The Cyclic Towers of Hanoi and Pseudo Ternary Codes

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

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Deep Learning to Ternary Hash Codes by Continuation

10.36227/techrxiv.17083019 ◽

2021 ◽

Author(s):

Mingrui Chen ◽

Weiyu Li ◽

weizhi lu

Keyword(s):

Deep Learning ◽

Image Retrieval ◽

Continuation Method ◽

Binary Codes ◽

Hard Thresholding ◽

Joint Learning ◽

Ternary Codes ◽

First Time ◽

Hash Codes ◽

Discrete Functions

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

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Perfect codes on the towers of Hanoi graph

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700031774 ◽

1998 ◽

Vol 57 (3) ◽

pp. 367-376 ◽

Cited By ~ 10

Author(s):

Chi-Kwong Li ◽

Ingrid Nelson

Keyword(s):

Short Proof ◽

Error Correcting Code ◽

Error Correcting Codes ◽

Perfect Codes ◽

Towers Of Hanoi

We characterise all the perfect k-error correcting codes that can be defined on the graph associated with the Towers of Hanoi puzzle. In particular, a short proof for the existence of 1-error correcting code on such a graph is given.

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