WO2003046886A1

WO2003046886A1 - Method for classifying a temporal series of events by means of a network containing pulsed neurones

Info

Publication number: WO2003046886A1
Application number: PCT/DE2002/004225
Authority: WO
Inventors: Gustavo Deco; Jan Storck
Original assignee: Siemens Aktiengesellschaft
Priority date: 2001-11-22
Filing date: 2002-11-14
Publication date: 2003-06-05
Also published as: DE10157220A1

Abstract

The invention relates to a method for classifying a temporal series of input variables by means of a neuronal network containing pulsed neurones. Oscillating neurones are used as pulsed neurones, and the mutual information between the stimulus category of the input variables and the pulse behaviour (= cost function) of the neurones is determined on the basis of a differential value.

Description

METHOD FOR CLASSIFYING A TIME SEQUENCE OF EVENTS USING A PULSE NEURONAL NETWORK.

description

Method for classifying a temporal sequence of input variables using a neural network containing pulsed neurons, neural network and arrangement for carrying out the method

The invention relates to a method for classifying a temporal sequence of input variables using a neural network containing pulsed neurons, a neural network which contains pulsed neurons in the form of oscillating neurons, and an arrangement for classifying a temporal sequence of input variables using a pulsed neuron containing neural network.

A neural network has neurons that are at least partially linked to one another. Input neurons of the neural network are supplied with input signals as input variables. The neural network usually has several layers. Depending on a neuron supplied to the neural network and an activation function provided for the neuron, a neuron generates a signal, which in turn is fed to neurons of a further layer as an input variable according to a predeterminable weighting. In an output layer, an output variable is generated in an output neuron as a function of quantities that are supplied to the output neuron by neurons of the previous layer.

The neural network encodes information by action potentials or "spikes" that characterize neural firing events (Rieke, F., Warland, D., de Ruyter van Steveninck, R. and Bialek,. (1997) , Spikes: Exploring the neural code. Cambridge: The MIT Press). In the context of time coding, so-called spatiotemporal firing patterns therefore encode information regarding sensory stimuli. In other words, different classes of Stimuli can be distinguished by different types of spatio-temporal firing patterns. In this context, the maximization of the transinformation as a means of describing the differentiability to achieve this goal has recently been proposed (Deco, G. and Schürmann, B. (1999), Spatio-temporal coding in the cortex: information flow based learning in spiking neural networks (Neural Computing, Vol. 11, pp. 919-934, 1999), planned publication in Neural Computation, March 1999). By maximizing the trans information between the name of the entered class and the resulting pulse pattern provided by the neurons that encode the presented stimulus, optimal discriminatory properties are ensured.

It is noted that it is not the input signal in its original form, which is extracted from the response of the network pulse pattern, but the name of the class to which it belongs that distinguishes this approach from the so-called Bialek reconstruction method. In this regard, classes are defined by user definitions. The following example is given here: Different speakers, men and women, each speak two languages, namely their mother tongue and a foreign language. The possible classification task can now consist of differentiating given recording sound tracks in accordance with i) the spoken language, ii) the gender of the speaker or iii) mother tongue versus non-mother tongue. The decision regarding the task to be solved, ie i) or ii) or iii) in the given example, must be made in advance together with the corresponding award of the training sample entered. Only when each of the input variables is identified as belonging to a certain class does the algorithm attempt the classes in the form of samples in the learning phase by adapting the network parameters to one another to maximize information separate, that is, the synaptic efficiencies that link the different neurons.

To clarify the foregoing against a biological background, it does not seem to be of much interest to one area of the brain to reveal the exact input signal it receives from another area in the brain, but rather to perform data compression before performing some tasks be tackled at a higher level. Since this kind of reasoning also seems to make sense from a purely technical point of view, this motivates the more "unbiological" approach of global optimization of a so-called cost function based on the mutual information.

In the last-mentioned publication, the principle of minimum time / maximum reliability (MTMR principle) has been proposed, which consists in limiting the number of pulses that are available for classification by limiting the time window. While this document discusses the basic usability of the cost function specified there, the invention aims at a much simpler framework (with regard to the predictability) for the stimulus classification.

