Above are papers related to the following paper: [Paper_ID] Paper #72056. 	[Title] MBP on T0: mixing floating- and fixed-point formats in BP learning [Abstract] We examine the efficient implementation of back prop type algorithms on T0 [4], a vector processor with a fixed point engine, designed for neural network simulation. A matrix formulation of back prop, Matrix Back Prop [1], has been shown to be very efficient on some RISCs [2]. Using Matrix Back Prop, we achieve an asymptotically optimal performance on T0 (about 0.8 GOPS) for both forward and backward phases, which is not possible with the standard on-line method. Since high efficiency is futile if convergence is poor (due to the use of fixed point arithmetic), we use a mixture of fixed and floating point operations. The key observation is that the precision of fixed point is sufficient for good convergence, if the range is appropriately chosen. Though the most expensive computations are implemented in fixed point, we achieve a rate of convergence that is comparable to the floating point version. The time taken for conversion between fixed and floating point is also shown to be reasonable. Please summarise all the given information.

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Above are papers related to the following paper: [Paper_ID] Paper #1120777. 	[Title] Modelling the Manifolds of Images of Handwritten Digits [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #12330. 	[Title] Recognizing Handwritten Digits Using Mixtures of Linear Models [Abstract] We construct a mixture of locally linear generative models of a collection of pixel-based images of digits, and use them for recognition. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EM-based algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane information [12] about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #2702. 	[Title] In  Fast Non-Linear Dimension Reduction [Abstract] We present a fast algorithm for non-linear dimension reduction. The algorithm builds a local linear model of the data by merging PCA with clustering based on a new distortion measure. Experiments with speech and image data indicate that the local linear algorithm produces encodings with lower distortion than those built by five layer auto-associative networks. The local linear algorithm is also more than an order of magnitude faster to train. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1135122. 	[Title] Quicknet on MultiSpert: Fast Parallel Neural Network Training [Abstract] The MultiSpert parallel system is a straight-forward extension of the Spert workstation accelerator, which is predominantly used in speech recognition research at ICSI. In order to deliver high performance for Artificial Neural Network training without requiring changes to the user interfaces, the exisiting Quicknet ANN library was modified to run on MultiSpert. In this report, we present the algorithms used in the parallelization of the Quicknet code and analyse their communication and computation requirements. The resulting performance model yields a better understanding of system speed-ups and potential bottlenecks. Experimental results from actual training runs validate the model and demonstrate the achieved performance levels. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #733534. 	[Title] SPERT-II: A Vector Microprocessor System and its Application to Large Problems in Backpropagation Training [Abstract] We report on our development of a high-performance system for neural network and other signal processing applications. We have designed and implemented a vector microprocessor and packaged it as an attached processor for a conventional workstation. We present performance comparisons with commercial workstations on neural network backpropagation training. The SPERT-II system demonstrates significant speedups over extensively hand optimization code running on the workstations. Please summarise all the given information.

Paper #72056 has the title `MBP on T0: mixing floating- and fixed-point formats in BP learning  
` and the abstract `We examine the efficient implementation of back prop type algorithms on T0 [4], a vector processor with a fixed point engine, designed for neural network simulation. A matrix formulation of back prop, Matrix Back Prop [1], has been shown to be very efficient on some RISCs [2]. Using Matrix Back Prop, we achieve an asymptotically optimal performance on T0 (about 0.8 GOPS) for both forward and backward phases, which is not possible with the standard on-line method. Since high efficiency is futile if convergence is poor (due to the use of fixed point arithmetic), we use a mixture of fixed and floating point operations. The key observation is that the precision of fixed point is sufficient for good convergence, if the range is appropriately chosen. Though the most expensive computations are implemented in fixed point, we achieve a rate of convergence that is comparable to the floating point version. The time taken for conversion between fixed and floating point is also shown to be reasonable. 
`.
Question: Which category should Paper #72056 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #72056 has the title `MBP on T0: mixing floating- and fixed-point formats in BP learning  
` and the abstract `We examine the efficient implementation of back prop type algorithms on T0 [4], a vector processor with a fixed point engine, designed for neural network simulation. A matrix formulation of back prop, Matrix Back Prop [1], has been shown to be very efficient on some RISCs [2]. Using Matrix Back Prop, we achieve an asymptotically optimal performance on T0 (about 0.8 GOPS) for both forward and backward phases, which is not possible with the standard on-line method. Since high efficiency is futile if convergence is poor (due to the use of fixed point arithmetic), we use a mixture of fixed and floating point operations. The key observation is that the precision of fixed point is sufficient for good convergence, if the range is appropriately chosen. Though the most expensive computations are implemented in fixed point, we achieve a rate of convergence that is comparable to the floating point version. The time taken for conversion between fixed and floating point is also shown to be reasonable. 
`.
Question: Which category should Paper #72056 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks