Abstract: A forward pass through a sequence of strokes representing a handwritten equation is performed from the first stroke to the last stroke in the sequence. At each stroke, a path score is determined for a plurality of symbol-relation pairs that each represents a symbol and its spatial relation to a predecessor symbol. A symbol graph having nodes and links is constructed by backtracking through the strokes from the last stroke to the first stroke and assigning scores to the links based on the path scores for the symbol-relation pairs. The symbol graph is used to recognize a mathematical expression based in part on the scores for the links and the mathematical expression is stored.

Abstract: Possible segmentations for an audio signal are scored based on distortions for feature vectors of the audio signal and the total number of segments in the segmentation. The scores are used to select a segmentation and the selected segmentation is used to identify a starting point and an ending point for a speech signal in the audio signal.

Abstract: A multi-state pattern recognition model with non-uniform kernel allocation is formed by setting a number of states for a multi-state pattern recognition model and assigning different numbers of kernels to different states. The kernels are then trained using training data to form the multi-state pattern recognition model.

Abstract: A method of speech recognition is provided that determines a production-related value, vocal-tract resonance frequencies in particular, for a state at a particular frame based on the production-related values associated with two preceding frames using a recursion. The production-related value is used to determine a probability distribution of the observed feature vector for the state. A probability for an observed value received for the frame is then determined from the probability distribution. Under one embodiment, the production-related value is determined using a noise-free recursive definition for the value. Use of the recursion substantially improves the decoding speed. When the decoding algorithm is applied to training data with known phonetic transcripts, forced alignment is created which improves the phone segmentation obtained from the prior art.

Abstract: A method of providing discriminative training of a speech recognition unit is discussed. The method includes receiving an acoustic indication of an utterance having a hypothesis space and comparing the hypothesis space against a reference. The method measures the Kullback-Leibler Divergence (KLD) between the reference and the hypothesis space to adjust the reference and stores the adjusted reference on a tangible storage medium.

Abstract: A method of speech recognition is provided that identifies a production-related dynamics value by performing a linear interpolation between a production-related dynamics value at a previous time and a production-related target using a time-dependent interpolation weight. The hidden production-related dynamics value is used to compute a predicted value that is compared to an observed value of acoustics to determine the likelihood of the observed acoustics given a sequence of hidden phonological units. In some embodiments, the production-related dynamics value at the previous time is selected from a set of continuous values. In addition, the likelihood of the observed acoustics given a sequence of hidden phonological units is combined with a score associated with a discrete class of production-related dynamic values at the previous time to determine a score for a current phonological state.

Abstract: A speech signal is decoded by determining a production-related value for a current state based on an optimal production-related value at the end of a preceding state, the optimal production-related value being selected from a set of continuous values. The production-related value is used to determine a likelihood of a phone being represented by a set of observation vectors that are aligned with a path between the preceding state and the current state. The likelihood of the phone is combined with a score from the preceding state to determine a score for the current state, the score from the preceding state being associated with a discrete class of production-related values wherein the class matches the class of the optimal production-related value.

Abstract: A method of speech recognition is provided that determines a production-related value, vocal-tract resonance frequencies in particular, for a state at a particular frame based on the production-related values associated with two preceding frames using a recursion. The production-related value is used to determine a probability distribution of the observed feature vector for the state. A probability for an observed value received for the frame is then determined from the probability distribution. Under one embodiment, the production-related value is determined using a noise-free recursive definition for the value. Use of the recursion substantially improves the decoding speed. When the decoding algorithm is applied to training data with known phonetic transcripts, forced alignment is created which improves the phone segmentation obtained from the prior art.

Abstract: A method of speech recognition is provided that identifies a production-related dynamics value by performing a linear interpolation between a production-related dynamics value at a previous time and a production-related target using a time-dependent interpolation weight. The hidden production-related dynamics value is used to compute a predicted value that is compared to an observed value of acoustics to determine the likelihood of the observed acoustics given a sequence of hidden phonological units. In some embodiments, the production-related dynamics value at the previous time is selected from a set of continuous values. In addition, the likelihood of the observed acoustics given a sequence of hidden phonological units is combined with a score associated with a discrete class of production-related dynamic values at the previous time to determine a score for a current phonological state.