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Steady-state visual evoked potential (SSVEP) is one of the most commonly used control signal in the brain-computer interface (BCI) systems. However, the conventional spatial filtering methods for SSVEP classification highly depend on the subject-specific calibration data. The need for the methods that can alleviate the demand for the calibration data become urgent. In recent years, developing the methods that can work in inter-subject classification scenario has become a promising new direction. As the popular deep learning model nowadays, Transformer has excellent performance and has been used in EEG signal classification tasks. Therefore, in this study, we propose a deep learning model for SSVEP classification based on Transformer structure in inter-subject classification scenario, termed as SSVEPformer, which is the first application of the transformer to the classification of SSVEP. Inspired by previous studies, the model adopts the frequency spectrum of SSVEP data as input, and explores the spectral and spatial domain information for classification. Furthermore, to fully utilize the harmonic information, an extended SSVEPformer based on the filter bank technology (FB-SSVEPformer) is proposed to further improve the classification performance. Experiments were conducted using two open datasets (Dataset 1: 10 subjects, 12-class task; Dataset 2: 35 subjects, 40-class task) in the inter-subject classification scenario. The experimental results show that the proposed models could achieve better results in terms of classification accuracy and information transfer rate, compared with other baseline methods. The proposed model validates the feasibility of deep learning models based on Transformer structure for SSVEP classification task, and could serve as a potential model to alleviate the calibration procedure in the practical application of SSVEP-based BCI systems.

In many areas of the brain, neural spiking activity covaries with features of the external world, such as sensory stimuli or an animal's movement. Experimental findings suggest that the variability of neural activity changes over time and may provide information about the external world beyond the information provided by the average neural activity. To flexibly track time-varying neural response properties, here we developed a dynamic model with Conway-Maxwell Poisson (CMP) observations. The CMP distribution can flexibly describe firing patterns that are both under- and over-dispersed relative to the Poisson distribution. Here we track parameters of the CMP distribution as they vary over time. Using simulations, we show that a normal approximation can accurately track dynamics in state vectors for both the centering and shape parameters ($\lambda$ and $\nu$). We then fit our model to neural data from neurons in primary visual cortex and "place cells" in the hippocampus. We find that this method out-performs previous dynamic models based on the Poisson distribution. The dynamic CMP model provides a flexible framework for tracking time-varying non-Poisson count data and may also have applications beyond neuroscience., Comment: 6 figures

Contains fulltext : 292135.pdf (Publisher’s version ) (Open Access) Recent artificial neural networks that process natural language achieve unprecedented performance in tasks requiring sentence-level understanding. As such, they could be interesting models of the integration of linguistic information in the human brain. We review works that compare these artificial language models with human brain activity and we assess the extent to which this approach has improved our understanding of the neural processes involved in natural language comprehension. Two main results emerge. First, the neural representation of word meaning aligns with the context-dependent, dense word vectors used by the artificial neural networks. Second, the processing hierarchy that emerges within artificial neural networks broadly matches the brain, but is surprisingly inconsistent across studies. We discuss current challenges in establishing artificial neural networks as process models of natural language comprehension. We suggest exploiting the highly structured representational geometry of artificial neural networks when mapping representations to brain data. 18 april 2023 19 p.

Traumatic brain injury is a global public health problem associated with chronic neurological complications and long-term disability. Biomarkers that map onto the underlying brain pathology driving these complications are urgently needed to identify individuals at risk for poor recovery and to inform design of clinical trials of neuroprotective therapies. Neuroinflammation and neurodegeneration are two endophenotypes potentially associated with increases in brain extracellular water content, but the nature of extracellular free water abnormalities after neurotrauma and its relationship to measures typically thought to reflect traumatic axonal injury are not well characterized. The objective of this study was to describe the relationship between a neuroimaging biomarker of extracellular free water content and the clinical features of a cohort with primarily complicated mild traumatic brain injury. We analyzed a cohort of 59 adult patients requiring hospitalization for non-penetrating traumatic brain injury of all severities as well as 36 healthy controls. Patients underwent brain MRI at two-weeks (n = 59) and six-months (n = 29) post-injury period, and controls underwent a single MRI. Of the participants with TBI, 50 underwent clinical neuropsychological assessment at two weeks and 28 at six months. For each subject, we derived a summary score representing deviations in whole brain white matter (1) extracellular free water volume fraction (VF) and (2) free water-corrected fractional anisotropy (fw-FA). The summary specific anomaly score (SAS) for VF was significantly higher in TBI patients at two-weeks and six-months post-injury relative to controls. SAS for VF exhibited moderate correlation with neuropsychological functioning, particularly on measures of executive function. These findings indicate abnormalities in whole brain white matter extracellular water fraction in patients with TBI and are an important step toward identifying and validating noninvasive biomarkers that map onto the pathology driving disability after TBI.

Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equilibrium feedback-driven Ising like class of neural networks that simultaneously and quantitatively captures scale-free avalanches and scale-specific oscillations. In the most simple yet fully microscopic model version we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations and collective behaviors of nearly-synchronous extreme events on multiple sensors, to neuronal avalanches unfolding over multiple sensors across multiple time bins. Importantly, the inferred parameters correlate with model-independent signatures of "closeness to criticality", indicating that the coexistence of scale-specific (neural oscillations) and scale-free (neuronal avalanches) dynamics in brain activity occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations., Comment: 29 pages, 20 figures

