Patent Application: US-78950210-A

Abstract:
this invention is in the field of machine learning and neural associative memory . in particular the invention discloses a neural associative memory structure for storing and maintaining associations between memory address patterns and memory content patterns using a neural network , as well as methods for storing and retrieving such associations . bayesian learning is applied to achieve non - linear learning .

Description:
neural associative memory networks as considered by this invention are single layer neural networks or perceptrons with fast “ one - shot ” learning corresponding to the storage of m discrete associations between pairs of binary pattern vectors {( u μ → v μ ): μ = 1 , . . . , m }. here u μ is the μ - th memory address pattern being a binary vector of size m . similarly , v μ is the μ - th memory content pattern being a binary vector of size n . further define the pattern activities k μ := ∑ i = 1 m ⁢ u i μ ⁢ ⁢ and ⁢ ⁢ l μ := ∑ j = 1 n ⁢ v j μ are defined as the number of one - entries in the μ - th memory address and memory content pattern , respectively . finally , k := e μ ( k μ ) and l := e μ ( l μ ) denote the average pattern activities . the “ one - shot ” constraint restricts the set of possible learning methods . for example , gradient descent methods ( as error backpropagation ) are not viable because they require repeated training of the whole pattern set . instead it is straight - forward to use simple hebbian - like learning rules : if , during presentation of a single pattern pair , both the presynaptic and postsynaptic neurons are active , then the synaptic weight must be increased . the performance of neural associative memory structures is commonly evaluated by the network storage capacity c measuring the stored information bits per synapse , a related performance measure is the output noise ε defined as the expected hamming distance d h ⁡ ( v μ , v ^ ) := ∑ j = 1 n ⁢ ( v j μ - v ^ j μ ) 2 between retrieval result { circumflex over ( v )} and original memory content pattern v μ normalized by the mean content pattern activity l , the goal is to maximize c and minimize ε . in contrast to previous solutions , the system described by this invention , under some assumptions , maximizes c and minimizes ε . many previous memory systems worked well only under artificial conditions , for example , presuming randomly generated “ uncorrelated ” memory address patterns u μ with independently generated pattern components , or assuming narrowly distributed pattern activities k μ ( for example constant k μ = k ). here numerical simulations have revealed that the current invention is much more robust against “ correlated ” patterns and broadly distributed pattern activities . further experiments have also shown that the current invention works much better than the previous approaches for “ pattern part retrieval ”, i . e ., when the set of active units in the input query patterns ũ are a subset of the active units in the original memory address patterns u μ , briefly ũ ⊂ u μ . pattern part retrieval is particularly important for spiking implementations where the most reliable units fire before the less reliable units . here , at least in an early phase of retrieval , the pattern part assumption ũ ⊂ u μ is fulfilled with high probability , and the current invention promises significantly improved performance . fig3 , for example , shows the nam considered by the present invention , which is a two - layer neural network consisting of an address population u ( size m ) and a content population v ( size n ). an address neuron u i can make synaptic contacts with weight onto content neuron v j . when addressing with a input query pattern ũ a content neuron v j gets active if the dendritic potential x j := ∑ i = 1 m ⁢ w ij ⁢ u ~ i exceeds the neuron &# 39 ; s firing threshold θ j . memory associations are stored in the synaptic weights and firing thresholds of the network . fig3 also shows an example of a hetero - associative memory . for identical u and v the network becomes an auto - associative memory with recurrent synaptic connections . fig4 illustrates the neuron and synapse model according to the current invention . each neuron j has a number of state variables : by m 1 ( j ) the “ unit usage ” counting the number of active memory components during the memory storage phase ( see below ) is denoted . similarly , m 0 ( j ) counts the occurrences of inactive memory components . then , more similar to previous models , each neuron has a continuously valued dendritic potential x ( j ) and a continuously valued spike threshold θ ( j ) which are determined