Due to the staggering complexity of the brain and its neural circuitry, neuroscientists rely on the analysis of mathematical models to elucidate its function. From Hodgkin and Huxley's detailed description of the action potential in 1952 to today, new theories and increasing computational power have opened up novel avenues to study how neural circuits implement the computations that underlie behaviour. Computational neuroscientists have developed many models of neural circuits that differ in complexity, biological realism or emergent network properties. With recent advances in experimental techniques for detailed anatomical reconstructions or large-scale activity recordings, rich biological data have become more available. The challenge when building network models is to reflect experimental results, either through a high level of detail or by finding an appropriate level of abstraction. Meanwhile, machine learning has facilitated the development of artificial neural networks, which are trained to perform specific tasks. While they have proven successful at achieving task-oriented behaviour, they are often abstract constructs that differ in many features from the physiology of brain circuits. Thus, it is unclear whether the mechanisms underlying computation in biological circuits can be investigated by analysing artificial networks that accomplish the same function but differ in their mechanisms. Here, we argue that building biologically realistic network models is crucial to establishing causal relationships between neurons, synapses, circuits and behaviour. More specifically, we advocate for network models that consider the connectivity structure and the recorded activity dynamics while evaluating task performance.

Neural computations emerge from local recurrent neural circuits or computational units such as cortical columns that comprise hundreds to a few thousand neurons. Continuous progress in connectomics, electrophysiology, and calcium imaging require tractable spiking network models that can consistently incorporate new information about the network structure and reproduce the recorded neural activity features. However, for spiking networks, it is challenging to predict which connectivity configurations and neural properties can generate fundamental operational states and specific experimentally reported nonlinear cortical computations. Theoretical descriptions for the computational state of cortical spiking circuits are diverse, including the balanced state where excitatory and inhibitory inputs balance almost perfectly or the inhibition stabilized state (ISN) where the excitatory part of the circuit is unstable. It remains an open question whether these states can co-exist with experimentally reported nonlinear computations and whether they can be recovered in biologically realistic implementations of spiking networks. Here, we show how to identify spiking network connectivity patterns underlying diverse nonlinear computations such as XOR, bistability, inhibitory stabilization, supersaturation, and persistent activity. We establish a mapping between the stabilized supralinear network (SSN) and spiking activity which allows us to pinpoint the location in parameter space where these activity regimes occur. Notably, we find that biologically-sized spiking networks can have irregular asynchronous activity that does not require strong excitation-inhibition balance or large feedforward input and we show that the dynamic firing rate trajectories in spiking networks can be precisely targeted without error-driven training algorithms.

The intensity and the features of sensory stimuli are encoded in the activity of neurons in the cortex. In the visual and piriform cortices, the stimulus intensity rescales the activity of the population without changing its selectivity for the stimulus features. The cortical representation of the stimulus is therefore intensity invariant. This emergence of network-invariant representations appears robust to local changes in synaptic strength induced by synaptic plasticity, even though (i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and (ii) in networks with balanced excitation and inhibition, synaptic plasticity determines the nonlinear network behavior. In this study we investigate the consistency of invariant representations with a variety of synaptic states in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the emergence of intensity-invariant or intensity-dependent selectivity. In particular, we demonstrate that an effective power-law synaptic transformation at the population level is necessary for invariance. In a range of firing rates, purely depressing short-term synapses fulfills this condition, and in this case, the network is contrast-invariant. Instead, facilitating short-term plasticity generally narrows the network selectivity. We found that facilitating and depressing short-term plasticity can be combined to approximate a power-law that leads to contrast invariance. These results explain how the physiology of individual synapses is linked to the emergence of invariant representations of sensory stimuli at the network level.

Neural computations emerge from recurrent neural circuits that comprise hundreds to a few thousand neurons. Continuous progress in connectomics, electrophysiology, and calcium imaging require tractable spiking network models that can consistently incorporate new information about the network structure and reproduce the recorded neural activity features. However, it is challenging to predict which spiking network connectivity configurations and neural properties can generate fundamental operational states and specific experimentally reported nonlinear cortical computations. Theoretical descriptions for the computational state of cortical spiking circuits are diverse, including the balanced state where excitatory and inhibitory inputs balance almost perfectly or the inhibition stabilized state (ISN) where the excitatory part of the circuit is unstable. It remains an open question whether these states can co-exist with experimentally reported nonlinear computations and whether they can be recovered in biologically realistic implementations of spiking networks. Here, we show how to identify spiking network connectivity patterns underlying diverse nonlinear computations such as XOR, bistability, inhibitory stabilization, supersaturation, and persistent activity. We established a mapping between the stabilized supralinear network (SSN) and spiking activity which allowed us to pinpoint the location in parameter space where these activity regimes occur. Notably, we found that biologically-sized spiking networks can have irregular asynchronous activity that does not require strong excitation-inhibition balance or large feedforward input and we showed that the dynamic firing rate trajectories in spiking networks can be precisely targeted without error-driven training algorithms.

