A Reward-Maximizing Spiking Neuron as a Bounded Rational Decision Maker

2015 ◽  
Vol 27 (8) ◽  
pp. 1686-1720 ◽  
Author(s):  
Felix Leibfried ◽  
Daniel A. Braun
Keyword(s):  
Mutual Information ◽  
Decision Maker ◽  
Sensory Input ◽  
Rate Distortion ◽  
Relevant Information ◽  
Motor Output ◽  
Spiking Neuron ◽  
Rational Decision ◽  
Rate Distortion Theory ◽  
The Many

Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded rational decision making, where decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded rational decision maker can be thought to optimize an objective function that trades off the decision maker’s utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded rational decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron’s input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron’s instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.

scholarly journals Mutual Information, the Linear Prediction Model, and CELP Voice Codecs

2019 ◽  
Author(s):  
Jerry Gibson
Keyword(s):  
Mutual Information ◽  
Linear Prediction ◽  
Rate Distortion ◽  
Source Model ◽  
Rate Distortion Theory ◽  
Input Source ◽  
Distortion Measure ◽  
Adaptive Codebook ◽  
Log Ratio ◽  
Linear Prediction Model

We write the mutual information between an input speech utterance and its reconstruction by a Code-Excited Linear Prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare to the performance of the AMR codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

scholarly journals The evolution of lossy compression

2017 ◽  
Vol 14 (130) ◽  
pp. 20170166 ◽  
Author(s):  
Sarah E. Marzen ◽  
Simon DeDeo
Keyword(s):  
Information Theory ◽  
Rate Distortion ◽  
Relevant Information ◽  
Lossy Compression ◽  
High Fidelity ◽  
Complex Environments ◽  
Environmental Complexity ◽  
Trade Off ◽  
Rate Distortion Theory ◽  
Unstructured Environments

In complex environments, there are costs to both ignorance and perception. An organism needs to track fitness-relevant information about its world, but the more information it tracks, the more resources it must devote to perception. As a first step towards a general understanding of this trade-off, we use a tool from information theory, rate–distortion theory, to study large, unstructured environments with fixed, randomly drawn penalties for stimuli confusion (‘distortions’). We identify two distinct regimes for organisms in these environments: a high-fidelity regime where perceptual costs grow linearly with environmental complexity, and a low-fidelity regime where perceptual costs are, remarkably, independent of the number of environmental states. This suggests that in environments of rapidly increasing complexity, well-adapted organisms will find themselves able to make, just barely, the most subtle distinctions in their environment.

scholarly journals Markov Information Bottleneck to Improve Information Flow in Stochastic Neural Networks

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 976 ◽  
Author(s):  
Thanh Tang Nguyen ◽  
Jaesik Choi
Keyword(s):  
Neural Networks ◽  
Information Flow ◽  
Latent Variables ◽  
Rate Distortion ◽  
Relevant Information ◽  
Variational Approximation ◽  
Stochastic Neural Networks ◽  
Rate Distortion Theory ◽  
Information Bottleneck ◽  
Hidden Layer

While rate distortion theory compresses data under a distortion constraint, information bottleneck (IB) generalizes rate distortion theory to learning problems by replacing a distortion constraint with a constraint of relevant information. In this work, we further extend IB to multiple Markov bottlenecks (i.e., latent variables that form a Markov chain), namely Markov information bottleneck (MIB), which particularly fits better in the context of stochastic neural networks (SNNs) than the original IB. We show that Markov bottlenecks cannot simultaneously achieve their information optimality in a non-collapse MIB, and thus devise an optimality compromise. With MIB, we take the novel perspective that each layer of an SNN is a bottleneck whose learning goal is to encode relevant information in a compressed form from the data. The inference from a hidden layer to the output layer is then interpreted as a variational approximation to the layer’s decoding of relevant information in the MIB. As a consequence of this perspective, the maximum likelihood estimate (MLE) principle in the context of SNNs becomes a special case of the variational MIB. We show that, compared to MLE, the variational MIB can encourage better information flow in SNNs in both principle and practice, and empirically improve performance in classification, adversarial robustness, and multi-modal learning in MNIST.

scholarly journals Research a New Tradeoff Method Between Privacy and Utility in Differential privacy

2021 ◽  
Author(s):  
panjun sun
Keyword(s):  
Mutual Information ◽  
Privacy Protection ◽  
Differential Privacy ◽  
Rate Distortion ◽  
Information Privacy ◽  
Distortion Function ◽  
Approximate Algorithm ◽  
Data Utility ◽  
Rate Distortion Theory ◽  
Privacy Leakage

