Entropic associative memory for manuscript symbols

Abstract

Manuscript symbols can be stored, recognized and retrieved from an entropic digital memory that is associative and distributed but yet declarative; memory retrieval is a constructive operation, memory cues to objects not contained in the memory are rejected directly without search, and memory operations can be performed through parallel computations. Manuscript symbols, both letters and numerals, are represented in Associative Memory Registers that have an associated entropy. The memory recognition operation obeys an entropy trade-off between precision and recall, and the entropy level impacts on the quality of the objects recovered through the memory retrieval operation. The present proposal is contrasted in several dimensions with neural networks models of associative memory. We discuss the operational characteristics of the entropic associative memory for retrieving objects with both complete and incomplete information, such as severe occlusions. The experiments reported in this paper add evidence on the potential of this framework for developing practical applications and computational models of natural memory.

Imagery in the entropic associative memory

“…The functions representing the inputs and the outputs are placed on another table, called the auxiliary register, with the same dimensions of the AMR. The -register is defined as the logical disjunction 1 , 2 or the addition 3 between the value of each cell in the auxiliary register and the value of the corresponding cell in the AMR; the -recognition is defined through the logical material implication between the cells in the auxiliary register and the corresponding cells in the AMR, so the operation is true if the cue is included in the memory and false otherwise; and the -retrieval selects a row of the AMR that corresponds to the value of the retrieved object, for all the cells used by the cue. These operations are illustrated diagrammatically in Figs.…”

“…The functions that are input to and output from the memory constitute abstract amodal representations of the stored modality-specific concrete images. These are placed in input and output buffers, such as pixel buffers in the case of visual images 1 , 2 and MFCC vectors in the case of phonetic information 3 . Such concrete images are mapped into their corresponding functions and vice versa through a coder and a decoder, respectively.…”

Imagery in the Entropic Associative Memory

“…The Entropic Associative Memory (EAM) [1][2][3] is a novel computational model of memory in which functions representing arbitrary concrete or abstract objects are stored in a bi-dimensional array or table, which is used as the representational medium. The columns and the rows stand for the arguments and their values, respectively, and the functional relation is represented by filling up the cell at the corresponding intersection, for all the columns.…”

“…In the basic EAM 1,2 all cells are on or off, but in its weighted version the W-EAM 3 the cells contain integer values, and λ -register increments by one the value of the cells of the memory corresponding to the cells used by the cue in the auxiliary register. The operation reinforces all the cells used by the cue simultaneously.…”

“…In summary, the present memory model is associative, declarative, abstractive, distributed, productive, constructive, indeterminate, and rejects cues not included in the memory directly without search, resembling the corresponding putative properties of human memory [4][5][6] . There are previous computational models aiming to capture some of these properties 7 , but this line of works opposes associative memories developed within the Artificial Neural Networks (ANNs) paradigm, such as Hopfield's 8 and further related work [9][10][11][12][13][14][15] , which are distributed but non-declarative -i.e., procedural or sub-symbolic-concrete, non-productive, determinate, reproductive, that need to search to reject objects not included in the memory and implement implicitly a form of the close-world assumption [1][2][3] .…”