dynamically during retrieval depending on the previously stored memories and the current input query pattern ũ . in some implementations the neuron has also two additional integer variables x ∞ ( j ) and θ ∞ ( j ) counting “ infinite components ” of dendritic potentials and spike thresholds , respectively . furthermore , each neuron j has two variables e 01 ( j ) and e 10 ( j ) estimating the “ error probabilities ”. here e 01 ( j ) estimates the probability that neuron j is active when it should be inactive . similarly , e 10 ( j ) estimates the probability that neuron j is inactive when it should be active . each synapse ij connecting neuron i to neuron j has the following state variables : by m 11 ( ij ) the “ synapse usage ” counting the number of co - activations of presynaptic neuron i and postsynaptic neuron j during the memory storage phase ( see below ) is denoted . similarly , m 10 counts the storage events where the presynaptic neuron is active and the postsynaptic neuron is inactive . similarly , m 00 counts the storage events where the presynaptic neuron is inactive and the postsynaptic neuron is active . similarly , m 00 counts the storage events where both presynaptic and postsynaptic neurons are inactive . then , more similar to the previous models , each synapse has a continuously valued synaptic weight w ( ij ). in some implementations each synapse additionally has a binary valued weight w ij ∞ counting “ infinite components ” of the synaptic weight . the left panel of fig4 shows that information about memory associations u μ → v μ is stored in neurons and synaptic connections . each presynaptic neuron i stores its unit usages m ′ 1 ( i ) and m ′ 0 ( i ). each postsynaptic neuron j stores its unit usages m 1 ( j ) and m 0 ( j ). each synapse connecting neuron i to neuron j stores its synapse usages m 11 ( ij ), m 10 ( ij ), m 01 ( ij ), and m 00 ( ij ). the right panel of fig4 shows that for retrieval of information the unit and synapse usages can be transformed to synaptic weights w ij and firing thresholds θ j assuming some query error estimates e 01 ( i ) and e 10 ( i ). synaptic inputs following the activation of an input query pattern ũ are summed in the dendritic potential x j and the corresponding output neuron becomes active { circumflex over ( v )} j = 1 , if the dendritic potential exceeds the firing threshold . an adequate handling of infinite weights and thresholds requires additional variables w ij ∞ , x j ∞ and θ j ∞ discussed below . the task is to store m associations between memory address patterns u μ and memory content patterns v μ where μ = 1 . . . m . it is assumed that all patterns are binary vectors . memory address patterns u μ have dimension m and memory content patterns v ′ dimension n . during storage , each address neuron and each content neuron j can memorize its unit usage m 0 ( j ):=#{ μ : v j μ = 0 }= m − m 1 ( j ) m ′ 0 ( i ):=#{ μ : u i μ = 0 }= m − m ′ 1 ( i ) m 11 ( ij ):=#{ μ : u i μ = 1 , v j μ = 1 } m 01 ( ij ):=#{ μ : u i μ = 0 , v j μ = 1 }= m 1 ( j )− m 11 ( i , j ) m 00 ( ij ):=#{ μ : u i μ = 0 , v j μ = 0 }= m ′ 0 ( j )− m 01 ( i , j ) m 10 ( ij ):=#{ μ : u i μ = 1 , v j μ = 0 }= m 0 ( j )− m 00 ( i , j ) where i = 1 , . . . , m and j = 1 , n . note that it is actually sufficient to memorize m , m 1 , m ′ 1 , and m 11 . this means , the variables m 0 , m ′ 0 , m 10 , m 01 , and m 00 must not necessarily be implemented . instead , each neuron requires access to m . therefore , an implementation on a digital computer requires only about ( mn + m + n + 1 ) ld m memory bits . given an input query pattern ũ the memory task is to find the “ most similar ” memory address pattern u μ and return a reconstruction { circumflex over ( v )} of the associated memory content pattern v μ . for this let us assume that the input query pattern u is a noisy version of u μ with estimated independent component error probabilities e 01 ( i ):= pr [ ũ i = 1 | u i μ = 0 ] e 10 ( i ):= pr [ ũ i = 0 | u i μ = 1 ] now the content neurons j have to decide independently of each other whether to be activated or to remain silent . given the input query pattern ũ , the optimal maximum - likelihood decision v ^ j = { 1 , pr ⁡ [ v j μ = 1 | u ~ ] pr ⁡ [ v j μ = 0 | u ~ ] ≥ 1 0 , otherwise d h ⁡ ( v μ , v ^ ) := ∑ j = 1 n ⁢  v j μ - v ^ j  between original and reconstructed content and , thus , output noise ε . if the input query pattern components are conditional independent given the activity of content neuron j , e . g ., assuming independently generated memory address pattern components , for a ε { 0 , 1 } there is with the bayes formula pr [ v j μ = a | ũ ]= pr [ ũ | v j μ = a ]/ pr [ v j μ = a ]/ pr [ ũ ] pr ⁡ [ v j μ = 1 | u ~ ] pr ⁡ [ v j μ = 0 | u ~ ] = ( m 0 ⁡ ( j ) m 1 ⁡ ( j ) ) m - 1 ⁢ ∏ i = 1 m ⁢ ⁢ m u ~ , 1 ⁡ ( ij ) ⁢ ( 1 - e u ~ i ⁡ ( 1 - u ~ i ) ⁡ ( i ) ) + m ( 1 - u ~ i ) ⁢ 1 ⁡ ( ij ) ⁢ e ( 1 - u ~ i ) ⁢ u ~ i ⁡ ( i ) m u ~ , 0 ⁡ ( ij ) ⁢ ( 1 - e u ~ i ⁡ ( 1 - u ~ i ) ⁡ ( i ) ) + m ( 1 - u ~ i ) ⁢ 0 ⁡ ( ij ) ⁢ e ( 1 - u ~ i ) ⁢ u ~ i ⁡ ( i ) ( 1 ) is obtained . for a more efficient and more plausible neural formulation logarithms of the probabilities can be taken and obtain synaptic weights w ij , dendritic potentials x j , and firing thresholds θ j , w ij = log ⁢ ( m 11 ⁡ ( 1 - e 01 ) + m 01 ⁢ e 01 ) ⁢ ( m 00 ⁡ ( 1 - e 01 ) + m 10 ⁢ e 10 ) ( m 10 ⁡ ( 1 - e 01 ) + m 01 ⁢ e 01 ) ⁢ ( m 01 ⁡ ( 1 - e 01 ) + m 11 ⁢ e 10 ) ( 2 ) x j = ∑ i = 0 m ⁢ w ij ⁢ u ~ i ( 3 ) θ j = - ( m - 1 ) ⁢ log ⁢ m 0 m 1 - ∑ i = 1 m ⁢ log ⁢ m 01 ⁡ ( 1 - e 01 ) + m 11 ⁢ e 10 m 00 ⁡ ( 1 - e 01 ) + m 10 ⁢ e 10 ( 4 ) where a content neuron fires , { circumflex over ( v )}= 1 , if the dendritic potential x j exceeds the firing threshold , x j ≧ θ j . note that indices of m 0 ( j ) m 1 ( j ) e 01 ( i ), e 10 ( i ), m 00 ( ij ) m 01 ( ij ), m 10 ( ij ), m 11 ( ij ) are skipped for the sake of readability . the previous sections describe an efficient implementation of the optimal neural associative network model based on bayesian probabilistic principles constituting a bayesian probability framework . there are a number of important aspects for a practical implementation ( see , e . g ., a . knoblauch . neural associative networks with optimal bayesian learning . hri - ed report 09 - 02 , honda research institute europe gmbh , d - 63073 offenbach / main , germany , may 2009 for more details ): note that the neural network formulation equation 3 is much cheaper ( in terms of required computation steps ) than equation 1 , in particular for sparse queries having only a small number of active components with ũ i = 1 . however , the synaptic weights equation 2 may not yet satisfy dale &# 39 ; s law that a neuron is either excitatory or inhibitory . to have only positive synaptic weights ( which may be more easily to implement and which is more consistent with biology ) a sufficiently large constant c :=− min ij w ij may be added to each weight . then all synapses have non - negative weights w ′ ij := w ij + c and the dendritic potentials remain unchanged if the last sum in equation 3 is replaced by here the negative sum could be realized , for example , by feed forward inhibition with a strength proportional to the input query pattern activity previously suggested ( cf ., e . g ., a . knoblauch . synchronization and pattern separation in spiking associative memory and visual cortical areas . phd thesis , department of neural information processing , university of ulm , germany , 2003 ). for “ pattern part retrieval ” assuming input query patterns ũ with vanishing add - noise , e 01 → 0 , the weights become essentially independent of the error estimates e 01 , e 10 , thus , for e 01 → 0 it is not necessary to recompute the synaptic weights whenever the expected error probabilities change . the synaptic weights w ij can become plus or minus infinity dependent on the synapse usages : for example , in equation 5 the synaptic weight will become plus infinity if m 10 = 0 or m 01 = 0 . similarly , the synaptic weight will become minus infinity for m 11 = 0 or m 00 = 0 . similar is true for the firing thresholds θ j ( see equation 4 ). however , a closer analysis ( going back to equation 1 ) reveals that naive implementations of infinite synaptic weights and infinite firing thresholds are not adequate and lead to suboptimal performance . instead it is necessary to let the positive and negative infinite components cancel each other . to account for this a neuron model has been developed where each synaptic weight and each neuron threshold is represented by two numbers representing finite and infinite contributions ( see fig4 ). with this model the synaptic weights and firing thresholds of the optimal associative memory compute as follows : compute two matrices representing finite and infinite synaptic weights w ij and w ij ∞ : for d 1 := m 11 ( 1 − e 10 )+ m 01 e 01 , d 2 := m 00 ( 1 − e 01 )+ m 10 e 10 , d 3 := m 10 ( 1 − e 10 )+ m 00 e 01 , d 4 := m 01 ( 1 − e 01 )+ m 11 e 10 w ij = log ⁢ f ⁡ ( d 1 ) ⁢ f ⁡ ( d 2 ) f ⁡ ( d 3 ) ⁢ f ⁡ ( d 4 ) w ij ∞ = g ⁡ ( d 3 ) + g ⁡ ( d 4 ) - g ⁡ ( d 1 ) - g ⁡ ( d 2 ) ∈ { - 2 , - 1 , 0 , 1 , 2 } with the gating functions f ( x )= x for x & gt ; 0 and f ( x )= 1 for x ≦ 0 , and g ( x )= 0 for x & gt ; 0 and g ( x )= 1 for x ≦ 0 . thus , w ij represents the finite weight neglecting infinite components , whereas