It is an object of the present invention to provide a method for classifying a temporal sequence of input variables using a neutral network containing pulsed neurons, which is achieved with significantly less computational effort than previously. The invention is also based on the object of specifying a corresponding neural network. Finally, it is an object of the present invention to provide an arrangement suitable for this.

This problem is solved by the method, the neural network and the arrangement with the features of the independent claims. In accordance with a first aspect, the present invention provides a method of classifying a temporal sequence of inputs using a neural network containing pulsed neurons, in which oscillating neurons are used as pulsed neurons, and in which, based on a discrimination value, the mutual information between The stimulus class of the input variables and pulse behavior (= cost function) of the neurons is determined.

According to a second aspect, the present invention provides a neural network, which contains pulsed neurons in the form of oscillating neurons, and which provides for classifying a chronological sequence of input variables: determining the mutual information between the stimulus class of the input variables and pulse behavior (= cost function) of the neurons becomes.

According to a third aspect, the present invention provides an arrangement for classifying a temporal sequence of input variables using a neural network containing pulsed neurons, with a processor which is designed such that the following steps can be carried out: a) oscillating neurons as pulsed neurons are used, and b) the mutual information between the stimulus class of the input variables and pulse behavior (= cost function) of the neurons is determined on the basis of a differentiation value.

The invention enables the classification of temporal sequences in question with less computational effort by using oscillating neurons that allow the phase to be the only relevant parameter for the temporal pulse profile. As a result, the calculation of the mutual information based on a cost function is compared to that dealt with above State of the art in terms of accuracy and especially in terms of time significantly improved because the density determination required for entropy calculation takes place in a room of much smaller dimensions. It is crucial that the need for classification in a minimum of time is already implicitly ensured by the fact that the cost function depends solely on the phases, which in turn can be calculated immediately after a single oscillation.

The inventive approach of using oscillating neurons as neurons makes the classification in question much easier and more precise to put into practice, which enables the use of much more complex types of stimuli.

Preferred developments of the invention result from the dependent claims.

The cost function is preferably determined on the basis of a differentiation value I (T) which satisfies the following rule:

in which

T is the observation time of an output pulse, s is the random variable that corresponds to the stimulus class, tj. denotes the time corresponding to the i-th firing of a neuron a, tci ^(cl> , • • •, t _kc ^(cK) the maximum values are less than T, and ci, ..., c _{κ are} certain code neurons.

Due to the use of oscillating neurons for the pulsed neurons, the distinctive value mentioned above can be simplified as follows: I (T) = / (r, {φ ^>, φW, ..., φ <*>})

where Φi ^(a> denotes the time corresponding to the ith firing of a neuron a with respect to a specific reference value, ie, the phases.

The input variables are preferably measured physical signals.

The method according to the invention and the arrangement according to the invention can thus be used in the context of the description of a technical system, in particular for the description, for example for examining a multichannel signal, has been recorded by an electroencephalograph. and describes an electroencephalogram.

The method and the system according to the invention can also be used for analyzing multivariate financial data in the field of the financial market and for analyzing economic relationships.

Furthermore, the method and the arrangement according to the invention are also suitable for the implementation of software for a processor as well as for hardware.

A preferred field of application of the method and the system according to the invention is in the field of speech analysis.

An embodiment of the invention is shown in the figures and is explained in more detail below.

Show it: 1 shows a first class of stimuli,

Fig. 2 a second class of stimuli,

3 phase distributions of code neurons before learning, in response to a stimulus 1,

Fig. 4 phase distributions of code neurons after learning, in response to a stimulus 1,

Fig. 5 phase distributions of code neurons before learning, in response to a stimulus 2,

6 phase distributions of code neurons after learning, in response to a stimulus 2.