Recent advances in high-resolution microscopy have allowed scientists to better understand the underlying brain connectivity. However, due to the limitation that biological specimens can only be imaged at a single timepoint, studying changes to neural projections is limited to general observations using population analysis. In this paper, we introduce NeuRegenerate, a novel end-to-end framework for the prediction and visualization of changes in neural fiber morphology within a subject, for specified age-timepoints.To predict projections, we present neuReGANerator, a deep-learning network based on cycle-consistent generative adversarial network (cycleGAN) that translates features of neuronal structures in a region, across age-timepoints, for large brain microscopy volumes. We improve the reconstruction quality of neuronal structures by implementing a density multiplier and a new loss function, called the hallucination loss.Moreover, to alleviate artifacts that occur due to tiling of large input volumes, we introduce a spatial-consistency module in the training pipeline of neuReGANerator. We show that neuReGANerator has a reconstruction accuracy of 94% in predicting neuronal structures. Finally, to visualize the predicted change in projections, NeuRegenerate offers two modes: (1) neuroCompare to simultaneously visualize the difference in the structures of the neuronal projections, across the age timepoints, and (2) neuroMorph, a vesselness-based morphing technique to interactively visualize the transformation of the structures from one age-timepoint to the other. Our framework is designed specifically for volumes acquired using wide-field microscopy. We demonstrate our framework by visualizing the structural changes in neuronal fibers within the cholinergic system of the mouse brain between a young and old specimen., Comment: Accepted for publication in IEEE Transactions on Visualization and Computer Graphics

In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community., deposited on: https://arxiv.org/abs/2003.13825

Upright stance tested with a superposition of support surface tilt and translation. Steady state response is characterized by frequency response function. Interaction between two stimuli absent in most of the cases. Larger stimuli may create interaction. Simulations suggest that the observed effects can be due to joint stiffness modulation., Comment: 10 pages, 7 figures

Background: A therapeutic intervention in psychiatry can be viewed as an attempt to influence the brain's large-scale, dynamic network state transitions underlying cognition and behavior. Building on connectome-based graph analysis and control theory, Network Control Theory is emerging as a powerful tool to quantify network controllability - i.e., the influence of one brain region over others regarding dynamic network state transitions. If and how network controllability is related to mental health remains elusive. Methods: From Diffusion Tensor Imaging data, we inferred structural connectivity and inferred calculated network controllability parameters to investigate their association with genetic and familial risk in patients diagnosed with major depressive disorder (MDD, n=692) and healthy controls (n=820). Results: First, we establish that controllability measures differ between healthy controls and MDD patients while not varying with current symptom severity or remission status. Second, we show that controllability in MDD patients is associated with polygenic scores for MDD and psychiatric cross-disorder risk. Finally, we provide evidence that controllability varies with familial risk of MDD and bipolar disorder as well as with body mass index. Conclusions: We show that network controllability is related to genetic, individual, and familial risk in MDD patients. We discuss how these insights into individual variation of network controllability may inform mechanistic models of treatment response prediction and personalized intervention-design in mental health., Comment: 24 pages, 1 figure

Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. Whether there exists an optimal network and STDP configuration at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. We expect such a configuration to enable the brain to make synergistic and optimal use of these phenomena to process information efficiently. This paper considers a small-world network of excitable Hodgkin-Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate specific network topology and STDP parameter intervals in which CR and SS can be simultaneously enhanced. Our results imply that an optimally tuned inherent background noise, STDP rule, and network topology can play a constructive role in enhancing both the time precision of firing and the synchronization in neural systems., 17 pages, 12 figures, 71 references

Electrical neuromodulation as a palliative treatment has been increasingly used in the control of epilepsy. However, current neuromodulations commonly implement predetermined actuation strategies and lack the capability of self-adaptively adjusting stimulation inputs. In this work, rooted in optimal control theory, we propose a Koopman-MPC framework for real-time closed-loop electrical neuromodulation in epilepsy, which integrates i) a deep Koopman operator based dynamical model to predict the temporal evolution of epileptic EEG with an approximate finite-dimensional linear dynamics and ii) a model predictive control (MPC) module to design optimal seizure suppression strategies. The Koopman operator based linear dynamical model is embedded in the latent state space of the autoencoder neural network, in which we can approximate and update the Koopman operator online. The linear dynamical property of the Koopman operator ensures the convexity of the optimization problem for subsequent MPC control. The proposed deep Koopman operator model shows greater predictive capability than the baseline models (e.g., vector autoregressive model, kernel based method and recurrent neural network (RNN)) in both synthetic and real epileptic EEG data. Moreover, compared with the RNN-MPC framework, our Koopman-MPC framework can suppress seizure dynamics with better computational efficiency in both the Jansen-Rit model and the Epileptor model. Koopman-MPC framework opens a new window for model-based closed-loop neuromodulation and sheds light on nonlinear neurodynamics and feedback control policies.

In the monograph, STRONG ARTIFICIAL INTELLIGENCE. On the Approaches to Superintelligence, published by Sberbank, provides a cross-disciplinary review of general artificial intelligence. As an anthropomorphic direction of research, it considers Brain Principles Programming, BPP) the formalization of universal mechanisms (principles) of the brain's work with information, which are implemented at all levels of the organization of nervous tissue. This monograph provides a formalization of these principles in terms of the category theory. However, this formalization is not enough to develop algorithms for working with information. In this paper, for the description and modeling of Brain Principles Programming, it is proposed to apply mathematical models and algorithms developed by us earlier that model cognitive functions, which are based on well-known physiological, psychological and other natural science theories. The paper uses mathematical models and algorithms of the following theories: P.K.Anokhin's Theory of Functional Brain Systems, Eleonor Rosh's prototypical categorization theory, Bob Rehter's theory of causal models and natural classification. As a result, the formalization of the BPP is obtained and computer examples are given that demonstrate the algorithm's operation., to be submitted to the AGI-22

In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms by which simple and forgetful units can organize to collectively generate dynamics on the long time-scales required for such computations. We discuss the myriad potential uses of attractor dynamics for computation in the brain, and showcase notable examples of brain systems in which inherently low-dimensional continuous attractor dynamics have been concretely and rigorously identified. Thus, it is now possible to conclusively state that the brain constructs and uses such systems for computation. Finally, we look ahead by highlighting recent theoretical advances in understanding how the fundamental tradeoffs between robustness and capacity and between structure and flexibility can be overcome by reusing and recombining the same set of modular attractors for multiple functions, so they together produce representations that are structurally constrained and robust but exhibit high capacity and are flexible.