Abstract The solution of the contradiction between privacy protection and data utility is a research hotspot in the field of privacy protection. Aiming at the problem of tradeoff between privacy and utility in the scenario of differential privacy offline data release, the optimal differential privacy mechanism is studied by using the rate distortion theory. Firstly, based on Shannon communication theory, the noise channel model of differential privacy is abstracted, and the mutual information and the distortion function is used to measure the privacy and utility of data publishing, and the optimization model based on rate distortion theory is constructed. Secondly, considering the influence of associated auxiliary background knowledge on mutual information privacy leakage, a mutual information privacy measure based on joint events is proposed, and a minimum privacy leakage model is proposed by modifying the rate distortion function. Finally, aiming at the difficulty in solving the Lagrange multiplier method, an approximate algorithm for solving the mutual information privacy optimization channel mechanism is proposed based on the alternating iterative method. The effectiveness of the proposed iterative approximation method is verified by experimental simulation. At the same time, the experimental results show that the proposed method reduces the mutual information privacy leakage under the condition of limited distortion, and improves the data utility under the same privacy tolerance

scholarly journals Mutual Information, the Linear Prediction Model, and CELP Voice Codecs

Information ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 179 ◽  
Author(s):  
Jerry Gibson
Keyword(s):  
Mutual Information ◽  
Linear Prediction ◽  
Rate Distortion ◽  
Source Model ◽  
Rate Distortion Theory ◽  
Input Source ◽  
Distortion Measure ◽  
Adaptive Codebook ◽  
Log Ratio ◽  
Linear Prediction Model

We write the mutual information between an input speech utterance and its reconstruction by a code-excited linear prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short-term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare these to the performance of the adaptive multirate (AMR) codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

The mamillothalamic pathways: my first encounter with the thalamus

2017 ◽  
Author(s):  
Ray Guillery
Keyword(s):  
Sensory Input ◽  
Great Success ◽  
Cortical Lesions ◽  
Head Direction ◽  
Thalamic Nuclei ◽  
Sensory Pathways ◽  
Cortical Areas ◽  
Thalamic Relay ◽  
The Many

My thesis studies had stimulated an interest in the mamillothalamic pathways but also some puzzlement because we knew nothing about the nature of the messages passing along these pathways. Several laboratories were studying the thalamic relay of sensory pathways with great success during my post-doctoral years. Each sensory relay could be understood in terms of the appropriate sensory input, but we had no way of knowing the meaning of the mamillothalamic messages. I introduce these nuclei as an example of the many thalamic nuclei about whose input functions we still know little or nothing. Early clinical studies of mamillary lesions had suggested a role in memory formation, whereas evidence from cortical lesions suggested a role in emotional experiences. Studies of the smallest of the three nuclei forming these pathways then showed it to be concerned with sensing head direction, relevant but not sufficient for defining an animal’s position in space. More recent studies based on studies of cortical activity or cortical damage have provided a plethora of suggestions: as so often, the answers reported depend on the questions asked. That simple conclusion is relevant for all transthalamic pathways. The evidence introduced in Chapter 1, that thalamocortical messages have dual meanings, suggests that we need to rethink our questions. It may prove useful to look at the motor outputs of relevant cortical areas to get clues about some appropriate questions.

scholarly journals Macphail (1987) Revisited: Pigeons Have Much Cognitive Behavior in Common With Humans

2021 ◽  
Vol 11 ◽  
Author(s):  
Thomas R. Zentall
Keyword(s):  
Cognitive Ability ◽  
Present Article ◽  
Sensory Input ◽  
Motor Output ◽  
Cognitive Behavior ◽  
Intellectual Abilities ◽  
Intelligent Behavior

The hypothesis proposed by Macphail (1987) is that differences in intelligent behavior thought to distinguish different species were likely attributed to differences in the context of the tasks being used. Once one corrects for differences in sensory input, motor output, and incentive, it is likely that all vertebrate animals have comparable intellectual abilities. In the present article I suggest a number of tests of this hypothesis with pigeons. In each case, the evidence suggests that either there is evidence for the cognitive behavior, or the pigeons suffer from biases similar to those of humans. Thus, Macphail’s hypothesis offers a challenge to researchers to find the appropriate conditions to bring out in the animal the cognitive ability being tested.

scholarly journals An Information-Theoretic Account of Semantic Interference in Word Production

2021 ◽  
Vol 12 ◽  
Author(s):  
Richard Futrell
Keyword(s):  
Mutual Information ◽  
Semantic Similarity ◽  
Rate Distortion ◽  
Word Production ◽  
Interference Effects ◽  
Semantic Interference ◽  
Information Theoretic ◽  
Human Data ◽  
Level Model ◽  
Computational Level

I present a computational-level model of semantic interference effects in online word production within a rate–distortion framework. I consider a bounded-rational agent trying to produce words. The agent's action policy is determined by maximizing accuracy in production subject to computational constraints. These computational constraints are formalized using mutual information. I show that semantic similarity-based interference among words falls out naturally from this setup, and I present a series of simulations showing that the model captures some of the key empirical patterns observed in Stroop and Picture–Word Interference paradigms, including comparisons to human data from previous experiments.

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