Visuomotor Associative Memory

The co-occurrence relationship between motor commands and sensory feedback during body babbling will develop the associations between these two occurrences. Based on this associative relationship, when actions of some other agent are perceived, might lead to an automatic and spontaneous generation of the motor output. We have developed an associative memory, called Topological Gaussian Adaptive Resonance Associative Memory (TGAR-AM), structure using two-layered architecture, namely the memory layer and the association layer (Fig 6). The memory layer encode the received data in the form of a topological structure in an incremental manner, and the association layer formulates the associative relationship between the input patterns. The association between the memorized patterns is developed based on the labels acquired through motion primitive segmentation. According to the labels of these input vectors, the memory layer stores these input patterns as a sub-network. The labels of these sub-networks in the memory layer are passed on to the association layer. Using TGARM, association is developed between the vision (key-vector) and action vectors (response vector). This association between the temporal sequences is represented through the edges between the vision and the action nodes.

The structure of Topological Gaussian Adaptive Resonance Associative Memory (TGAR-AM) is based on TGARM and performs incremental topology representation without calling for a priori definition of the structure and size of the network. For each class of the input feature vectors, we utilized TGARM to represent the distribution of that labelled segment. Based on this theory, the patterns are associated incrementally without defiling the stored knowledge. The proposed associative memory system is able to memorize temporal sequence information as patterns with a consecutive relation.

The main task of behavior generation phase is to find the most likely motion primitive sequence to perform the observed behavioral action. For this purpose the desired behavioral action is presented as an image sequence to the associative memory module. Next, the label of the observed images is estimated using the auto-associative mode and the motion label associated with this observed image is selected. Later, observation sequence from the current observation to the goal observation is generated by most likely path sequence. The TGAR-HMM’s observation-to-observation transition probabilities are used for this purpose to generate the most likely motion primitive sequence.

The memory layer learns input vectors as nodes incrementally, and memorizes the labels of each input vector. When some feature vector is provided as input to the memory layer, if at that point there is no sub-network representing the class label of that input feature vector, then create a new sub-network with the input vector as the first node of the new sub-network and mark this new sub-network with the label of the input feature vector. If there is already a sub-network with the same class name as the input vector, then update the weight vector of the node of the sub-network representing that particular class label. Similar to TGARM, if there is no edge connecting the two nodes, then create and edge linking the two winning nodes. If the label of the input vector does not belong to an existing class in the memory layer, a new network representing the new label is added to the layer. Otherwise, a node is added to the corresponding sub-network. Both the vision vectors and the action vectors are represented by separate sub-networks.

New classes are learned incrementally by adding new subnetworks; for example, learning new patterns belonging to one class is done incrementally by integrating new nodes to an existent subnetwork. The amount of subnetworks is not fixed beforehand, rather determined incrementally based on the number of classes of input patterns. When an input feature vector representing a new class emerges, the memory layer processes the new class without defiling previously learned classes.

The association layer builds an association between the vision vectors and the action vectors using their class labels. Suppose we have vision vector (Vt) which we label as visual feature class (ν_t) or the key class, similarly, we have motion vectors (At) labelled as action feature class (a_t) or the response class. Each node in the association layer represents one class and all the nodes are connected through edges—the origin of the edge indicates the visual feature class and the end of the edge points to the corresponding action feature class. During the learning of the association layer, an association paired data consisting of the visual feature and action vector, is utilized as input vectors. First, TGARM algorithm is employed to memorize information of both the vision and the motion feature vectors. The class name of the new class is sent to the association layer. Similar to the memory layer, if the class label of the node in the memory layer does not exist in the association layer, a new node representing the new class label is added to the association layer.

In the association layer, the weight vector of each node is picked out from the corresponding subnetwork of the memory layer. If nodes that represent the vision class (key-class) and action class (response-class) already exist, we link up their nodes with an arrow edge. The origin of the edge indicates the key-class and the end of the edge points to the corresponding response-class. This develops an associative relationship joining the key-class and the response-class.

When a key-vector is presented as an input, the associative memory is required to recall the corresponding response vector associated with that particular key from the memory. The recall process employed both auto-associative and hetero-associative mechanism. Behavior generation phase can be described as a two-step problem:

Category Estimation: Given the visual stimuli observation sequence represented by slow features, the role of category estimation is to determine the label of the unlabelled input visual features. This is accomplished through the auto-associative recall process.

Motion Primitive Sequence Generation: Given the category of the observed visual stimuli and HMM, the purpose of sequence generation step is to find the associated action category label. This is determined using the hetero-associative mode. After finding the associated category label, the corresponding most likely state sequence for motion generation is estimated.

Algorithm 2 Algorithm for Auto-associative Recall

1: Input the observation vector Vt.

2: for all the nodes in the Memory Layer. do

3: Calculate the weight sum of input vector as:

4: ϑi(Vt)=NiTVt-12∥Ni∥2 where N is the weight of the nodes in the memory layer.

5: end for

6: Find: ϑk(Vt)=max∀nodesϑi(Vt)

7: if ∥Vt∥2-2ϑk(Vt)>θ. then

8: OUTPUT: Failed to Recall the memorized pattern.

9: else

10: Find the node Vt corresponding to the sub-network ν_t.

11: end if

In the first step the auto-associative mechanism is invoked which recognizes the key vector class resembling the input patterns stored in the memory. The input pattern may be noise polluted. We find the distance between the input vector (Vt) and the weight vector of the stored patterns (NiT). If the distance (ϑ) Eq (24) between the two vector lies within the Voronoi region, i.e. the distance is larger than the threshold Eq (23), then the memorized pattern is recalled. Otherwise, the system fails to recall. The threshold value is determined by the vigilance parameter (ρ) used during TGARM learning.

Once the class of the key-vector ν_t is determined using Algorithm 2, the hetero-associative mechanism is employed to recall the corresponding class label a_t. During this process the key-vectors determined in the previous phase are presented to the system as sequence of cues, and the system recalls the appropriate class labels associated with that key vector.