Recent experiments reveal that 6- to 12-month-old infants can learn probabilities and reason with them. In this work, we present a novel computational system called Neural Probability Learner and Sampler (NPLS) that learns and reasons with probabilities, providing a computationally sufficient mechanism to explain infant probabilistic learning and inference. In 24 computer simulations, NPLS simulations show how probability distributions can emerge naturally from neural-network learning of event sequences, providing a novel explanation of infant probabilistic learning and reasoning. Three mathematical proofs show how and why NPLS simulates the infant results so accurately. The results are situated in relation to seven other active research lines. This work provides an effective way to integrate Bayesian and neural-network approaches to cognition., To be published in Psychological Review

Objective: The next generation prosthetic hand that moves and feels like a real hand requires a robust neural interconnection between the human minds and machines. Methods: Here we present a neuroprosthetic system to demonstrate that principle by employing an artificial intelligence (AI) agent to translate the amputee's movement intent through a peripheral nerve interface. The AI agent is designed based on the recurrent neural network (RNN) and could simultaneously decode six degree-of-freedom (DOF) from multichannel nerve data in real-time. The decoder's performance is characterized in motor decoding experiments with three human amputees. Results: First, we show the AI agent enables amputees to intuitively control a prosthetic hand with individual finger and wrist movements up to 97-98% accuracy. Second, we demonstrate the AI agent's real-time performance by measuring the reaction time and information throughput in a hand gesture matching task. Third, we investigate the AI agent's long-term uses and show the decoder's robust predictive performance over a 16-month implant duration. Conclusion & significance: Our study demonstrates the potential of AI-enabled nerve technology, underling the next generation of dexterous and intuitive prosthetic hands.

An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; (iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al. [Neural Computation, 29, 2925--2954 (2017)], which considers Nonnegative Independent Component Analysis (NICA), a special case of blind source separation that assumes the mixture is a linear combination of uncorrelated, nonnegative sources. They derive an algorithm with a biologically plausible 2-layer network implementation. In this work, we improve upon their result by deriving 2 algorithms for NICA, each with a biologically plausible single-layer network implementation. The first algorithm maps onto a network with indirect lateral connections mediated by interneurons. The second algorithm maps onto a network with direct lateral connections and multi-compartmental output neurons., Comment: Updated version includes a second single-layer network with indirect lateral connections for solving NICA

Several models of working memory (WM) have been proposed in the literature. Most of the research on the architecture of WM is based on adults or older children, but less is known about younger children. In this study, we tested various models of WM on a sample of 739 Italian children from 3 to 8 years old. Participants were assessed with 12 WM tasks, systematically varying the modality and level of executive control required (based on the number of activities to be performed at once: retention alone, ignoring distractors, and dealing with dual tasks). We examined younger children, n = 501, Mage = 56.8 months (SD = 6.4, 48% males) and older children, n = 238, Mage = 80.0 months (SD = 9.0, 58% males) separately using multigroup confirmatory factor analyses. A Bayesian analytical approach was adopted. Our results suggested that a four-factor model distinguishing between verbal, visual, spatial-simultaneous, and spatial-sequential components of WM achieved the best fit. Overall, the WM structure was very similar in the two groups. We further explored this result with an additional model with a central executive factor loaded on high-control tasks only, and found evidence for the presence of an executive control component. The contribution of this factor in terms of explained variance was only modest, however. Our findings demonstrate that it is important to distinguish between WM components in young children.

The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on surprisal (a.k.a., self-information). This upper bound can be read as a Bayesian prediction error. Equivalently, its negative is a lower bound on Bayesian model evidence (a.k.a., marginal likelihood). In short, certain random dynamical systems evince a kind of self-evidencing. Here, we reformulate the FEP in the formal setting of spacetime-background free, scale-free quantum information theory. We show how generic quantum systems can be regarded as observers, which with the standard freedom of choice assumption become agents capable of assigning semantics to observational outcomes. We show how such agents minimize Bayesian prediction error in environments characterized by uncertainty, insufficient learning, and quantum contextuality. We show that in its quantum-theoretic formulation, the FEP is asymptotically equivalent to the Principle of Unitarity. Based on these results, we suggest that biological systems employ quantum coherence as a computational resource and - implicitly - as a communication resource. We summarize a number of problems for future research, particularly involving the resources required for classical communication and for detecting and responding to quantum context switches., Comment: 57 pgs, 6 figs

In recent years, recurrent quantification analysis (RQA) and its multi-dimensional version (MdRQA) have emerged as a popular tool for assessing interpersonal behavioral or physiological synchrony in groups of two or more individuals. While experimental data in such studies are typically collected for a fixed, pre-determined duration, naturally occurring phenomena may often reach a state of transition after an unpredictable or varying duration of time. The resulting recurrence plots(RPs) across groups cannot be compared directly via linear scaling because the sensitivity of RQA variables to local dynamics would vary. We propose to address this by using the sliding window technique on individual RPs and using the summary statistics of the different RQA variable distributions computed across the sliding windows to differentiate the dynamics of the original time series of unequal durations. We tested our approach in two models: 1) the Rossler attractor and 2) the Kuramoto model. We compared the ability of different summary statistics of RQA variable distributions to accurately predict the dynamic states of the system across varying levels of noise, unequal lengths of time series, and, in the case of the Kuramoto model, different numbers of oscillators across samples. We found that while the mean, compared to other measures of central tendency, was a more accurate predictor of the underlying dynamic state of the system at high noise conditions, the mode was the most robust to the degree of noise in the signals, performing better than RQA variables from the whole RP, in general. To our knowledge, this is the first systematic attempt to validate the use of MdRQA in computing and comparing synchrony between systems of non-uniform composition and unequal time series data, paving the way for future work that examines interpersonal synchrony in more naturalistic, ecologically valid contexts.

Objective: We introduce a methodology for selecting biomarkers from activation and connectivity derived from Electrophysiological Source Imaging (ESI). Specifically, we pursue the selection of stable biomarkers associated with cognitive decline based on source activation and connectivity patterns of resting-state EEG theta rhythm, used as predictors of physical performance decline in aging individuals measured by a Gait Speed (GS) slowing. Methods: Our two-step methodology involves estimating ESI using flexible sparse-smooth-nonnegative models, from which activation ESI (aESI) and connectivity ESI (cESI) features are derived. The Stable Sparse Classifier method then selects potential biomarkers related to GS changes. Results and Conclusions: Our predictive models using aESI outperform traditional methods such as the LORETA family. The models combining aESI and cESI features provide the best prediction of GS changes. Potential biomarkers from activation/connectivity patterns involve orbitofrontal and temporal cortical regions. Significance: The proposed methodology contributes to the understanding of activation and connectivity of GS-related ESI and provides features that are potential biomarkers of GS slowing. Given the known relationship between GS decline and cognitive impairment, this preliminary work opens novel paths to predict the progression of healthy and pathological aging and might allow an ESI-based evaluation of rehabilitation programs.

Working memory (WM), a fundamental cognitive process facilitating the temporary storage, integration, manipulation, and retrieval of information, plays a vital role in reasoning and decision-making tasks. Robust benchmark datasets that capture the multifaceted nature of WM are crucial for the effective development and evaluation of AI WM models. Here, we introduce a comprehensive Working Memory (WorM) benchmark dataset for this purpose. WorM comprises 10 tasks and a total of 1 million trials, assessing 4 functionalities, 3 domains, and 11 behavioral and neural characteristics of WM. We jointly trained and tested state-of-the-art recurrent neural networks and transformers on all these tasks. We also include human behavioral benchmarks as an upper bound for comparison. Our results suggest that AI models replicate some characteristics of WM in the brain, most notably primacy and recency effects, and neural clusters and correlates specialized for different domains and functionalities of WM. In the experiments, we also reveal some limitations in existing models to approximate human behavior. This dataset serves as a valuable resource for communities in cognitive psychology, neuroscience, and AI, offering a standardized framework to compare and enhance WM models, investigate WM's neural underpinnings, and develop WM models with human-like capabilities. Our source code and data are available at https://github.com/ZhangLab-DeepNeuroCogLab/WorM.

Deep Learning (DL) , a variant of the neural network algorithms originally proposed in the 1980s, has made surprising progress in Artificial Intelligence (AI), ranging from language translation, protein folding, autonomous cars, and more recently human-like language models (CHATbots), all that seemed intractable until very recently. Despite the growing use of Deep Learning (DL) networks, little is actually understood about the learning mechanisms and representations that makes these networks effective across such a diverse range of applications. Part of the answer must be the huge scale of the architecture and of course the large scale of the data, since not much has changed since 1987. But the nature of deep learned representations remain largely unknown. Unfortunately training sets with millions or billions of tokens have unknown combinatorics and Networks with millions or billions of hidden units cannot easily be visualized and their mechanisms cannot be easily revealed. In this paper, we explore these questions with a large (1.24M weights; VGG) DL in a novel high density sample task (5 unique tokens with at minimum 500 exemplars per token) which allows us to more carefully follow the emergence of category structure and feature construction. We use various visualization methods for following the emergence of the classification and the development of the coupling of feature detectors and structures that provide a type of graphical bootstrapping, From these results we harvest some basic observations of the learning dynamics of DL and propose a new theory of complex feature construction based on our results.

Recent advances in neuroscientific experimental techniques have enabled us to simultaneously record the activity of thousands of neurons across multiple brain regions. This has led to a growing need for computational tools capable of analyzing how task-relevant information is represented and communicated between several brain regions. Partial information decompositions (PIDs) have emerged as one such tool, quantifying how much unique, redundant and synergistic information two or more brain regions carry about a task-relevant message. However, computing PIDs is computationally challenging in practice, and statistical issues such as the bias and variance of estimates remain largely unexplored. In this paper, we propose a new method for efficiently computing and estimating a PID definition on multivariate Gaussian distributions. We show empirically that our method satisfies an intuitive additivity property, and recovers the ground truth in a battery of canonical examples, even at high dimensionality. We also propose and evaluate, for the first time, a method to correct the bias in PID estimates at finite sample sizes. Finally, we demonstrate that our Gaussian PID effectively characterizes inter-areal interactions in the mouse brain, revealing higher redundancy between visual areas when a stimulus is behaviorally relevant.

Identifying causal relationships among distinct brain areas, known as effective connectivity, holds key insights into the brain's information processing and cognitive functions. Electroencephalogram (EEG) signals exhibit intricate dynamics and inter-areal interactions within the brain. However, methods for characterizing nonlinear causal interactions among multiple brain regions remain relatively underdeveloped. In this study, we proposed a data-driven framework to infer effective connectivity by perturbing the trained neural networks. Specifically, we trained neural networks (i.e., CNN, vanilla RNN, GRU, LSTM, and Transformer) to predict future EEG signals according to historical data and perturbed the networks' input to obtain effective connectivity (EC) between the perturbed EEG channel and the rest of the channels. The EC reflects the causal impact of perturbing one node on others. The performance was tested on the synthetic EEG generated by a biological-plausible Jansen-Rit model. CNN and Transformer obtained the best performance on both 3-channel and 90-channel synthetic EEG data, outperforming the classical Granger causality method. Our work demonstrated the potential of perturbing an artificial neural network, learned to predict future system dynamics, to uncover the underlying causal structure., 7 pages, 3 figures, 1 table

In computational neuroscience, fixed points of recurrent neural network models are commonly used to model neural responses to static or slowly changing stimuli. These applications raise the question of how to train the weights in a recurrent neural network to minimize a loss function evaluated on fixed points. A natural approach is to use gradient descent on the Euclidean space of synaptic weights. We show that this approach can lead to poor learning performance due, in part, to singularities that arise in the loss surface. We use a re-parameterization of the recurrent network model to derive two alternative learning rules that produces more robust learning dynamics. We show that these learning rules can be interpreted as steepest descent and gradient descent, respectively, under a non-Euclidean metric on the space of recurrent weights. Our results question the common, implicit assumption that learning in the brain should necessarily follow the negative Euclidean gradient of synaptic weights.

