Tag: neuron level

Generating coherent patterns of activity from chaotic neural networks.

Sussillo, D. and Abbott, L. F.
Neuron, 63:544–557, 2009
DOI, Google Scholar

Abstract

Neural circuits display complex activity patterns both spontaneously and when responding to a stimulus or generating a motor output. How are these two forms of activity related? We develop a procedure called FORCE learning for modifying synaptic strengths either external to or within a model neural network to change chaotic spontaneous activity into a wide variety of desired activity patterns. FORCE learning works even though the networks we train are spontaneously chaotic and we leave feedback loops intact and unclamped during learning. Using this approach, we construct networks that produce a wide variety of complex output patterns, input-output transformations that require memory, multiple outputs that can be switched by control inputs, and motor patterns matching human motion capture data. Our results reproduce data on premovement activity in motor and premotor cortex, and suggest that synaptic plasticity may be a more rapid and powerful modulator of network activity than generally appreciated.

Review

The authors present a new way of reservoir computing. The setup apparently (haven’t read the paper) is very similar to the echo state networks of Herbert Jaeger (Jaeger and Haas, Science, 2004); the difference being the signal that is fed back to the reservoir from the output. While Jaeger fed back the target value f(t), they feed back the error between f(t) and the prediction given the current weights and reservoir activity. Key to their approach then is that they use a weight update rule which almost instantaneously provides weights that minimise the error. While this obviously leads to a very high variability of the weights across time steps at the start of learning, they argue that this variability diminishes during learning and weights eventually stabilise such that, when learning is switched off, the target dynamics is reproduced. They present a workaround which may make it possible to also learn non-periodic functions, but it’s clearly better suited for periodic functions.

I wonder how the learning is divided between feedback mechanism and weight adaptation (network model of Fig. 1A). In particular, it could well be that the feedback mechanism is solely responsible for successfull learning while the weights just settle to a more or less arbitrary setting once the dynamics is stabilised through the feedback (making weights uninterpretable). The authors also report how the synapses within the reservoir can be adapted to reproduce the target dynamics when no feedback signal is given from the network output (structure in Fig. 1C). Curiously, the credit assignment problem is solved by ignoring it: for the adaptation of reservoir synapses the same network level output error is used as for the adaptation of output weights.

It’s interesting that it works, but to know why and how it works would be good. The main argument of the authors why their proposal is better than echo state networks is that their proposal is more stable. They present corresponding results in Fig. 4, but they never tell us what they mean by stable. So how stable are the dynamics learnt by FORCE? How much can you perturb the network dynamics before it stops being able to reproduce the target dynamics. In other words, how far off the desired dynamics can you initialise the network state?

They have an interesting principal components analysis of network activity suggesting that the dynamics converges to the same values for the first principal components for different starting states, but I haven’t understood it well enough during this first read to comment further on that.

The Neural Costs of Optimal Control.

Gershman, S. J. and Wilson, R. C.
in: Advances in Neural Information Processing Systems 23, 2010
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Abstract

Optimal control entails combining probabilities and utilities. However, for most practical problems, probability densities can be represented only approximately. Choosing an approximation requires balancing the benefits of an accurate approximation against the costs of computing it. We propose a variational framework for achieving this balance and apply it to the problem of how a neural population code should optimally represent a distribution under resource constraints. The essence of our analysis is the conjecture that population codes are organized to maximize a lower bound on the log expected utility. This theory can account for a plethora of experimental data, including the reward-modulation of sensory receptive fields, GABAergic effects on saccadic movements, and risk aversion in decisions under uncertainty.

Review

Within the area of decision theory they consider the problem of evaluating the expected utility of an action given a posterior. They propose a variational framework analogously to the one used for the EM algorithm in which the utility replaces the likelihood and the posterior replaces the prior. Their main contribution is to include a cost penalising the complexity of the approximation of the posterior and use the so defined lower bound on the expected utility to simultaneously optimise the density used to approximate the posterior. As the utility does not only contain the cost of the approximation, but also the actual utility of an action in the considered states, this model predicts that the approximating density should also reflect what is behaviourally relevant instead of only trying to represent the natural posterior distribution optimally.

In the results section they then show that under this model the approximated posterior can (and will) indeed put more probability mass on states with larger utility, something which has apparently been found in grasshoppers. Additionally they show that increasing the cost of spikes results in smaller firing rates which, as they argue, leads to response latencies as seen in experiments. Finally, they show that under the assumption that high utility or very costly states are rare, the model will automatically account for the nonlinear weighting of probabilities in risky choice observed in humans. The model therefore explains this irrational behaviour by noting that “under neural resource constraints, the approximate density will be biased towards high reward regions of the state space.”

I don’t know enough to judge the correspondence of the model behaviour/predictions with the experimental results, or whether the model contradicts some other results. However, the paper is quite inspiring in the sense that it presents an intuitive idea which potentially has big implications for how populations of neurons code probability distributions, namely that the neuronal codes are influenced as much by expected rewards as by the natural distribution. Of course, the paper leaves many questions open. The authors only show results for when the approximate distributions are optimised alone, but what happens when actions and distribution are optimised simultaneously? What are the timescales of the distribution optimisation? Is it really instantanious (on the same timescale as action selection) as the authors indicate, or is it rather a slower process? Their proposal also has the potential to explain how the dimensionality of the state space can be reduced by only considering states which are behaviourally relevant. However, it remains unclear to what extent this specialisation should be implemented. In other words, is the posterior dependent, e.g., on the precise goal in the task, or is it rather only dependent on the selected task? Especially the cost of spiking example suggests a connection between the proposed mechanism and attention. Can attention be explained by this low-level description of biased representations of the posterior distribution?

