Patent Application: US-201514826300-A

Abstract:
a brain machine interface to control a device is provided . the bmi has a neural decoder , which is a neural to kinematic mapping function with neural signals as input to the neural decoder and kinematics to control the device as output of the neural decoder . the neural decoder is based on a continuous - time multiplicative recurrent neural network , which has been trained as a neural to kinematic mapping function . an advantage of the invention is the robustness of the decoder to perturbations in the neural data ; its performance degrades less — or not at all in some circumstances — in comparison to the current state decoders . these perturbations make the current use of bmi in a clinical setting extremely challenging . this invention helps to ameliorate this problem . the robustness of the neural decoder does not come at the cost of some performance , in fact an improvement in performance is observed .

Description:
the present invention also referred to as big - data multiplicative recurrent neural network ( bd - mrnn ) is a supervised neural network and training method for incorporating and modifying multiple previous days training datasets ( historical data ) to improve both raw performance and robustness in the daily operation of brain - machine interface ( bmi ) decoders . the generic recurrent network model is defined by an n - dimensional vector of activation variables , x , and a vector of corresponding “ firing rates ”, r = tan h ( x ). both x and r are continuous in time and take continuous values . in a standard rnn model , the input affects the dynamics as an additive time - dependent bias in each dimension . in the mrnn model , the input instead directly parameterizes the weight matrix , allowing for multiplicative interactions between the input and the hidden state . one view of this multiplicative interation is that the hidden state of the recurrent network is selecting an appropriate decoder for the statistics of the current dataset . the equation governing the dynamics of the activation vector is of the form suggested in suskever 2011 , but adapted for this invention to continuous time τ { dot over ( x )}( t )=− x ( t )+ j u ( t ) r ( t )+ b x . ( 0 . 1 ) the n × n × f tensor j u ( t ) defines the values of the recurrent connections of the network , which are dependent on the i - dimensional input , u ( t ). in the mrnn , j u ( t ) is factorized such that the input is linearly combined into f factors . specifically , j u ( t ) is factorized according to j u ( t ) = j xf · diag ( j fu u ( t ))· j fx , ( 0 . 2 ) where j xf has dimension n × f , j fu has dimension f × i , j fx has dimension f × n , and diag ( v ) takes a vector , v , and returns a diagonal matrix with v along the diagonal . one directly controls the complexity of interactions by choosing the number of factors , f . if f = n 2 , we recover a full n × n × n tensor . if f = 1 , j u ( t ) is a rank - one matrix whose singular value is function of u ( t ). finally , the network has a constant bias , b x , and the neuronal time constant , t , sets the time scale of the network . the output of the network is a weighted sum of the network firing rates plus a bias , defined by z ( t )= w o t r ( t )+ b z , ( 0 . 3 ) where w o is an n × m matrix and b z is an m - dimensional bias . the network equations defined above are used according to the following procedures and parameters in order to build the bd - mrnn bmi decoder . for our online experiments , the size of the networks are set to n = 100 and n = 50 with f = n in both cases ( see table 1 ). one subject uses a single multi - unit electrode arrays ( i = 96 ), while the second uses two ( i = 192 ). the non - zero elements of the non - sparse matrices j xf , j fu , j fx are drawn independently from a gaussian distribution with zero mean and variance g xf / f , g fu / i , and g fx / n with g xf , g fu , and g fx defined in table 1 for the specific bmi task . the elements of w o are initialized to zero , and the bias vectors b x and b z are also initialized to 0 . the input u ( t ), to the mrnn , is the vector of binned spikes measured from neural data ( see , for example , sus sillo 2012 for details on standard preprocessing of neural signals , see δt in table 1 for bin sizes ). by input to the mrnn , we mean in the sense of equation 0 . 1 . this results in a data matrix , u j , of binned spikes of size i × t j for each actual trial , where t j is the number of time steps for the j th trial . five actual trials are then concatenated together to make one “ training ” trial . the first two actual trials in a training trial are used for seeding the hidden state of the mrnn , and are not used for learning , whereas the final 3 actual trials in the training trial are used for learning . in this way , excepting the first two actual trials in the day &# 39 ; s dataset , the entire set of actual trials are used for learning , by incrementing the actual trial index that begins a training trial . a key element of training robustness to nonstationarities in the neural code is the introduction of perturbations to the neural spike trains that are used to train the mrnn . the concatenated input in a given training trial , û =[ u i , . . . , u i + 4 ] are perturbed by adding and removing spikes from each channel . we focus on channel c of the j th training trial , i . e ., a row vector of data , û c ,: j . let the number of spikes in û c ,: j be n c j before perturbation . this number is perturbed according to where both η j and η c are gaussian variables with a mean of one and standard deviations of σ trial and σ channel , respectively ( see table 1 ). conceptually , η j models a global modulation in the array across all channels ( e . g . changes in subject arousal ), while η c models channel by channel perturbations , such as uncontrolled channel dropping or moving baselines in individual neurons . if n c j is less than zero or greater than 2n c j , it is resampled according to equation 0 . 