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory storage and retrieval pose a significant challenge for these networks to implement or learn. Recently, a family of models described by neural ordinary differential equations (nODEs) has emerged as powerful dynamical neural network models capable of capturing complex dynamics. Here, we extend nODEs by endowing them with adaptive timescales using gating interactions. We refer to these as gated neural ODEs (gnODEs). Using a task that requires memory of continuous quantities, we demonstrate the inductive bias of the gnODEs to learn (approximate) continuous attractors. We further show how reduced-dimensional gnODEs retain their modeling power while greatly improving interpretability, even allowing explicit visualization of the structure of learned attractors. We introduce a novel measure of expressivity which probes the capacity of a neural network to generate complex trajectories. Using this measure, we explore how the phase-space dimension of the nODEs and the complexity of the function modeling the flow field contribute to expressivity. We see that a more complex function for modeling the flow field allows a lower-dimensional nODE to capture a given target dynamics. Finally, we demonstrate the benefit of gating in nODEs on several real-world tasks.

In neural information processing, an input modulates neural dynamics to generate a desired output. To unravel the dynamics and underlying neural connectivity enabling such input-output association, we proposed an exactly soluble neural-network model with a connectivity matrix explicitly consisting of inputs and required outputs. An analytic form of the response upon the input is derived, whereas three distinctive types of responses including chaotic dynamics as bifurcation against input strength are obtained depending on the neural sensitivity and number of inputs. Optimal performance is achieved at the onset of chaos, and the relevance of the results to cognitive dynamics is discussed.

Animals must constantly make decisions on the move, such as when choosing among multiple options, or "targets", in space. Recent evidence suggests that this results from a recursive feedback between the (vectorial) neural representation of the targets and the resulting motion defined by this consensus, which then changes the egocentric neural representation of the the options, and so on. Here we employ a simple model of this process to both explore how its dynamics account for the experimentally-observed abruptly-branching trajectories exhibited by animals during spatial decision-making, and to provide new insights into spatiotemporal computation. Essential neural dynamics, notably local excitation and long-range inhibition, are captured in our model via spin-system dynamics, with groups of Ising-spins representing neural "activity bumps" corresponding to target directions. Analysis, employing a novel "mean-field trajectory" approach, reveals the nature of the spontaneous symmetry breaking - bifurcations in the model that result in literal bifurcations in trajectory space and how it results in new geometric principles for spatiotemporal decision-making. We find that all bifurcation points, beyond the very first, fall on a small number of "bifurcation curves". It is the spatial organization of these curves that is shown to be key to determining the shape of the trajectories, such as self-similar or space filling, exhibited during decision-making, irrespective of the trajectory's starting point. Furthermore, we find that a non-Euclidean representation of space considerably reduces the number of bifurcation points in many geometrical configurations, preventing endless indecision and promoting effective spatial decision-making. This suggests that a non-Euclidean neural representation of space may be expected to have evolved across species in order to facilitate spatial decision-making., 19 pages, 10 figures

The process of quantifying and analyzing animal behavior involves translating the naturally occurring descriptive language of their actions into machine-readable code. Yet, codifying behavior analysis is often challenging without deep understanding of animal behavior and technical machine learning knowledge. To limit this gap, we introduce AmadeusGPT: a natural language interface that turns natural language descriptions of behaviors into machine-executable code. Large-language models (LLMs) such as GPT3.5 and GPT4 allow for interactive language-based queries that are potentially well suited for making interactive behavior analysis. However, the comprehension capability of these LLMs is limited by the context window size, which prevents it from remembering distant conversations. To overcome the context window limitation, we implement a novel dual-memory mechanism to allow communication between short-term and long-term memory using symbols as context pointers for retrieval and saving. Concretely, users directly use language-based definitions of behavior and our augmented GPT develops code based on the core AmadeusGPT API, which contains machine learning, computer vision, spatio-temporal reasoning, and visualization modules. Users then can interactively refine results, and seamlessly add new behavioral modules as needed. We benchmark AmadeusGPT and show we can produce state-of-the-art performance on the MABE 2022 behavior challenge tasks. Note, an end-user would not need to write any code to achieve this. Thus, collectively AmadeusGPT presents a novel way to merge deep biological knowledge, large-language models, and core computer vision modules into a more naturally intelligent system. Code and demos can be found at: https://github.com/AdaptiveMotorControlLab/AmadeusGPT., demo available https://github.com/AdaptiveMotorControlLab/AmadeusGPT

New mental tasks were investigated for suitability in Brain-Computer Interface (BCI). Electroencephalography (EEG) signals were collected and analyzed to identify these mental tasks. MS Windows-based software was developed for investigating and classifying recorded EEG data with unnecessary frequencies filtered out with Bandpass filtering. To identify the best feature vector construction method for a given mental task, feature vectors were constructed using Bandpower, Principal Component Analysis, and Downsampling separately. These feature vectors were then classified with Linear Discriminant Analysis, Linear Support Vector Machines, Critical Distance Classifiers, Nearest Neighbor Classifiers, and their Non-Linear counterparts to find the best-performing classifier. For comparison purposes, performances of already well-known mental tasks in the BCI community were computed along with that of new mental tasks introduced in this thesis. In the preliminary studies, it was found that the most promising new mental task which a BCI system could identify is the imagination of hitting a given square with an imaginary arrow from above (or below) and right, (or left) to the screen. The group of these mental tasks was named as 'Hit Series' (HS). A detailed investigation of HS was carried out and compared with the performance of Motor Imagery (MI) events which are the most heavily used mental tasks in EEG-based BCI systems. One subject achieved the maximum average performance for HS, 100 pct in the binary classifications while 99 pct in overall combined performance. The best average performances of the other two subjects for the same mental tasks were 93 pct and 87pct with the overall performance of 89 pct and 78 pct. Performances of the same three subjects for mental tasks in MI were relatively poor. The average performances were 92, 78, and 92 pct while overall performances were 87, 69, and 88 pct., arXiv admin note: text overlap with arXiv:1404.1100 by other authors