The paper is quite inspiring and you kind of wonder why nobody has made these ideas explicit before, or maybe somebody has? Actually Maneesh Sahani had a NIPS paper in 2004 which they cite, but not comment on, and which looks very similar to what they do here (from the abstract).

Winnerless competition between sensory neurons generates chaos: A possible mechanism for molluscan hunting behavior.

Varona, P., Rabinovich, M. I., Selverston, A. I., and Arshavsky, Y. I.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 12:672–677, 2002
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Abstract

In the presence of prey, the marine mollusk Clione limacina exhibits search behavior, i.e., circular motions whose plane and radius change in a chaotic-like manner. We have formulated a dynamical model of the chaotic hunting behavior of Clione based on physiological in vivo and in vitro experiments. The model includes a description of the action of the cerebral hunting interneuron on the receptor neurons of the gravity sensory organ, the statocyst. A network of six receptor model neurons with Lotka-Volterra-type dynamics and nonsymmetric inhibitory interactions has no simple static attractors that correspond to winner take all phenomena. Instead, the winnerless competition induced by the hunting neuron displays hyperchaos with two positive Lyapunov exponents. The origin of the chaos is related to the interaction of two clusters of receptor neurons that are described with two heteroclinic loops in phase space. We hypothesize that the chaotic activity of the receptor neurons can drive the complex behavior of Clione observed during hunting.

Review

see Levi2005 for short summary in context

My biggest concern with this paper is that the changes in direction of the mollusc may also result from feedback from the body and especially the stratocysts during its accelerated swimming. The question is, are these direction changes a result of chaotic, but deterministic dynamics in the sensory network as suggested by the model, or are they a result of essentially random processes which may be influenced by feedback from other networks? The authors note that in their model “The neurons keep the sequence of activation but the interval in which they are active is continuously changing in time”. After a day of search for papers which have investigated the swimming behaviour of Clione limacina (the mollusc in question) I came to the conclusion that the data schown in Fig. 1 likely is the only data set of swimming behaviour that was published. This small data set suggests random changes in direction, in contrast to the model, but it does not allow to draw any definite conclusions about the repetitiveness of direction changes.

The role of sensory network dynamics in generating a motor program.

Levi, R., Varona, P., Arshavsky, Y. I., Rabinovich, M. I., and Selverston, A. I.
J Neurosci, 25:9807–9815, 2005
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Abstract

Sensory input plays a major role in controlling motor responses during most behavioral tasks. The vestibular organs in the marine mollusk Clione, the statocysts, react to the external environment and continuously adjust the tail and wing motor neurons to keep the animal oriented vertically. However, we suggested previously that during hunting behavior, the intrinsic dynamics of the statocyst network produce a spatiotemporal pattern that may control the motor system independently of environmental cues. Once the response is triggered externally, the collective activation of the statocyst neurons produces a complex sequential signal. In the behavioral context of hunting, such network dynamics may be the main determinant of an intricate spatial behavior. Here, we show that (1) during fictive hunting, the population activity of the statocyst receptors is correlated positively with wing and tail motor output suggesting causality, (2) that fictive hunting can be evoked by electrical stimulation of the statocyst network, and (3) that removal of even a few individual statocyst receptors critically changes the fictive hunting motor pattern. These results indicate that the intrinsic dynamics of a sensory network, even without its normal cues, can organize a motor program vital for the survival of the animal.

Review

The authors investigate the neural mechanisms of hunting behaviour in a mollusk. It’s simplicity allows that the nervous system can be completely stripped apart from the rest of the body and be investigated in isolation from the body, but as a whole. In particular, the authors are interested in the causal influence of sensory neurons on motor activity.

The mollusk has two types of behaviour for positioning its body in the water: 1) it uses gravitational sensors (statocysts) to maintain a head-up position in the water under normal circumstances and 2) it swims in apparently chaotic, small loops when it suspects prey in its vicinity (searching). In this paper the authors present evidence that the searching behaviour 2) is still largely dependent on the (internal) dynamics of the statocysts.

The model is as follows (see Varona2002): without prey inhibitory connections between sensory cells in the stratocysts make sure that only a small proportion of cells are firing (those that are activated by mechanoreceptors according to gravitation acting on a stone-like structure in the statocysts), but when prey is in the vicinity of the mollusk (as indicated by e.g. chemoreceptors) cerebral hunting neurons additionally excite the statocyst cells inducing chaotic dynamics between them. The important thing to note is that then the statocysts still influence motor behaviour as shown in the paper. So the argument is that the same mechanism for producing motor output dependent on statocyst signals can be used to generate searching just through changing the activity of the sensory neurons.

Overall the evidence presented in the paper is convincing that statocyst activity influences the activity of the motor neurons also in the searching behaviour, but it cannot be said concludingly that the statocysts are necessary for producing the swimming, because the setup allowed only the activity of motor neurons to be observed without actually seeing the behaviour (actually Levi2004 show that the typical searching behaviour cannot be produced when the statocysts are removed). For the same reason, the experiments also neglected possible feedback mechanisms between body/mollusk and environment, e.g. in the statocyst activity due to changing gravitational state, i.e. orientation. The argument there is, though not explicitly stated, that the statocyst stops computing the actual orientation of the body, but is purely driven through its own dynamics. Feedback from the peripheral motor system is not modelled (Varona2002, argueing that for determining the origin of the apparent chaotic behaviour this is not necessary).

For us this is a nice example for how action can be a direct consequence of perception, but even more so that internal sensory dynamics can produce differentiated motor behaviour. The connection between sensory states and motor activity is relatively fixed, but different motor behaviour may be generated by different processing in the sensory system. The autonomous dynamics of the statocysts in searching behaviour may also be interpreted as being induced from different, high-precision predictions on a higher level. It may be questioned how good a model the mollusk nervous system is for information processing in the human brain, but maybe they share these principles.