Recurrent correlation associative memories

Abstract

A model for a class of high-capacity associative memories is presented. Since they are based on two-layer recurrent neural networks and their operations depend on the correlation measure, these associative memories are called recurrent correlation associative memories (RCAMs). The RCAMs are shown to be asymptotically stable in both synchronous and asynchronous (sequential) update modes as long as their weighting functions are continuous and monotone nondecreasing. In particular, a high-capacity RCAM named the exponential correlation associative memory (ECAM) is proposed. The asymptotic storage capacity of the ECAM scales exponentially with the length of memory patterns, and it meets the ultimate upper bound for the capacity of associative memories. The asymptotic storage capacity of the ECAM with limited dynamic range in its exponentiation nodes is found to be proportional to that dynamic range. Design and fabrication of a 3-mm CMOS ECAM chip is reported. The prototype chip can store 32 24-bit memory patterns, and its speed is higher than one associative recall operation every 3 mus. An application of the ECAM chip to vector quantization is also described.

Memórias Associativas Nebulosas Implicativas Baseadas Em Normas Triangulares Arquimedianas

“…Resumidamente, as pesquisas em memória associativa iniciaram na metade do século XX e receberam mais atenção nos anos 1980 após a publicação do famoso artigo de Hopfield [2,11]. Nos anos 1990, foram apresentados vários modelos que estendem a rede de Hopfield, por exemplo, a Memória Associativa de Capacidade Exponencial (ECAM) [4] e a Memória Associativa Bidirecional (BAM) [17]. Entretanto, tanto a rede de Hopfield como a ECAM e a BAM, são modelos usados para armazenar padrões binários.…”

Distance-Based Sparse Associative Memory Neural Network Algorithm for Pattern Recognition

“…Chiueh and Goodman had analyzed that the capacity of ECAM scales exponentially with N (the length of the stored vectors) in [8], and as its variants, we conjecture that DB-ECAM, DBS-ECAM, MECAM, DB-MECAM, and DBS-MECAM also possess comparable storage capacity to ECAM. But in fact, to prove this claim theoretically is difficult, if not impossible.…”

“…Chieuh and Goodman [8] have demonstrated that ECAM is asymptotically stable in both synchronous and asynchronous update modes by defining a Liapunov energy function. They have also shown that the asymptotic storage capacity of the ECAM scales exponentially with the length of memory patterns theoretically.…”

“…However, the storage capacity of the HOCAM is only asymptotically proportional to N q , where q is greater than 1 and denotes an order of the high-order polynomial used. Although the PFCAM's capacity grows exponentially with the number of components in memory patterns, the primary disadvantage of this model is that hardware implementation can be cumbersome [8]. Later, Chieuh and Goodman [8] proposed Exponential Correlation Associative Memory (ECAM) with comparable storage capacity to PFCAM which has an advantage of easier hardware implementation.…”

“…Although the PFCAM's capacity grows exponentially with the number of components in memory patterns, the primary disadvantage of this model is that hardware implementation can be cumbersome [8]. Later, Chieuh and Goodman [8] proposed Exponential Correlation Associative Memory (ECAM) with comparable storage capacity to PFCAM which has an advantage of easier hardware implementation. On the other hand, many efforts have also been made and focused on the two aspects: (1) one is to enlarge the processed data (value) range from just binary to multi-value; (2) the other is to change recalling mode from auto-association to hetero-association to realize multidirectional association.…”