First, the neuron model and the architecture of the neural network, which are the basis of the invention, will be discussed. It is assumed that only the pulse event itself, i.e. the precise pulse times that forms the carrier for the information and that the exact form of the pulses and the dentritic signals contain no relevant information. At the neuron level, an integration and firing model with internal driving force is used, which is described, for example, in Tuckwell, H. (1981), Stochastic Nonlinear Systems, pp. 162-171, edited by Arnold, L. and Lefever, R. , Berlin: Springer Verlag, and Tuckwell, H. (1981), Introduction to Theoretical Neurobiology, Cambridge: Cambridge University Press. This process can be expressed by the stochastic Itδ differential equation, which is taken from Gardener, C. (1990), Handbook of Stochastic Methods, Berlin: Springer Verlag:

In equation (1), the constant τ describes the decay of the membrane potential when there are no input signals. The linkage with other neurons is given by dS (t) = ∑χδ (t- t _x ) dt, which is a jump process that occurs when the incoming pulses hit the Times t _{α is} defined. The synaptic strength is denoted by w. The constant ω is the internal drive (drive) that leads to a periodic pulse train when there are no pulse signals: charge is collected until the membrane potential V (t) reaches a predetermined threshold θ, which leads to a pulse generation (discharge). After the pulse has been generated, the model is reset to a predetermined initial potential V (0) (in the present case this potential is set to zero), and the charging process starts again. Additional indices are now being introduced for the designation of the neuron. Each neuron i is described by a membrane potential V _{± which} follows an equation of the type of equation (1). The output pulse train corresponding to the neuron i is therefore described by the pulse generation times tι ^(1> , ..., t _k ^(1> , ..., and it is by o _± (t) = ∑ _k δ (tt _k ^(l) ) given.

The neural network containing N neurons is described by the following system of differential equations:

+ L ιYfi {t → ψ) dt

+ iύidt + li (t) dt

(2]

where i = 1, ..., N. In equation (2) w _{± j} denotes the synaptic strength between a neuron i and a neuron, the direction running from j to i, Ii (t) denotes the external stimulus, which acts as an additional input variable with constant weight, and ω _± denotes the internal drive of the neuron.

The differential system according to equation (2) can be represented numerically and discretely in the following way (Euler integration) V, (* + Δr) = V, (+ - ^) (3)

It is assumed that each neuron has an absolute refractory period after the emission of a pulse during which it cannot fire again. In the present simulations, both Δt and the time of death were chosen to be 1 ms, θ = 2π mV, ω _± = 0.125 mV and τ _± = 250 ms for all neurons. I _± (t) is fed into the input neurons with a strength of 0.2.

The architecture used here is a fully linked network similar to that described in Storck, J. and Deco, G. (1998), Spike-Based Hebbian Learning for Stimulus Discrimination, In Artificial Neural Networks - ICANN '98, Skövde, Sweden, Springer-Verlag, Heidelberg, suggests: Each neuron sends its action potentials and receives input from all other neurons via synaptic efficiencies with adaptive strength. The axonal transmission delay was chosen randomly in the range between 0 and 2 ms.

It is important that a state of weak coupling between the neurons is ensured. This precludes an interruption of the predefined oscillations of the neuronal activity, and only phases of these oscillating pulse neurons remain as unlimited variables.

The process of updating these weak synaptic couplings will now be explained.

A cost function is introduced for global optimization. The pure parameters, that is, the synaptic efficiencies zen are designed so that the stimulus presented at the entrance can be classified as reliably as possible. For this reason, the mutual information between the stimulus class and the pulse response of the network is introduced as a measure of the differentiability. The aim here is not, as has been the case up to now, to reconstruct the input or the input variables from the output or the output variables, but to derive the name of the class to which the presented stimulus belongs, namely from a set of given classes.

The random variable that corresponds to the class of the stimulus is denoted by s, ie the results of s are s ^(j) with the probability pj. From the information-theoretical point of view, a measure of the distinguishability for an observation time T of the output pulses can be defined by the mutual information between the random variables s and the pyramidal pulse times of certain code neurons Ci, ...., c _κ , ie by the following differentiation value:

where ti ^<a) denotes the time it takes for the i th firing of a _t (ύ _t (ct)

Neurons corresponds to a, and where ^ * denote the maximum values that are smaller than T.