Feature bagging is a well-established ensembling method which aims to reduce prediction variance by training estimators in an ensemble on random subsamples or projections of features. Typically, ensembles are chosen to be homogeneous, in the sense the the number of feature dimensions available to an estimator is uniform across the ensemble. Here, we introduce heterogeneous feature ensembling, with estimators built on varying number of feature dimensions, and consider its performance in a linear regression setting. We study an ensemble of linear predictors, each fit using ridge regression on a subset of the available features. We allow the number of features included in these subsets to vary. Using the replica trick from statistical physics, we derive learning curves for ridge ensembles with deterministic linear masks. We obtain explicit expressions for the learning curves in the case of equicorrelated data with an isotropic feature noise. Using the derived expressions, we investigate the effect of subsampling and ensembling, finding sharp transitions in the optimal ensembling strategy in the parameter space of noise level, data correlations, and data-task alignment. Finally, we suggest variable-dimension feature bagging as a strategy to mitigate double descent for robust machine learning in practice.

The human brain possesses the extraordinary capability to contextualize the information it receives from our environment. The entorhinal-hippocampal plays a critical role in this function, as it is deeply engaged in memory processing and constructing cognitive maps using place and grid cells. Comprehending and leveraging this ability could significantly augment the field of artificial intelligence. The multi-scale successor representation serves as a good model for the functionality of place and grid cells and has already shown promise in this role. Here, we introduce a model that employs successor representations and neural networks, along with word embedding vectors, to construct a cognitive map of three separate concepts. The network adeptly learns two different scaled maps and situates new information in proximity to related pre-existing representations. The dispersion of information across the cognitive map varies according to its scale - either being heavily concentrated, resulting in the formation of the three concepts, or spread evenly throughout the map. We suggest that our model could potentially improve current AI models by providing multi-modal context information to any input, based on a similarity metric for the input and pre-existing knowledge representations.

Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be common quantitative rules and constraints. However, there are also reasons to believe they should be different. For example, while the environments of trees may be relatively simple, neurons are constructed by a complex iterative program where synapses are made and pruned. This complexity may make neurons less self-similar than trees. Here we test this hypothesis by comparing the features of segmented sub-trees with those of the whole tree. We indeed find more self-similarity within actual trees than neurons. At the same time, we find that many other features are somewhat comparable across the two. Investigation of shapes and behaviors promises new ways of conceptualizing the form-function link.

Under the framework of network-based neurodegeneration, brain functional connectome (FC)-based Graph Neural Networks (GNN) have emerged as a valuable tool for the diagnosis and prognosis of neurodegenerative diseases such as Alzheimer's disease (AD). However, these models are tailored for brain FC at a single time point instead of characterizing FC trajectory. Discerning how FC evolves with disease progression, particularly at the predementia stages such as cognitively normal individuals with amyloid deposition or individuals with mild cognitive impairment (MCI), is crucial for delineating disease spreading patterns and developing effective strategies to slow down or even halt disease advancement. In this work, we proposed the first interpretable framework for brain FC trajectory embedding with application to neurodegenerative disease diagnosis and prognosis, namely Brain Tokenized Graph Transformer (Brain TokenGT). It consists of two modules: 1) Graph Invariant and Variant Embedding (GIVE) for generation of node and spatio-temporal edge embeddings, which were tokenized for downstream processing; 2) Brain Informed Graph Transformer Readout (BIGTR) which augments previous tokens with trainable type identifiers and non-trainable node identifiers and feeds them into a standard transformer encoder to readout. We conducted extensive experiments on two public longitudinal fMRI datasets of the AD continuum for three tasks, including differentiating MCI from controls, predicting dementia conversion in MCI, and classification of amyloid positive or negative cognitively normal individuals. Based on brain FC trajectory, the proposed Brain TokenGT approach outperformed all the other benchmark models and at the same time provided excellent interpretability. The code is available at https://github.com/ZijianD/Brain-TokenGT.git, MICCAI 2023

Despite being recognized as neurobiologically plausible, active inference faces difficulties when employed to simulate intelligent behaviour in complex environments due to its computational cost and the difficulty of specifying an appropriate target distribution for the agent. This paper introduces two solutions that work in concert to address these limitations. First, we present a novel planning algorithm for finite temporal horizons with drastically lower computational complexity. Second, inspired by Z-learning from control theory literature, we simplify the process of setting an appropriate target distribution for new and existing active inference planning schemes. Our first approach leverages the dynamic programming algorithm, known for its computational efficiency, to minimize the cost function used in planning through the Bellman-optimality principle. Accordingly, our algorithm recursively assesses the expected free energy of actions in the reverse temporal order. This improves computational efficiency by orders of magnitude and allows precise model learning and planning, even under uncertain conditions. Our method simplifies the planning process and shows meaningful behaviour even when specifying only the agent's final goal state. The proposed solutions make defining a target distribution from a goal state straightforward compared to the more complicated task of defining a temporally informed target distribution. The effectiveness of these methods is tested and demonstrated through simulations in standard grid-world tasks. These advances create new opportunities for various applications., 23 pages, 7 figures. Project repo: https://github.com/aswinpaul/dpefe_2023