Network selectivity for orientation is invariant to changes in the stimulus contrast in the primary visual cortex. Similarly, the selectivity for odor identity is invariant to changes in odorant concentration in the piriform cortex. Interestingly, invariant network selectivity appears robust to local changes in synaptic strength induced by synaptic plasticity, even though: i) synaptic plasticity can potentiate or depress connections between neurons in a feature-dependent manner, and ii) in networks with balanced excitation and inhibition, synaptic plasticity is a determinant for the network non-linearity. In this study, we investigate whether network contrast invariance is consistent with a variety of synaptic states and connectivities in balanced networks. By using mean-field models and spiking network simulations, we show how the synaptic state controls the non-linearity in the network response to contrast and how it can lead to the emergence of contrast-invariant or contrast-dependent selectivity. Different forms of synaptic plasticity sharpen or broaden the network selectivity, while others do not affect it. Our results explain how the physiology of individual synapses is linked to contrast-invariant selectivity at the network level.

The causal dependences (in a dynamical sense) between the dynamics of three different coupled ocean–atmosphere basins, the North Atlantic, the North Pacific and the tropical Pacific region (Nino3.4), have been explored using data from three reanalysis datasets, namely ORA-20C, ORAS4 and ERA-20C. The approach is based on convergent cross mapping (CCM) developed by Sugihara et al. (2012) that allows for evaluating the dependences between variables beyond the classical teleconnection patterns based on correlations.The use of CCM on these data mostly reveals that (i) the tropical Pacific (Nino3.4 region) only influences the dynamics of the North Atlantic region through its annual climatological cycle; (ii) the atmosphere over the North Pacific is dynamically forcing the North Atlantic on a monthly basis; (iii) on longer timescales (interannual), the dynamics of the North Pacific and the North Atlantic are influencing each other through the ocean dynamics, suggesting a connection through the thermohaline circulation.These findings shed a new light on the coupling between these three different regions of the globe. In particular, they call for a deep reassessment of the way teleconnections are interpreted and for a more rigorous way to evaluate dynamical dependences between the different components of the climate system.

Dear Editor We would like first to thank you for the very constructive comments that you have made during this second round of review. Please find below how we address your three different points that have to be settled. The additional text is colored in green in the pdf version of the new manuscript. 1. Causality: There is a clash of cultures between physical and the kinematicgeometric views. In fundamental Physics and most fields of natural science, causality pertains cause-effect relationships. This is what had been meant as causality in the previous editorial report. In kinematic-geometric approaches to dynamical systems, there is no proven cause-effect among co-members of a dynamical system, but rather a codependence bond as expressed through kinematic-geometric couplings, which may be physically non-causal. The term causation mentioned in the author response is yet another concept that is physically different from that of causality but is not the object of study in the manuscript, therefore the only note I leave in that regard is that these are not equivalent concepts. Closing the matters on point 1 , the conceptual debate on causality can be avoided in the revised manuscript by clearly reiterating that the work addresses causality from a dynamical systems perspective, and acknowledging that this is not to be confused with the physical cause-effect definition. This way, causality statements on the manuscript will be positioned on their specific kinematic-geometric context, deploying the analysis and discussion without conceptual clashes. We indeed do agree with your point. The notion of causality is multifaceted and it is not easy to grasp this concept in one definition. In order to clarify the specific definition used here, we have introduced the following text at page 3, line 23: It must be stressed here that the notion of causality is used in the very specific context of dynamical systems theory discussed above, that should not be confused with the traditional cause-effect relationship. From now on, the words causality and dependences will be used equivalently.

The causal dependences between the dynamics of three different coupled ocean-atmosphere basins, The North Atlantic, the North Pacific and the Tropical Pacific region, NINO3.4, have been explored using data from three reanalyses datasets, namely the ORA-20C, the ORAS4 and the ERA-20C. The approach is based on the Convergent Cross Mapping (CCM) developed by Sugihara et al (2012) that allows for evaluating the dependences between variables beyond the classical teleconnection 5 patterns based on correlations. The use of CCM on these data mostly reveals that (i) the Tropical Pacific (NINO3.4 region) only influences the dynamics of the North Atlantic region through its annual climatological cycle; (ii) the atmosphere over the North Pacific is dynamically forcing the North Atlantic on a monthly basis; (iii) on longer time scales (interannual), the dynamics of the North Pacific and the North Atlantic are influencing each other through the ocean dynamics, suggesting a connection through the thermohaline 10 circulation. These findings shed a new light on the coupling between these three different important regions of the globe. In particular they call for a deep reassessment of the way teleconnections are interpreted, and for a more rigorous way to evaluate causality and dependences between the different components of the climate system. Copyright statement. TEXT 15

nual time scales, between the climate dynamics of three ocean-atmosphere basins (The North Atlantic, the North Pacific and the Tropical Pacific region) using three reanalyses datasets (ORA-20C, ORAS4 and ERA-20C). The applied methodology, Convergent Cross Mapping (CCM) has been applied to other systems, but has not yet been used (to the best of my knowledge) to investigate climate causal relationships. I found this study very interesting. As the authors acknowledge in the introduction, unveiling causal relations is a very challenging task, and different methods (also depending on the choice of variables), are likely to yield different results. Here the CCM method is well motivated and described, and also the datasets used for reconstructing threedimensional attractors are well justified. The results obtained are sound. Therefore, I am happy to recommend the acceptance of this manuscript, after the authors have taken the following points.