w ij ∞ counts the number of contributions towards plus and minus infinity . compute two vectors representing finite and infinite neuron thresholds θ ( j ) and θ ∞ ( j ): d 5 := m 01 ( 1 − e 01 )+ m 11 e 10 and d 6 := m 00 ( 1 − e 01 )+ m 110 e 10 then the corresponding operations to compute a retrieval are as follows : activate a postsynaptic neuron j if either x j ∞ & gt ; θ j ∞ or x j ∞ = θ j ∞ and x j ≧ θ j . note that thus there are three ways to implement the optimal associative memory leading to different storage and computation requirements . the first way is to store only the unit and synapse usages as described above . this requires to store only m + n + mn integers each of size log 2 m bits . however , this method requires more computation time because it is necessary , for each input query pattern , to recompute the synaptic weights and firing thresholds or , alternatively , to evaluate equation 1 . this method may be advantageous if the error estimates e 01 and e 10 are quickly changing such that synaptic weights would have to be recomputed anyway . the second way is to store the synaptic weights and firing thresholds as described above . a naive implementation will require to store n + mn floating point values . correspondingly , a retrieval takes only zn + n steps where z := 101 is the number of one - entries in the query vector . the third way is to account for infinite weights and thresholds as described above . then storage requires n + mn floating point values and additional mn integers of size log 2 5 ≦ 3 bits and n integers of size log 2 2m bits . also note that instead of applying fixed optimal thresholds alternatively an 1 - winner - takes - all activation can be used if the number of active units l in a memory pattern ( e . g ., if l μ is constant ) is known . so far the invention describes a hetero - associative memory which corresponds to a feedforward network between two distinct neuron populations u and v ( see fig2 ). if u and v are identical the networks becomes a recurrently connected auto - associative memory performing pattern completion . the invention applies also to the auto - associative case . note that here the optimal bayesian synaptic weights are generally asymmetric , w ij ≠ w ji . this is in contrast to both hopfield and willshaw - type networks . this is also in contrast to theoretical stability conditions based on statistical mechanics . symmetric weights are obtained only in the asymptotic limit when bayesian learning becomes equivalent to the linear covariance rule ( see above ) or if one assumes zero add - noise , e 01 = 0 . the core idea of this invention is to improve learning in neural associative memory structures by applying bayesian learning principles including estimates of input query component error probabilities . this leads to a novel non - linear learning method given by equations 2 and 5 . in practice , an implementation of the corresponding optimal memory system requires the storage of unit usages ( e . g ., m 1 ( j )) and synapse usages ( e . g ., m 11 ( ij )) as well as two - dimensional representations of synaptic weights ( w ( ij ) and w ∞ ( ij )), firing thresholds ku and ( θ ( j ) and θ ∞ ( j )), and dendritic potentials ( x ( j )) and x ′( j )). the two - dimensional variables are required to adequately represent finite and infinite contributions as described above . bayesian neural associative memory as described in the previous sections in a four - layer neural network for information retrieval can generally be applied for efficient implementing nearest neighbor search ( fig5 ). for example , this system for accelerating object recognition systems is used ( cf ., e . g ., s . hasler , h . wersing , and e . korner . a comparison of features in parts - based object recognition hierarchies . in j . marques de sa , l . a . alexandre , w . duch , and d . p . mandic , editors , proceedings of the 17th international conference on artificial neural networks ( icann ), part ii , lncs 4668 , pages 210 - 219 , berlin , heidelberg , 2007 . springer verlag ; s . kirstein , h . wersing , and e . komer . a biologically motivated visual memory architecture for online learning of objects . nwral networks , 21 ( 1 ): 65 - 77 , 2008 ; h . wersing and e . körner . learning optimized features for hierarchical models of invariant object recognition . neural computation , 15 : 1559 - 1588 , 2003 ) or any other application based on nearest neighbor search on high - dimensional sparse data ( see fig6 ; for more details see a . knoblauch . on the computational benefits of inhibitory neural associative networks . hri - eu report 07 - 05 , honda research institute europe gmbh , d - 63073 offenbach / main , germany , may 2007 ; 10 . a . knoblauch . best - match hashing with inhibitory associative networks for real - world object recognition . hri - eu report 08 - 05 , honda research institute europe gmbh , d - 63073 offenbach / main , germany , october 2008 and the previous patent application . here the inhibibitory associative network ( network iam of the previous patent application ) was replaced by the bayesian associative network ( see bam in fig5 , 6 ). this can considerably improve retrieval accuracy at the cost of increased memory and / or computation requirements . fig5 illustrates a four - layer system for information retrieval according to one embodiment of the invention . the system is basically identical to a system based on inhibitory associative memory ( iam ) proposed in the previous patent application except that the iam of the previous invention was replaced by the bayesian associative memory ( bam ) of the current invention . here memory address patterns u μ are mapped to ( carefully chosen ) index representations w μ 1 via an bam which maps via an error - correcting compressed look - up - table ( clut ) to the memory content patterns v μ . fig6 shows a block diagram of a system for visual object recognition using a bayesian associative memory ( bam ) according to one embodiment of the invention . during learning , images i μ are preprocessed in a visual feature hierarchy . the resulting continuous valued feature vector u is binarized resulting in a binary address vector u μ , which is associated with the content or class label v μ employing the four - layer - system described in fig5 . during recognition , a test image ĩ μ is processed in a similar way . the system ( with bam replaced by an iam ) is described in detail in the previous patent application . further possible applications include efficient implementations of lvq ( learning vector quantization ), in particular , if the pattern vectors are high - dimensional and moderately sparse and if a very large number of pattern vectors must be stored . similarly , potential applications include efficient implementations of clustering algorithms or self - organizing maps if the number of cluster prototypes is large and the prototype vectors are high - dimensional and moderately sparse . another potential application is document retrieval : here the database may consist of a large set of text documents , for example taken from the internet . each text document consists of ( possibly many ) words and can be indexed by selecting a relatively small set of key words . the result is a sparse binary feature vector for each text document . given an input query pattern consisting of a set of key words the task is to find the most relevant documents . this retrieval can be accelerated by the methods proposed here . a complementary idea is to represent the words in a text document by applying an n - gram code . for example the 1 - grams ( or monograms ) of “ memory ” are simply the letters “ m ”, “ e ”, “ m ”, “ o ”, “ r ”, “ y ”. similarly , the 2 - grams ( or digrams ) are “ me ”, “ em ”, “ mo ”, “ or ”, “ ry ”, and the 3 - grams are “ mem ”, “ emo ”, “ mor ”, “ ory ”. by that a sparse and fault tolerant code already is obtained very naturally at the word level . for example , for an alphabet of 26 letters , the 2 - gram code represents the word “ memory ” by a binary vector of dimension 26 2 = 676 where only 5 components are active . this method can be used , for example , to implement a fault - tolerant code for the keywords described in the previous item . additionally , the n - gram method can be used to code keyword order and key word sequences in a manner suitable for the associative memory models discussed in this application . in summary , the inhibitory neural networks and algorithms proposed in this application can be used for any application involving the best match or nearest - neighbor problem if the underlying pattern vectors are high - dimensional and ( moderately ) sparse . it should be understood that the foregoing relates only to embodiments of the present invention and that numerous changes and modifications made therein may be made without departing from the scope of the invention as set forth in the following claims . 1 . a . w . burks , h . h . goldstine , and j . von neumann . preliminary discussion of the logical design of an electronic computing instrument . report 1946 , u . s . army ordonance department , 1946 . 2 . p . dayan and d . j . wilishaw . optimising synaptic learning rules in linear associative memory . biological cybernetics , 65 : 253 - 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