Functional Connectivity between brain regions is known to be altered in Alzheimer's disease, and promises to be a biomarker for early diagnosis of the disease. While several approaches for functional connectivity obtain an un-directed network representing stochastic associations (correlations) between brain regions, association does not necessarily imply causation. In contrast, Causal Functional Connectivity is more informative, providing a directed network representing causal relationships between brain regions. In this paper, we obtained the causal functional connectome for the whole brain from recordings of resting-state functional magnetic resonance imaging (rs-fMRI) for subjects from three clinical groups: cognitively normal, mild cognitive impairment, and Alzheimer's disease. We applied the recently developed Time-aware PC (TPC) algorithm to infer the causal functional connectome for the whole brain. TPC supports model-free estimation of whole brain causal functional connectivity based on directed graphical modeling in a time series setting. We then identified the causal brain connections between brain regions which have significantly different strengths between pairs of subject groups, and over the three subject groups. We used the significant causal brain connections thus obtained to compile a comprehensive list of brain regions impacted by Alzheimer's disease according to the current data set. The obtained brain regions are in agreement with existing literature published by researchers from clinical/medical institutions thus validating the approach. We then discuss the soundness and completeness of the results and the potential for using causal functional connectivity obtained using this methodology as a basis for the prognosis and diagnosis of Alzheimer's disease.

We present the unified computational framework for modeling the sulcal patterns of human brain obtained from the magnetic resonance images. The Wasserstein distance is used to align the sulcal patterns nonlinearly. These patterns are topologically different across subjects making the pattern matching a challenge. We work out the mathematical details and develop the gradient descent algorithms for estimating the deformation field. We further quantify the image registration performance. This method is applied in identifying the differences between male and female sulcal patterns., In press in IEEE ISBI

This work reviews the human auditory system, elucidating some of the specialized mechanisms and non-linear pathways along the chain of events between physical sound and its perception. Customary relationships between frequency, time, and phase--such as the uncertainty principle--that hold for linear systems, do not apply straightforwardly to the hearing process. Auditory temporal resolution for certain processes can be a hundredth of the period of the signal, and can extend down to the microseconds time scale. The astonishingly large number of variations that correspond to the neural excitation pattern of 30000 auditory nerve fibers, originating from 3500 inner hair cells, explicates the vast capacity of the auditory system for the resolution of sonic detail. And the ear is sensitive enough to detect a basilar-membrane amplitude at the level of a picometer, or about a hundred times smaller than an atom. This article surveys and provides new insights into some of the impressive capabilities of the human auditory system and explores their relationship to fidelity in reproduced sound., 32 pages + contents, 22 figures, 19 equations, 221 cited references

A satisfactory understanding of information processing in spiking neural networks requires appropriate computational abstractions of neural activity. Traditionally, the neural population state vector has been the most common abstraction applied to spiking neural networks, but this requires artificially partitioning time into bins that are not obviously relevant to the network itself. We introduce a distinct set of techniques for analyzing spiking neural networks that decomposes neural activity into multiple, disjoint, parallel threads of activity. We construct these threads by estimating the degree of causal relatedness between pairs of spikes, then use these estimates to construct a directed acyclic graph that traces how the network activity evolves through individual spikes. We find that this graph of spiking activity naturally decomposes into disjoint connected components that overlap in space and time, which we call Graphical Neural Activity Threads (GNATs). We provide an efficient algorithm for finding analogous threads that reoccur in large spiking datasets, revealing that seemingly distinct spike trains are composed of similar underlying threads of activity, a hallmark of compositionality. The picture of spiking neural networks provided by our GNAT analysis points to new abstractions for spiking neural computation that are naturally adapted to the spatiotemporally distributed dynamics of spiking neural networks.

The stochastic exploration of the configuration space and the exploitation of optimal functional states underlie many biological processes. The evolutionary dynamics stands out as a remarkable example. Here, we introduce a novel formalism that mimics evolution and encodes a general exploration-exploitation dynamics for biological networks. We apply it to the brain wiring problem, focusing on the maturation of the C.elegans connectome. We demonstrate that a parsimonious maxent description of the adult brain combined with our framework is able to track down the entire developmental trajectory.

To resolve disputes or determine the order of things, people commonly use binary choices such as tossing a coin, even though it is obscure whether the empirical probability equals to the theoretical probability. The geomagnetic field (GMF) is broadly applied as a sensory cue for various movements in many organisms including humans, although our understanding is limited. Here we reveal a GMF-modulated probabilistic abstract decision-making in humans and the underlying mechanism, exploiting the zero-sum binary stone choice of Go game as a proof-of-principle. The large-scale data analyses of professional Go matches and in situ stone choice games showed that the empirical probabilities of the stone selections were remarkably different from the theoretical probability. In laboratory experiments, experimental probability in the decision-making was significantly influenced by GMF conditions and specific magnetic resonance frequency. Time series and stepwise systematic analyses pinpointed the intentionally uncontrollable decision-making as a primary modulating target. Notably, the continuum of GMF lines and anisotropic magnetic interplay between players were crucial to influence the magnetic field resonance-mediated abstract decision-making. Our findings provide unique insights into the impact of sensing GMF in decision-makings at tipping points and the quantum mechanical mechanism for manifesting the gap between theoretical and empirical probability in 3-dimensional living space., 32 pages, 5 figures, 4 supplementary figures, 2 supplementary tables, and separate 15 ancillary files

The relationship between blood flow and neuronal activity is widely recognized, with blood flow frequently serving as a surrogate for neuronal activity in fMRI studies. At the microscopic level, neuronal activity has been shown to influence blood flow in nearby blood vessels. This study introduces the first predictive model that addresses this issue directly at the explicit neuronal population level. Using in vivo recordings in awake mice, we employ a novel spatiotemporal bimodal transformer architecture to infer current blood flow based on both historical blood flow and ongoing spontaneous neuronal activity. Our findings indicate that incorporating neuronal activity significantly enhances the model's ability to predict blood flow values. Through analysis of the model's behavior, we propose hypotheses regarding the largely unexplored nature of the hemodynamic response to neuronal activity.

Recurrent neural network-based reinforcement learning systems are capable of complex motor control tasks such as locomotion and manipulation, however, much of their underlying mechanisms still remain difficult to interpret. Our aim is to leverage computational neuroscience methodologies to understanding the population-level activity of robust robot locomotion controllers. Our investigation begins by analyzing topological structure, discovering that fragile controllers have a higher number of fixed points with unstable directions, resulting in poorer balance when instructed to stand in place. Next, we analyze the forced response of the system by applying targeted neural perturbations along directions of dominant population-level activity. We find evidence that recurrent state dynamics are structured and low-dimensional during walking, which aligns with primate studies. Additionally, when recurrent states are perturbed to zero, fragile agents continue to walk, which is indicative of a stronger reliance on sensory input and weaker recurrence.

We present a simulated biologically plausible language organ, made up of stylized but realistic neurons, synapses, brain areas, plasticity, and a simplified model of sensory perception. We show through experiments that this model succeeds in an important early step in language acquisition: the learning of nouns, verbs, and their meanings, from the grounded input of only a modest number of sentences. Learning in this system is achieved through Hebbian plasticity, and without backpropagation. Our model goes beyond a parser previously designed in a similar environment, with the critical addition of a biologically plausible account for how language can be acquired in the infant's brain, not just processed by a mature brain., 9 pages, 4 figures

In principle, dynamic functional connectivity in fMRI is just a statistical measure. A passer-by might think it to be a specialist topic, but it continues to attract widespread attention and spark controversy. Why?

Although normal homologous brain structures are approximately symmetrical by definition, they also have shape differences due to e.g. natural ageing. On the other hand, neurodegenerative conditions induce their own changes in this asymmetry, making them more pronounced or altering their location. Identifying when these alterations are due to a pathological deterioration is still challenging. Current clinical tools rely either on subjective evaluations, basic volume measurements or disease-specific deep learning models. This paper introduces a novel method to learn normal asymmetry patterns in homologous brain structures based on anomaly detection and representation learning. Our framework uses a Siamese architecture to map 3D segmentations of left and right hemispherical sides of a brain structure to a normal asymmetry embedding space, learned using a support vector data description objective. Being trained using healthy samples only, it can quantify deviations-from-normal-asymmetry patterns in unseen samples by measuring the distance of their embeddings to the center of the learned normal space. We demonstrate in public and in-house sets that our method can accurately characterize normal asymmetries and detect pathological alterations due to Alzheimer's disease and hippocampal sclerosis, even though no diseased cases were accessed for training. Our source code is available at https://github.com/duiliod/DeepNORHA.

Inferring the mechanisms underlying physiological and pathological processes in the brain from recorded electrical activity is challenging. Bayesian model selection and dynamic causal modelling aim to identify likely biophysical models to explain data and to fit the model parameters. Here, we use data generated by simulations to investigate the effectiveness of Bayesian model selection and dynamic causal modelling when applied at steady state in the frequency domain to identify and fit Jansen-Rit models. We first investigate the impact of the necessary assumption of linearity on the dynamics of the Jansen-Rit model. We then apply dynamic causal modelling and Bayesian model selection to data generated from simulations of linear neural mass models, non-linear neural mass models, and networks of discrete spiking neurons. Action potentials are a characteristic feature of neuronal dynamics but have not previously been explicitly included in simulations used to test Bayesian model selection or dynamic causal modelling. We find that the assumption of linearity abolishes the qualitative transitions seen as a function of the connectivity parameter in the original Jansen-Rit model. As with previous work, we find that the recovery procedures are effective when applied to data from linear Jansen-Rit neural mass models, however, when applying them to non-linear neural mass models and networks of discrete spiking neurons we find that their effectiveness is significantly reduced, suggesting caution is required when applying these methods., 18 pages, 15 figures

The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential equations employed in combination with the alleged functional production of the mind by the brain. Then, we demonstrate that a mind--brain theory consistent with causally potent conscious experiences is provided by modern quantum physics, in which the unobservable conscious mind is reductively identified with the quantum state of the brain and the observable brain is constructed by the physical measurement of quantum brain observables. The resulting quantum stochastic dynamics obtained from sequential quantum measurements of the brain is governed by stochastic differential equations, which permit genuine free will exercised through sequential conscious choices of future courses of action. Thus, quantum reductionism provides a solid theoretical foundation for the causal potency of consciousness, free will and cultural transmission., 47 pages, 7 figures. International Journal of Modern Physics B (2023)

Brain graphs, which model the structural and functional relationships between brain regions, are crucial in neuroscientific and clinical applications involving graph classification. However, dense brain graphs pose computational challenges including high runtime and memory usage and limited interpretability. In this paper, we investigate effective designs in Graph Neural Networks (GNNs) to sparsify brain graphs by eliminating noisy edges. While prior works remove noisy edges based on explainability or task-irrelevant properties, their effectiveness in enhancing performance with sparsified graphs is not guaranteed. Moreover, existing approaches often overlook collective edge removal across multiple graphs. To address these issues, we introduce an iterative framework to analyze different sparsification models. Our findings are as follows: (i) methods prioritizing interpretability may not be suitable for graph sparsification as they can degrade GNNs' performance in graph classification tasks; (ii) simultaneously learning edge selection with GNN training is more beneficial than post-training; (iii) a shared edge selection across graphs outperforms separate selection for each graph; and (iv) task-relevant gradient information aids in edge selection. Based on these insights, we propose a new model, Interpretable Graph Sparsification (IGS), which enhances graph classification performance by up to 5.1% with 55.0% fewer edges. The retained edges identified by IGS provide neuroscientific interpretations and are supported by well-established literature., To appear in Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 23)

We present a didactic introduction to spectral Dynamic Causal Modelling (DCM), a Bayesian state-space modelling approach used to infer effective connectivity from non-invasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modelling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all variables--at all time lags--including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.