4 , which keeps the average number of perturbed spikes in a given channel and training trial the same as the average number of unperturbed spikes in the same channel and training trial . otherwise , if { circumflex over ( n )} c j is greater than n c j , then { circumflex over ( n )} c j − n c j spikes are added to random time bins of the training trial . if { circumflex over ( n )} c j is less than n c j , then n c j −{ circumflex over ( n )} c j spikes are randomly removed from time bins of the training trial that already had spikes . finally , if { circumflex over ( n )} c j = n c j , nothing is changed . the process of perturbing the binned spiking data occurs on every iteration of the optimization algorithm . for example , in a batch gradient descent algorithm , the perturbation described by equation 0 . 4 happens after each update of the network parameters . the typical methodology for training a closed - loop bmi decoder involves training on a session - by - session basis . this means that every day , the subject engages in a control task , for which both input ( neural ) and supervisory ( kinematics ) signals are collected . after this session - by - session training period , a bmi is optimized to perfrom well on this data exclusively . the second critical component to acheiving both performance and robustness in the bd - mrnn decoder is using many days of training data . in our laboratory experiments , we use multiple years of training data ( see table 1 ). because of the extreme nonstationarities of the neural data , this aspect of the bd - mrnn training methodology is unintuitive . the nonlinear , multiplicative architecture of the mrnn utilizes the regularities that across many days do exist in a dataset comprising many days . in comparison , the ( due to bd - mrnn , no longer ) state - of - the - art linear kalman filter methods , including previous days data would result in potentially very poor decoders . we train two mrnn networks to each output a 2 - dimensional signal . one network is trained to output the normalized position through time in both the horizontal ( x ) and vertical ( y ) spatial dimensions . the other mrnn is trained to output the velocity through time , also in the x and y dimensions . we calculate the hand velocities from the positions numerically using central differences . since the mrnn decoder outputs both normalized position and velocity , we combine both for our final decoded position signal . the decode used during bmi mode , d x ( t ), d y ( t ) is a mix of both velocity and position , defined by d x ( t )= β ( d x ( t − δt )+ γ v ν x ( t − δt ) δ t )+( 1 − β ) γ p p x ( t ) ( 0 . 5 ) d y ( t )= β ( d y ( t − δt )+ γ v ν y ( t − δt ) δ t )+( 1 − β ) γ p p y ( t ) ( 0 . 6 ) where v x , v y , p x , p y are the normalized velocity and positions in the x and y dimensions and γ v , γ p are factors that convert from the normalized velocity and position , respectively , to the physical values associated with the workspace . the parameter β sets the amount of velocity vs . position decoding ( see table 1 ). a network is simulated by integrating equation 0 . 1 using the euler method at a time step of δt = τ / 5 and then evaluating equation 0 . 3 . the parameters of the network are trained offline to reduce the averaged squared error between the measured kinematic training data and the output of the network , z ( t ). specifically , we use the hessian - free ( hf ) optimization method for rnns ( but adapted to the continuous - time mrnn architecture ). hf is an exact 2 nd order method that uses back - propagation - through - time to compute the gradient of the error with respect to the network parameters . the set of trained parameters is { j xf , j fu , j fx , b x , b z }. the hf algorithm has some critical parameters , such as the minibatch size , the initial lambda setting , and the max number of cg iterations . we set these parameters to ⅕ times the total number of trials , 0 . 1 , and 50 , respectively . after training , the networks are copied into the embedded real - time environment ( xpc ), and run in closed - loop , to operate online in bmi mode . specifically , at each time point the rnn module receives binned spikes and outputs the current estimate of the hand position , which is used to display the cursor position on the screen . during bmi mode the neural spikes are not perturbed in any way . the values v x ( 0 ) and v y ( 0 ) are initialized to 0 , as is the mrnn hidden state . the parameters of the model of an exemplary embodiment are listed in table 1 . one critical aspect of the invention is using multiple days of training data . at first glance , it may seem straightforward that more data should always improve the quality of performance on some supervised system , such as a neural network . however , this is only true under a very specific and very commonly met assumption . this assumption is * not * met in the bmi setting . the assumption is that the data used to optimize (“ train ”) the neural network comes from the same distribution as the data used in the network during operation ( during so - called “ validation ” or “ testing ”). when this assumption is met , indeed more training data leads to a better neural network that performs better on generalization testing . to reiterate , this assumption is * not * met in the neural data used to train bmis . as an example analogous to the bmi setting , imagine that we are interested in building a neural network to classify hand written letters from different users . specifically , we want to classify different users based on how they write the letter ‘ h ’ ( e . g . user 1 wrote these ‘ h ’ letters , while user 2 wrote those ‘ h ’ letters .) if our dataset contained only handwritten ‘ h ’ letters , then adding more and more ‘ h ’ letters would definitely improve our classification of user 1 from user 2 , as per common understanding . however , imagine that we had