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We study the optimality conditions of information transfer in systems with memory in the low signal-to-noise ratio regime of vanishing input amplitude. We find that the optimal mutual information is represented by a maximum-variance of the signal time course, with correlation structure determined by the Fisher information matrix. We provide illustration of the method on a simple biologically-inspired model of electro-sensory neuron. Our general results apply also to the study of information transfer in single neurons subject to weak stimulation, with implications to the problem of coding efficiency in biological systems.
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The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($Phi$) in the brain is related to the level of consciousness. IIT proposes that to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that if a measure of $Phi$ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of $Phi$ is submodular, the lat
Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with quasi-random phase relative to the stimulus. We propose a model to reproduce characteristic features of oscillatory spike trains, such as histograms of inter-spike intervals and phase locking of spikes to an oscillatory influence. The proposed model is based on an inhomogeneous Gamma process governed by a density function that is a product of the usual stimulus-dependent rate and a quasi-periodic function. Further, we present an analysis method generalizing the direct method (Rieke et al, 1999; Brenner et al, 2000) to assess the information content in such data. We demonstrate these tools on recordings from relay cells in the lateral geniculate nucleus of the cat.
The Integrated Information Theory provides a quantitative approach to consciousness and can be applied to neural networks. An embodied agent controlled by such a network influences and is being influenced by its environment. This involves, on the one hand, morphological computation within goal directed action and, on the other hand, integrated information within the controller, the agents brain. In this article, we combine different methods in order to examine the information flows among and within the body, the brain and the environment of an agent. This allows us to relate various information flows to each other. We test this framework in a simple experimental setup. There, we calculate the optimal policy for goal-directed behavior based on the planning as inference method, in which the information-geometric em-algorithm is used to optimize the likelihood of the goal. Morphological computation and integrated information are then calculated with respect to the optimal policies. Comparing the dynamics of these measures under changing morphological circumstances highlights the antagonistic relationship between these two concepts. The more morphological computation is involved, the less information integration within the brain is required. In order to determine the influence of the brain on the behavior of the agent it is necessary to additionally measure the information flow to and from the brain.
Determining how much of the sensory information carried by a neural code contributes to behavioral performance is key to understand sensory function and neural information flow. However, there are as yet no analytical tools to compute this information that lies at the intersection between sensory coding and behavioral readout. Here we develop a novel measure, termed the information-theoretic intersection information $I_{II}(S;R;C)$, that quantifies how much of the sensory information carried by a neural response R is used for behavior during perceptual discrimination tasks. Building on the Partial Information Decomposition framework, we define $I_{II}(S;R;C)$ as the part of the mutual information between the stimulus S and the response R that also informs the consequent behavioral choice C. We compute $I_{II}(S;R;C)$ in the analysis of two experimental cortical datasets, to show how this measure can be used to compare quantitatively the contributions of spike timing and spike rates to task performance, and to identify brain areas or neural populations that specifically transform sensory information into choice.
In many neural systems anatomical motifs are present repeatedly, but despite their structural similarity they can serve very different tasks. A prime example for such a motif is the canonical microcircuit of six-layered neo-cortex, which is repeated across cortical areas, and is involved in a number of different tasks (e.g.sensory, cognitive, or motor tasks). This observation has spawned interest in finding a common underlying principle, a goal function, of information processing implemented in this structure. By definition such a goal function, if universal, cannot be cast in processing-domain specific language (e.g. edge filtering, working memory). Thus, to formulate such a principle, we have to use a domain-independent framework. Information theory offers such a framework. However, while the classical framework of information theory focuses on the relation between one input and one output (Shannons mutual information), we argue that neural information processing crucially depends on the combination of textit{multiple} inputs to create the output of a processor. To account for this, we use a very recent extension of Shannon Information theory, called partial information decomposition (PID). PID allows to quantify the information that several inputs provide individually (unique information), redundantly (shared information) or only jointly (synergistic information) about the output. First, we review the framework of PID. Then we apply it to reevaluate and analyze several earlier proposals of information theoretic neural goal functions (predictive coding, infomax, coherent infomax, efficient coding). We find that PID allows to compare these goal functions in a common framework, and also provides a versatile approach to design new goal functions from first principles. Building on this, we design and analyze a novel goal function, called coding with synergy. [...]
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