Internal representation

Rumelhart, D.E., Hinton, G.E. and Williams, R.J. (1986) Learning internal representations by error propagation. In Parallel Distributed Processing, Rumelhart, D.E. and McClelland, J.L. (eds.), M.I.T. Press, Cambridge, Mass. 

The Validity of Drawn Diagrams in Representing Internal Representations... 

D.E. Rumelhart, J.L. McClelland Parallel Distributed Processing Explorations in the microstructure of cognition Vol.l Learning internal representations by error propagation, MIT Press, Cambridge (MA, USA) 1986... 

Figure 3.7 and Figure 3.8 show that the internal representation and interactions differ widely between the implementations. Our behavior specification must abstract these irrelevant internal interactions and include only interactions with objects that the client should be aware of.6 What we really want to specify is the calendar together with some abstraction of its (hidden) event container, hashtable, vector, and so on (see Figure 3.9). 

Decide How Objects, Links, and Actions Are Implemented. This is highly dependent on the answers to the preceding question. Each component may have its own internal representation of objects as C structures, as Java or C++ objects, or as files or database records. Links may be memory addresses, URLs, CORBA identifiers, database keys, or customer reference numbers, or they may be refined to further objects. Actions may be further refined and ultimately be function calls, Ada rendezvous, signals, or Internet messages. 

An example of a problem solving tree for the synthesis of Darvon appears in Figure 3. The tree contains both AND nodes and OR nodes (7). The AND branches, connected by double arcs, indicate that both compounds are required to make the compound above them. The OR branches (there are three OR paths to make compound II) indicate different routes for making the compound. The terminal nodes corresponding to starting materials are enclosed in boxes. At present, a branch is terminated when the number of clauses in the clause list, the internal representation of the goal, is less than or equal to six or the clause list matches the clause list of a starting material molecule. 

The thalamus is the gateway to cortical processing of all incoming sensory information, represented in Figure 2.1 by the three major systems somatosensory (S), auditory (A), and visual (V). Primary sensory cortices (SI, Al, VI) receive information from the appropriate input modules (sensory organ -I- thalamus). The association cortex integrates information from primary cortices, from subcortical structures, and from brain areas affiliated with memory to create an internal representation of the sensory information. The medial temporal lobe (i.e., hippocampus, amygdala) serves two major... 

A well-assorted, international representation of authorship is evident in recent volumes of Advances the original British-American liaison on which the publication was founded has been substantially expanded to the international level. The present volume includes, in addition to contributions from North America and Great Britain, articles from continental Europe and, coincidentally, three separate chapters by authors based at different points on the African continent. 

While some researchers feel that individual components making up the sensory response need to be characterized (9), others feel that methods dealing with the composite sensation are more appropriate. For this reason methods which do not rely on internal representation of terms have been applied. One such method is multidimensional scaling (MBS), which treats data based on a persons total perception of the dissimilarity between objects.(10)... 

Before introducing the method for calculating the internal representation the psychoacoustic fundamentals of the perceptual model is explained in the next chapter. 

In thinking about how to calculate the internal representation of a signal one could dream of a method where all the transformation characteristics of the individual elements of the human auditory system would be measured and modelled. In this exact approach one would have the, next to impossible, task of modelling the ear, the transduction mechanism and the neural processing at a number of different abstraction levels. 

One can doubt whether it is necessary to have an exact model of the lower abstraction levels of the auditory system (outer-, middle-, inner ear, transduction). Because audio quality judgements are, in the end, a cognitive process a crude approximation of the internal representation followed by a crude cognitive interpretation may be more appropriate then having an exact internal representation without cognitive interpretation of the differences. 

After having applied the time-frequency smearing operation one gets an excitation pattern representation of the audio signal in (dl 1 exc, seconds, Bark). This representation is then transformed to an internal representation using a non-linear compression function. The form of this compression function can be derived from loudness experiments. 

Scaling experiments using steady-state signals have shown that the loudness of a sound is a non-linear function of the intensity. Extensive measurements on the relationship between intensity and loudness have led to the definition of the Sone. A steady-state sinusoid of 1 kHz at a level of 40 dB SPL is defined to have a loudness of one Sone. The loudness of other sounds can be estimated in psychoacoustic experiments. In a first approximation towards calculating the internal representation one would map the physical representation in dB/Bark onto a representation in Sone/Bark ... 

Figure 1.7 Overview of the basic transformations which are used in the development of the PAQM (Perceptual Audio Quality Measure). The signals x(t) and y t) are windowed with a window w(t) and then transformed to the frequency domain. The power spectra as function of time and frequency, Px (t, f) and Py(t, /) are transformed to power spectra as function of time and pitch, px(t, z) and py(t, z) which are convolved with the smearing function resulting in the excitations as a function of pitch Ex (/, z) ar 6Ey(t, z). After transformation with the compression function we get the internal representations x(f, z)and ,(, z) from which the average noise disturbance Cn over the audio fragment can be calculated.

The internal representation of any audio signal can now be calculated by using the transformations given in the previous section. The quality of an audio device can thus be measured with test signals (sinusoids, sweeps, noise etc) as well as real life signals (speech, music). Thus the method is universally applicable. In general audio devices are tested for transparency (i.e. the output must resemble the input as closely as possible) in which case the input and output are both mapped onto their internal representations and the quality of the audio device is determined by the difference between these input (the reference) and output internal representations. 

In the internal representation model the time-frequency plane is divided in cells with a resolution of 20 ms along in the time axis (time index m) and of 0.2 Bark along the frequency axis (frequency index /). A first approach was to use the power ratio between the output y and input x, py px in every (At, A f) cell (m, /) as a correction factor for the noise disturbance L (m, l) in that cell (nomenclature is chosen to be consistent with [Beerends and Stemerdink, 1992]). 

Although the PSQM uses a rather simple internal representation model the correlation with the subjectively perceived speech quality is very high. For the two speech quality databases that were used in the PAQM validation the method even gives a minor improvement in correlation. Because of a difference in the mapping from intensity to loudness a different weighting for the silent intervals has to be used (compare Figs. 1.16, 1.17 with 1.18,10 1.1911). 

The perceptual model as developed in this chapter is used to map the input and output of the audio device onto internal representations that are as close as possible to the internal representations used by the subject to judge the quality of the audio device. It is shown that the difference in internal representation can form the basis of a perceptual audio quality measure (PAQM) that has a high correlation with the subjectively perceived audio quality. Furthermore it is shown that with a simple cognitive module that interprets the difference in internal representation the correlation between objective and subjective results is always above 0.9 for both wideband music and telephone-band speech signals. For the measurement of the quality of telephone-band speech codecs a simplified version of the PAQM, the perceptual speech quality measure (PSQM), is presented. 

For non-stationary sounds the internal representation is best described by means of a temporal representation. The internal representation can be measured by means of a test signal of short duration. A schematic example for a single click (masker) is given in Fig. 1.3 where the masked threshold of such a click is measured with a second click (target). The masked threshold can be interpreted as the result of an internal, smeared out, representation of the puls (Fig. 1.3, excitation pattern). 

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