access to other letters that the users wrote , such as ‘ n ’, and ‘ x ’. if our job is only to classify different users based on the letter ‘ h ’, then it appears that including ‘ x ’ as training data to an ‘ h ’ classifier could only hurt the it &# 39 ; s performance on classifying the letter ‘ h ’. however , you could also reason that if you included ‘ n ’ in your ‘ h ’ classifier , perhaps one could still improve the classifier because the letter ‘ n ’ shares some common features with the letter ‘ h ’. it &# 39 ; s not at all clear what would happen if we threw in the letters from ‘ a ’ to ‘ z ’. we can summarize that adding more training data ( letters different from ‘ h ’), when the data does not come from the test distribution (‘ h ’ letters ), will not obviously help improve the network &# 39 ; s performance . the previous example is analogous to current situation in bmi research . we would like to classify different user intentions , such as moving a computer cursor up or down ( analogous to classifying user 1 or user 2 ) based on neural data ( the letters ). however , each day the neural data upon which we classify changes dramatically ( some days we have ‘ h ’ letters to classify user 1 vs user 2 , some days we have ‘ x ’ letters ). further , the changes in neural data are not under our control . so we never know whether we are going to be looking at an ‘ h ’ or an ‘ x ’ or a ‘ n ’. if it &# 39 ; s an ‘ h ’ day , than using a previous ‘ x ’ day seems like a bad idea . it is a fact , in the bmi setting , the neural data collected using modern devices ( e . g ., utah multi electrode array ) varies dramatically from day - to - day , even when the subject is requested to perform the exact same task , and the experimental conditions are reproduced to as exacting conditions as the experimental environment will allow . it is unclear why the neural data varies so dramatically , although many believe it is a combination of the underlying complexities of the neural code , combined with the inevitable limitations of reading biological electrical signals with limited silicon - based hardware . the variation in neural signals has led to the widely held view in the bmi field that using data from multiple days is in fact quite problematic . as a result , the standard — and state of the art — practice is to record training data each and every day , and perhaps more than once a day . this training data is then used to run a bmi decoder for some amount of time on that same day . anecdotally , many researchers have tried to incorporate more data than just a single day , though it is widely held as a bad idea because it often fails to improve things . sometimes using yesterday &# 39 ; s data as well as today &# 39 ; s data improves things , sometimes it does not . surely using data from over 1 month ago is a bad idea to include in a training set for today &# 39 ; s bmi decoder . these widely held views about which data to use for training a closed - loop bmi decoder are based primarily on using a linear decoding method , the kalman filter . as a linear method , the kalman filter can only give an average response to many days of training data , so if neural data from one month ago is indeed different from today &# 39 ; s neural data , indeed the kalman filter trained using the old data will result in a very poor decoder on new data from today . thus the vast majority of experts ( likely all ) in the field would consider it non - straightfoward to devise a method whereby previous data from three to six months ago , as we have shown empirically , is helping to decode today &# 39 ; s neural data . for our invention , we made a systematic study of how one day &# 39 ; s neural data compares to another day &# 39 ; s . we did this using an analysis technique called the principal subspace angle . the scientific result of this analysis is that some days are more similar to others , while some days are very different . further , similar neural data tends to come in blocks of time , but oddly , data from many months ago can be quite similar to today &# 39 ; s neural data ( the exact similarity structure is beyond the scope of this introduction ). naturally , it would be desirable to use only training data from days that are similar to the day on which you were interested in running the decoder ( use ‘ n ’ s and not ‘ x ’ s to help classify the users 1 and 2 based on how they write the letter ‘ h ’). however , it is very hard to know , a priori , which days will help . to sidestep this problem , we used a highly nonlinear decoder , a multiplicative recurrent neural network ( mrnn ). the mrnn is powerful enough to handle the varying neural data from many days , even when the neural data is significantly different from day to day . so long as there are some similarities in the neural data between days ( e . g . a ‘ n ’ similar to an ‘ h ’), the mrnn is smart enough to use this data to improve the bmi decode . if the training data bears little similarity to today &# 39 ; s neural data (‘ x ’ letters are not similar to ‘ h ’ letters ), the mrnn is smart enough to ignore it while decoding today &# 39 ; s neural data . embodiments of the invention could be envisioned as a brain machine interface controlling a device such as a robotic arm , a prosthetic device or a cursor on a computer screen . the brain machine interface receives neural signals from a subject &# 39 ; s brain , which are processed by one or more neural decoders . the neural decoders are either functionalized with method steps to execute the signal processing steps and / or are hardware systems for processing the neural signals as described herein . the neural decoders could include computer hardware and software devices / technology for its operation ( s ). the neural decoders are interfaced with the device to control the kinematics of the device based on the processed neural signals . john p cunningham et al . a closed - 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