The use of oscillating neurons according to the invention simplifies equation (1)

where Φ _± ^(a> denotes the time corresponding to the ith firing of a neuron a with respect to a specific reference value, that is, the phases (since the firing time of one of the code neurons can be used as a self-reference, so that the number of relative phases is actually reduced to K - 1).

The maximum value of I is given by the entropy of the random variable s, e.g. in the case of two equally probable stimuli H (s) = in 2 nats «0.69 nats. If the maximum is achieved by the differentiation value I (T), this means that the pyramidal space / time patterns contained in the observation time T contain sufficient information to perfectly classify the classes of presented input stimuli; i.e. the neural network acts as a perfect means of classification. In contrast to the previous MTMR principle, the minimal time limitation no longer occurs in the case of oscillating neurons in the present case, because it is sufficient to know a single (i.e., the first) pulse time per neuron. This greatly simplifies the calculation of the probabilities that are necessary to determine a mutual information term:

I (XY) = J f fay) VX _j $ d »i

(6)

The classification of temporal sequences or sequences which are generated by non-homogeneous Poisson processes will now be explained with reference to FIGS. 1 to 6. In the case shown in FIGS. 1 to 6, the external stimulus (the input or the input variable) consists of three non-homogeneous Poisson processes which are fed into the network simultaneously and represent a three-dimensional input current. 1 shows such a three-dimensional input current for a first stimulus class and FIG. 2 for a second stimulus class. Both classes consist of three dimensions, each with a non-homogeneous Poisson process for each dimension. In the first two components the sine wave rates follow (in FIGS. 1 and 2 the upper curve profiles in each case), while the third component (in FIGS. 1 and 2, the lower curves in each case) is determined by a completely random rate. The difference between the two classes relates to the relationship between the first two components: there is a phase shift for class 1 (FIG. 1), while there is no phase shift for class 2 (FIG. 2). In order to determine whether a pulse is present at the current time, a sample is taken from a Poisson process at a given rate using the classifications mentioned above.

In other words, the functions that describe the change in the different Poisson rates as a function of time in the three inputs define two different input classes. One class is sampled on the basis of the three rate curves (for input variable 1, 2 or 3), as shown in FIG. 1, while the rates for class 2 are shown in FIG. 2. These two stimuli differ only in the coherence (the temporal relationship) of their various components, which makes the classification task a kind of temporal clustering.

The neural network for this experiment consists of fully linked neurons. Due to the three-dimensional nature of the input signal, there are consequently three input neurons that receive the time-dependent stimulus. Such an input neuron receives no input or input zero if the Poisson process does not generate a pulse to which it belongs and a stimulus 0.2 in the case of an input pulse event. The remaining or hidden neurons receive no external input at all. In order to keep the computing effort low, the cost function is determined from a subset of the total number of neurons. These code neurons, which are taken into account when calculating the mutual information, are chosen arbitrarily, but to the exclusion of the input neurons. This ensures that the information is with regard to the stimulus has to be extracted from the hidden dynamics of the network, whereby the consideration is limited to the actually interesting case of an internal information coding of a network of pulse neurons. Each time the cost function is updated, the statistics required to calculate the mutual information probabilities are obtained by the pulse patterns (ie, the phase patterns) in response to 500 input samples for each of the two different stimuli. Such a sample (name) in turn consists of a string of input pulses with which the network is then driven until the phases are measured and the procedure can proceed to the next sampling. Finally I (T) is calculated and the weight update of the current iteration can be started. Before the whole process is restarted for.

In this context, an optimization method can be used, such as the ALOPEX algorithm described in Storck, J. and Deco, G. (1998), Spike-Based Hebbian Learning for Stimulus Discrimination. Artificial Neural Networks - ICANN '98, Skövde, Sweden, Springer-Verlag, Heidelberg.

For the experiment attracted, the mutual information could be maximized to the optimal value of I = 0.69 nats. The complete information, which determines the value of the cost function, and thus the degree of distinctness, is contained in the common distribution of the phases, the size of which is equal to the number of code neurons. A visualization of the common distribution of the phases of the code neurons is therefore only possible for up to two of them. The present experiment uses three code neurons, which leads to two relative phases, for which the result is shown in FIGS. 3 to 6. However, even for a larger number of code neurons in even more complex applications, the probability structure be derived from the two-dimensional distributions of subsets.

3 to 6 show in detail the phase distributions of the code neurons before and after the learning. Before learning, the phase distributions in response to stimulus 1 (FIG. 3) and stimulus 2 (FIG. 5) show an unstructured form due to the random initialization of the synaptic efficiencies. Their similarity leads to a low value of the cost function, i.e. the mutual information.

After learning, the majority of the probability mass accumulates in the center of the covered area for stimulus 1 (FIG. 4), while the highest density values occur at the edges for stimulus 2 (FIG. 6). This complementary pattern of response behavior corresponds to a high value of the mutual information term by definition and thus represents a high degree of distinctiveness.

Claims

claims

1. Method for classifying a temporal sequence of input variables using a neural network containing pulsed neurons, in which a) oscillating neurons are used as pulsed neurons, and b) the mutual information between the stimulus class of the input variables and pulse behavior (= cost function) on the basis of a distinctive value ) of the neurons is determined.

2. The method according to claim 1, wherein the distinctive value I (T) satisfies the following requirement:

in which

T is the observation time of an output pulse, s is the random variable that corresponds to the stimulus class, tι ^(a) denotes the time corresponding to the ith firing of a neuron a, tkci ^(cl) - • • t _kcK ^(cK) the maximum values less than T are, and

Cι, ..., c _{κ are} certain code neurons.

3. The method according to claim 2, wherein the differentiation value I (T) using oscillating neurons satisfies the following rule:

where Φi ^(a) denotes the time corresponding to the ith firing of a neuron a with respect to a specific reference value, ie, the phases.

4. The method according to any one of claims 1 to 3, wherein the input variables are measured physical signals.

5. The method of claim 4, wherein the physical signals are measured signals in speech analysis.

6. Neural network, which contains pulsed neurons in the form of oscillating neurons, and which provides for classifying a chronological sequence of input variables: determining the mutual information between the stimulus class of the input variables and pulse behavior (= cost function) of the neurons.

7. Neural network according to claim 6, in which the differentiation value I (T) satisfies the following requirement:

κn ι {* {>, ..., ig, # *, .. g})

in which

Is a random variable that corresponds to the stimulus class, ti ^(a) denotes the time corresponding to the i-th firing of a neuron a, tkci ^(cl) ι • • • ι t _kcK ^(cK) the maximum values are less than T, and ci _,. .., c _{κ are} certain code neurons.

8. Neural network according to claim 7, in which the differentiation value I (T) using oscillating neurons satisfies the following rule:

where Φι ⁽⁾ denotes the time corresponding to the i-th firing of a neuron a with respect to a specific reference value, ie, the phases.

9. Neural network according to one of claims 6 to 7, used for the classification of a physical signal.

10. The neural network of claim 9, wherein the physical signal is a signal measured in speech analysis.

11. Arrangement for classifying a time sequence of input variables using a neural network containing pulsed neurons, with a processor which is designed such that the following steps can be carried out: a) oscillating neurons are used as pulsed neurons, and b) on the basis A distinctive value is used to determine the mutual information between the stimulus class of the input variables and pulse behavior (= cost function) of the neurons.

12. Arrangement according to claim 11, in which the differentiation value I (T) satisfies the following requirement:

in which

T is the observation time of an output pulse, s is the random variable that corresponds to the stimulus class, t _! ^(a) denotes the time corresponding to the i-th firing of a neuron a, tkci ^(cl) , • • •, t _kcK ^(cK) the maximum values are less than T, and cι, ..., c _{κ are} certain code neurons.

13. Arrangement according to claim 12, in which the distinction value I (T) using oscillating neurons satisfies the following requirement:

14. Arrangement according to one of claims 11 to 13, used for the classification of a physical signal.

15. The arrangement according to claim 14, wherein the physical signal is a signal measured in speech analysis.