Bonny Banerjee

An Architecture for Problem Solving with Diagrams

In problem solving a goal/subgoal is either solved by generating needed information from current information, or further decomposed into additional subgoals. In traditional problem solving, goals, knowledge, and problem states are all modeled as expressions composed of symbolic predicates, and information generation is modeled as rule application based on matching of symbols. In problem solving with diagrams on the other hand, an additional means of generating information is available, viz., by visual perception on diagrams. A subgoal is solved opportunistically by whichever way of generating information is successful. Diagrams are especially effective because certain types of information that is entailed by given information is explicitly available – as emergent objects and emergent relations – for pickup by visual perception. We add to the traditional problem solving architecture a component for representing the diagram as a configuration of diagrammatic objects of three basic types, point, curve and region; a set of perceptual routines that recognize emergent objects and evaluate a set of generic spatial relations between objects; and a set of action routines that create or modify the diagram. We discuss how domain-specific capabilities can be added on top of the generic capabilities of the diagram system. The working of the architecture is illustrated by means of an application scenario.

Augmenting cognitive architectures to support diagrammatic imagination.

Diagrams are a form of spatial representation that supports reasoning and problem solving. Even when diagrams are external, not to mention when there are no external representations, problem solving often calls for internal representations, that is, representations in cognition, of diagrammatic elements and internal perceptions on them. General cognitive architectures--Soar and ACT-R, to name the most prominent--do not have representations and operations to support diagrammatic reasoning. In this article, we examine some requirements for such internal representations and processes in cognitive architectures. We discuss the degree to which DRS, our earlier proposal for such an internal representation for diagrams, meets these requirements. In DRS, the diagrams are not raw images, but a composition of objects that can be individuated and thus symbolized, while, unlike traditional symbols, the referent of the symbol is an object that retains its perceptual essence, namely, its spatiality. This duality provides a way to resolve what anti-imagists thought was a contradiction in mental imagery: the compositionality of mental images that seemed to be unique to symbol systems, and their support of a perceptual experience of images and some types of perception on them. We briefly review the use of DRS to augment Soar and ACT-R with a diagrammatic representation component. We identify issues for further research.

A self-organizing auto-associative network for the generalized physical design of microstrip patches

The current work deals with the efficient physical design of patch antennas given the desired parameters like resonant frequency f/sub r/, feed point position a/sub f/, substrate thickness h, relative permittivity /spl epsiv//sub r/, input impedance Z (=R+jX), and efficiency /spl eta/. Based loosely on the analogy of perception of the human brain, a neurocomputing network has been designed, consisting of two distinct phases, namely, the training phase and the application phase. The training phase accepts as input the exhaustive set of the said parameters for patches of different shapes and sizes and determines the optimized processors (processors that adequately define the information topology of the input data set) from the exhaustive training instances using a set of information extracting self-organizing neural networks. The outputs of the training phase are n sets of processors, n being the number of different shapes of patches taken into consideration. The application phase determines the shape and size of a microstrip antenna when its desired parameters are presented to the network as the external input. This is achieved by comparing the external input with each set of processors, hence determining the cost due to each comparison. A cost matrix is thus formed which when passed through an optimization network gives the best match and hence the shape and shape determining attributes of the patch whose parameters had been passed as external input.

A constraint satisfaction framework for executing perceptions and actions in diagrammatic reasoning

Diagrammatic reasoning (DR) is pervasive in human problem solving as a powerful adjunct to symbolic reasoning based on language-like representations. The research reported in this paper is a contribution to building a general purpose DR system as an extension to a soar-like problem solving architecture. The work is in a framework in which DR is modeled as a process where subtasks are solved, as appropriate, either by inference from symbolic representations or by interaction with a diagram, i.e., perceiving specified information from a diagram or modifying/creating objects in a diagram in specified ways according to problem solving needs. The perceptions and actions in most DR systems built so far are hand-coded for the specific application, even when the rest of the system is built using the general architecture. The absence of a general framework for executing perceptions/ actions poses as a major hindrance to using them opportunistically - the essence of open-ended search in problem solving. Our goal is to develop a framework for executing a wide variety of specified perceptions and actions across tasks/domains without human intervention. We observe that the domain/task-specific visual perceptions/actions can be transformed into domain/taskindependent spatial problems. We specify a spatial problem as a quantified constraint satisfaction problem in the real domain using an open-ended vocabulary of properties, relations and actions involving three kinds of diagrammatic objects - points, curves, regions. Solving a spatial problem from this specification requires computing the equivalent simplified quantifier-free expression, the complexity of which is inherently doubly exponential. We represent objects as configuration of simple elements to facilitate decomposition of complex problems into simpler and similar subproblems. We show that, if the symbolic solution to a subproblem can be expressed concisely, quantifiers can be eliminated from spatial problems in low-order polynomial time using similar previously solved subproblems. This requires determining the similarity of two problems, the existence of a mapping between them computable in polynomial time, and designing a memory for storing previously solved problems so as to facilitate search. The efficacy of the idea is shown by time complexity analysis. We demonstrate the proposed approach by executing perceptions and actions involved in DR tasks in two army applications.

SELP: A general-purpose framework for learning the norms from saliencies in spatiotemporal data

Abstract Sensors that monitor around the clock are everywhere. Due to the sheer amount of data these sensors can generate, the resources required to store, protect personal information, and analyze them are enormous. Since noteworthy events happen only occasionally, it is not necessary to store or analyze the data generated at every instant of time. Rather, it is imperative for a smart memory to learn the norms in such data so that only the abnormal (or salient) events may be stored. We present a general-purpose biologically plausible computational framework, called SELP, for learning the norms (or invariances) as a hierarchy of features from space- and time-varying data in an unsupervised and online manner from saliencies or surprises in the data. Given streaming data, this framework runs a relentless cycle – detect unexpected or S alient event, E xplain the salient event, L earn from its explanation, P redict the future events – involving the real external world and its internal model, and hence the name. Experimental results from different functions of this framework are presented with a particular emphasis on the role of lateral connections in each layer.

Hierarchical feature learning from sensorial data by spherical clustering

Surveillance sensors are a major source of unstructured Big Data. Discovering and recognizing spatiotemporal objects (e.g., events) in such data is of paramount importance to the security and safety of facilities and individuals. What kind of computational model is necessary for discovering spatiotemporal objects at the level of abstraction they occur? Hierarchical invariant feature learning is the crux to the problems of discovery and recognition in Big Data. We present a multilayered convergent neural architecture for storing repeating spatially and temporally coincident patterns in data at multiple levels of abstraction. A node is the canonical computational unit consisting of neurons. Neurons are connected in and across nodes via bottom-up, top-down and lateral connections. The bottom-up weights are learned to encode a hierarchy of overcomplete and sparse feature dictionaries from space- and time-varying sensorial data by recursive layer-by-layer spherical clustering. The model scales to full-sized high-dimensional input data and also to an arbitrary number of layers thereby having the capability to capture features at any level of abstraction. The model is fully-learnable with only two manually tunable parameters. The model is generalpurpose (i.e., there is no modality-specific assumption for any spatiotemporal data), unsupervised and online. We use the learning algorithm, without any alteration, to learn meaningful feature hierarchies from images and videos which can then be used for recognition. Besides being online, operations in each layer of the model can be implemented in parallelized hardware, making it very efficient for real world Big Data applications.

Efficient learning from explanation of prediction errors in streaming data

Streaming data from different kinds of sensors contributes to Big Data in a significant way. Recognizing the norms and abnormalities in such spatiotemporal data is a challenging problem. We present a general-purpose biologically-plausible computational model, called SELP, for learning the norms or invariances as features in an unsupervised and online manner from explanations of saliencies or surprises in the data. Given streaming data, this model runs a relentless cycle of Surprise → Explain → Learn → Predict involving the real external world and its internal model, and hence the name. The key characteristic of the model is its efficiency, crucial for streaming Big Data applications, which stems from two functionalities exploited at each sampling instant - it operates on the change in the state of data between consecutive sampling instants as opposed to the entire state of data, and it learns only from surprise or prediction error to update its internal state as opposed to learning from the entire input. The former allows the model to concentrate its computational resources on spatial regions of the data changing most frequently and ignore others, while the latter allows it to concentrate on those instants of time when its prediction is erroneous and ignore others. The model is implemented in a neural network architecture. We show the performance of the network in learning and retaining sequences of handwritten numerals. When exposed to natural videos acquired by a camera mounted on a cats head, the neurons learn receptive fields resembling simple cells in the primary visual cortex. The model leads to an agent-dependent framework for mining streaming data where the agent interprets and learns from the data in order to update its internal model.

A framework of Voronoi diagram for planning multiple paths in free space

Most of the emphasis in path planning, a topic of much interest in several domains, has been on finding the optimal path or at most k optimal paths. However, in domains such as adversarial planning, one of the agents might deliberately take less optimal paths to confuse the opponent, and by the same token an agent, for inferring opponents intent, has to consider all possible paths that the opponent might take. We introduce the notion of representative paths in free space (2D) and study the problem of computing all representative paths with different properties, such as all representative paths with at most L loops, among polygonal regions using a framework of Voronoi diagram. We prove three properties: (1) the upper and lower bounds to the number of simple paths in a Voronoi graph (2) given any path, a homotopic path can always be obtained from the Voronoi diagram of the regions and (3) all representative paths with a given property might not be always obtainable from the Voronoi graph even after searching the graph exhaustively and present an algorithm to work around this limitation. We also show how our findings can be applied for efficient entity re-identification, a problem involving a large number of dynamic entities and obstacles in the military domain.

Improved speech inversion using general regression neural network.

The problem of nonlinear acoustic to articulatory inversion mapping is investigated in the feature space using two models, the deep belief network (DBN) which is the state-of-the-art, and the general regression neural network (GRNN). The task is to estimate a set of articulatory features for improved speech recognition. Experiments with MOCHA-TIMIT and MNGU0 databases reveal that, for speech inversion, GRNN yields a lower root-mean-square error and a higher correlation than DBN. It is also shown that conjunction of acoustic and GRNN-estimated articulatory features yields state-of-the-art accuracy in broad class phonetic classification and phoneme recognition using less computational power.

An Online Clustering Algorithm That Ignores Outliers: Application to Hierarchical Feature Learning from Sensory Data

Surveillance sensors are a major source of unstructured Big Data. Discovering and recognizing spatiotemporal objects (e.g., events) in such data is of paramount importance to the security and safety of facilities and individuals. Hierarchical feature learning is at the crux to the problems of discovery and recognition. We present a multilayered convergent neural architecture for storing repeating spatially and temporally coincident patterns in data at multiple levels of abstraction. The bottom-up weights in each layer are learned to encode a hierarchy of over complete and sparse feature dictionaries from space- and time-varying sensory data by recursive layer-by-layer spherical clustering. This density-based clustering algorithm ignores outliers by the use of a unique adaptive threshold in each neurons transfer function. The model scales to full-sized high-dimensional input data and also to an arbitrary number of layers, thereby possessing the capability to capture features at any level of abstraction. It is fully-learnable with only two manually tunable parameters. The model was deployed to learn meaningful feature hierarchies from audio, images and videos which can then be used for recognition and reconstruction. Besides being online, operations in each layer of the model can be implemented in parallelized hardware, making it very efficient for real world Big Data applications.