2/25/2024 0 Comments Kgb archiver![]() In PAQ7 and later versions under certain conditions, the state also represents the value of the last bit or the entire sequence. In versions through PAQ6, the state represents a pair of counters ( n 0, n 1). Furthermore, for each input prediction there may be several inputs which are nonlinear functions of P i(1) in addition to stretch(P(1)).Įach model partitions the known bits of s into a set of contexts and maps each context to a bit history represented by an 8-bit state. Some versions use multiple networks whose outputs are combined with one more network prior to the SSE stages. Most versions of PAQ use a small context to select among sets of weights for the neural network. This is because the goal of the neural network is to minimize coding cost, not root mean square error. The weight update algorithm differs from backpropagation in that the terms P(1)P(0) are dropped. Where η is the learning rate (typically 0.002 to 0.01), y is the predicted bit, and ( y − P(1)) is the prediction error. squash( x) = 1 / (1 + e − x) (inverse of stretch).Īfter each prediction, the model is updated by adjusting the weights to minimize coding cost:.Where P(1) is the probability that the next bit will be a 1, P i(1) is the probability estimated by the i-th model, and These predictions are averaged in the logistic domain: w i ← w i + error.īeginning with PAQ7, each model outputs a prediction (instead of a pair of counts).If the bit to be coded is y, then the weight adjustment is: (Order- n contexts had a weight of n 2.) Beginning with PAQ4, the weights were adjusted adaptively in the direction that would reduce future errors in the same context set. ![]() Through PAQ3, the weights were fixed and set in an ad-hoc manner. Where w i is the weight of the i-th model. The probabilities are computed by weighted addition of the 0 and 1 counts: In PAQ1 through PAQ3, each prediction is represented as a pair of bit counts ( n 0, n 1 ) and a 1 is observed, then the counts are updated to (7, 4).Ī bit is arithmetically coded with space proportional to its probability, either P(1) or P(0) = 1 − P(1).There are three methods for combining predictions, depending on the version: Once the next-bit probability is determined, it is encoded by arithmetic coding. specialized models, such as x86 executables, BMP, TIFF, or JPEG images these models are active only when the particular file type is detected.Īll PAQ versions predict and compress one bit at a time, but differ in the details of the models and how the predictions are combined and postprocessed.two-dimensional contexts (useful for images, tables, and spreadsheets) the row length is determined by finding the stride length of repeating byte patterns."analog" contexts, consisting of the high-order bits of previous 8- or 16-bit words (useful for multimedia files)."sparse" contexts, for example, the second and fourth bytes preceding the predicted symbol (useful in some binary formats).whole-word n-grams, ignoring case and nonalphabetic characters (useful in text files).n-grams the context is the last n bytes before the predicted symbol (as in PPM).Most PAQ versions collect next-symbol statistics for the following contexts: Unlike PPM, a context doesn't need to be contiguous. Context mixing is related to prediction by partial matching (PPM) in that the compressor is divided into a predictor and an arithmetic coder, but differs in that the next-symbol prediction is computed using a weighted combination of probability estimates from a large number of models conditioned on different contexts. PAQ is free software distributed under the GNU General Public License. ![]() Specialized versions of PAQ have won the Hutter Prize and the Calgary Challenge. PAQ is a series of lossless data compression archivers that have gone through collaborative development to top rankings on several benchmarks measuring compression ratio (although at the expense of speed and memory usage). ( March 2011) ( Learn how and when to remove this template message) Please help to improve this article by introducing more precise citations. ![]() This article includes a list of general references, but it lacks sufficient corresponding inline citations.
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