Machine learning for sequential data: A review <s> Recurrent Sliding Windows <s> This chapter contains sections titled: The Problem, The Generalized Delta Rule, Simulation Results, Some Further Generalizations, Conclusion <s> BIB001 </s> Machine learning for sequential data: A review <s> Recurrent Sliding Windows <s> Time underlies many interesting human behaviors. Thus, the question of how to represent time in connectionist models is very important. One approach is to represent time implicitly by its effects on processing rather than explicitly (as in a spatial representation). The current report develops a proposal along these lines first described by Jordan (1986) which involves the use of recurrent links in order to provide networks with a dynamic memory. In this approach, hidden unit patterns are fed back to themselves; the internal representations which develop thus reflect task demands in the context of prior internal states. A set of simulations is reported which range from relatively simple problems (temporal version of XOR) to discovering syntactic/semantic features for words. The networks are able to learn interesting internal representations which incorporate task demands with memory demands; indeed, in this approach the notion of memory is inextricably bound up with task processing. These representations reveal a rich structure, which allows them to be highly context-dependent while also expressing generalizations across classes of items. These representations suggest a method for representing lexical categories and the type/token distinction. <s> BIB002 </s> Machine learning for sequential data: A review <s> Recurrent Sliding Windows <s> ABSTRACT A theory of learned sequential behavior is presented, with a focus on coarticulatory phenomena in speech. The theory is implemented as a recurrent parallel distributed processing network that is trained via a generalized error-correcting algorithm. The basic idea underlying the theory is that both serial order and coarticulatory overlap can be represented in terms of relative levels of activation in a network if a clear distinction is made between the state of the network and the output of the network. <s> BIB003
One way that sliding window methods can be improved is to make them recurrent. In a recurrent sliding window method, the predicted value y i,t is fed as an input to help make the prediction for y i,t+1 . Specifically, with a window of half- Bakiri and Dietterich  applied this technique to the English pronunciation problem using a 7-letter window and a decision-tree algorithm. Table 1 summarizes the results they obtained when training on 1000 words and evaluating the performance on a separate 1000-word test data set. The baseline sliding window method correctly pronounces 12.5% of the words and 69.6% of the individual letters in the words. A recurrent sliding window moving left-to-right improves the word-level performance but worsens the pronunciations of individual letters. However, a right-to-left sliding window improves both the word-level and letterlevel performance. Indeed, the percentage of correct word-level pronunciations has nearly doubled! Clearly, the recurrent method captures predictive information that was not being captured by the simple 7-letter sliding window. But why is the right-to-left scan superior? It appears that in English, the right-to-left scan is able to capture long-distance effects such as those mentioned above for "thought" and "photography". For example, the right-most window can correctly pronounce the "y" of "photography". This information is then available when the system attempts to pronounce the "a". And this information in turn is available when the system is pronouncing the second "o", and so on. Because the stress patterns in English are determined by the number of syllables to the right of the current syllable, a right-to-left recurrent window is able to correctly predict these stresses, and hence, choose the correct pronunciations for the vowels in each syllable. One issue arises during training: What values should be used for the y i,t inputs when training the window classifier? One approach would be to first train a non-recurrent classifier, and then use its y i,t predictions as the inputs. This process can be iterated, so that the predicted outputs from each iteration are employed as inputs in the next iteration. Another approach is to use the correct labels y i,t as the inputs. The advantage of using the correct labels is that training can be performed with the standard supervised learning algorithms, since each training example can be constructed independently. This was the choice made by Bakiri and Dietterich. In addition to recurrent decision trees, many other classifiers can be made recurrent. Recurrent neural networks are of particular interest. Figure 1 shows two of the many architectures that have been explored. Part (a) shows a network in which the output units are fed as inputs to the hidden units at the next time step. This is essentially identical to the recurrent decision trees employed by Bakiri and Dietterich, except that during training, the predicted outputs y i,t−1 are used as the inputs at time t. Networks similar to this were first introduced by Jordan BIB003 . Part (b) shows a network in which the hidden unit activations at time t − 1 are fed as additional inputs at time t. This allows the network to develop a representation for the recurrent information that is separate from the representation of the output y values. This architecture was introduced by Elman BIB002 . These networks are usually trained iteratively via a procedure known as backpropagation-through-time (BPTT) in which the network structure is "unrolled" for the length of the input and output sequences x i and y i BIB001 . Recurrent networks have been applied to a variety of sequence-learning problems  .