definite (SPD) Matrix Quantization' and the 'Coding over SPD Atoms'. The presented approach paves the way for robust and efficient neuroscientific explorations that exploit Riemannian geometry schemes.

Geometric learning of functional brain network on the correlation manifold

The correlation matrix is a typical representation of node interactions in functional brain network analysis. The analysis of the correlation matrix to characterize brain networks observed in several neuroimaging modalities has been conducted predominantly in the Euclidean space by assuming that pairwise interactions are mutually independent. One way to take account of all interactions in the network as a whole is to analyze the correlation matrix under some geometric structure. Recent studies have focused on the space of correlation matrices as a strict subset of symmetric positive definite (SPD) matrices, which form a unique mathematical structure known as the Riemannian manifold. However, mathematical operations of the correlation matrix under the SPD geometry may not necessarily be coherent (i.e., the structure of the correlation matrix may not be preserved), necessitating a post-hoc normalization. The contribution of the current paper is twofold: (1) to devise a set of inferential methods on the correlation manifold and (2) to demonstrate its applicability in functional network analysis. We present several algorithms on the correlation manifold, including measures of central tendency, cluster analysis, hypothesis testing, and low-dimensional embedding. Simulation and real data analysis support the application of the proposed framework for brain network analysis.

Caveats and Nuances of Model-Based and Model-Free Representational Connectivity Analysis

Brain connectivity analyses have conventionally relied on statistical relationship between one-dimensional summaries of activation in different brain areas. However, summarizing activation patterns within each area to a single dimension ignores the potential statistical dependencies between their multi-dimensional activity patterns. Representational Connectivity Analyses (RCA) is a method that quantifies the relationship between multi-dimensional patterns of activity without reducing the dimensionality of the data. We consider two variants of RCA. In model-free RCA, the goal is to quantify the shared information for two brain regions. In model-based RCA, one tests whether two regions have shared information about a specific aspect of the stimuli/task, as defined by a model. However, this is a new approach and the potential caveats of model-free and model-based RCA are still understudied. We first explain how model-based RCA detects connectivity through the lens of models, and then present three scenarios where model-based and model-free RCA give discrepant results. These conflicting results complicate the interpretation of functional connectivity. We highlight the challenges in three scenarios: complex intermediate models, common patterns across regions, and transformation of representational structure across brain regions. The article is accompanied by scripts (https://osf.io/3nxfa/) that reproduce the results. In each case, we suggest potential ways to mitigate the difficulties caused by inconsistent results. The results of this study shed light on some understudied aspects of RCA, and allow researchers to use the method more effectively.