Maxpolynomial Division with Application To Neural Network Simplification

Smyrnis, Georgios; Maragos, Petros; Retsinas, George

doi:10.1109/icassp40776.2020.9053540

Cited by 8 publications

(11 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The source query is transferred at first, and then the query annotated in the why-provenance is executed. Since the why-provenance and executing queries over polynomials contain all other semirings, which have homomorphisms with polynomial semantics, the processes aim at utilizing the polynomials semiring as a universal memory [50]. The algebraic framework of provenance semiring tables is displayed in Fig.…”

Section: Provenance Semiring and Semiring Homomorphismmentioning

confidence: 99%

Annolog: A Query Processing Framework for Modelling and Reasoning with Annotated Data

Zou¹,

Zou²,

Wang³

2023

Journal of Computers

View full text Add to dashboard Cite

<p>Data annotation is the categorization and labelling of data for applications, such as machine learning, artificial intelligence, and data integration. The categorization and labelling are done to achieve a specific use case in relation to solving problems. Existing data annotation systems and modules face imperfections such as knowledge and annotation not being formally integrated, narrow application range, and difficulty to apply on existing database management applications. To analyze and process annotated data, obtain the relationship between different annotations, and capture metainformation in data provenance and probabilistic databases, in this paper, we design a back-end query processing framework as a supplementary interface for the database management system to extend operation to datasets and boost efficiency. The framework utilizes Java language and the MVC model for development to achieve lightweight, cross-platform, and high adaptability identities. The contribution of this paper is mainly reflected in two aspects. The first contribution is to implement query processing, provenance semiring, and semiring homomorphism over annotated data. The second contribution is to combine query processing and provenance with SQL statements in order to enable the database manager to invoke operations to annotation.</p> <p> </p>

show abstract

Section: Provenance Semiring and Semiring Homomorphismmentioning

confidence: 99%

Annolog: A Query Processing Framework for Modelling and Reasoning with Annotated Data

Zou¹,

Zou²,

Wang³

2023

Journal of Computers

View full text Add to dashboard Cite

show abstract

“…1) Given a fixed ReLU network, we can attempt to construct a smaller neural network whose Newton polytopes closely approximate the polytopes of the original network. The resulting algorithm is constructive and relies on the concept of tropical polynomial division [100], which approximates the dividend using the Newton polytopes of the divisor and quotient. Since this method constructs a network from scratch, it can be much faster than pruning methods in practice.…”

Section: ) Tropical Polynomial Division and Network Simplificationmentioning

confidence: 99%

“…Suppose that we wish to fit a general max-tropical plane p (x, y) = max (a x, b y, c) (100) to the given data (xi, yi, zi) ∈ R 3 , i = 1, . .…”

Section: B Generalized Tropical Regressionmentioning

confidence: 99%

Tropical Geometry and Machine Learning

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recently, the field of tropical geometry has been associated with this class of morphological networks [5,6,7,8,9,10]. Tropical geometry studies piecewise linear (PWL) surfaces whose arithmetic is governed by a tropical semiring, where ordinary addition is replaced by the maximum or minimum and ordinary multiplication is replaced by ordinary addition.…”

Section: Introductionmentioning

confidence: 99%

Advances in Morphological Neural Networks: Training, Pruning and Enforcing Shape Constraints

Dimitriadis

Maragos

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

View full text Add to dashboard Cite

In this paper, we study an emerging class of neural networks, the Morphological Neural networks, from some modern perspectives. Our approach utilizes ideas from tropical geometry and mathematical morphology. First, we state the training of a binary morphological classifier as a Difference-of-Convex optimization problem and extend this method to multiclass tasks. We then focus on general morphological networks trained with gradient descent variants and show, quantitatively via pruning schemes as well as qualitatively, the sparsity of the resulted representations compared to FeedForward networks with ReLU activations as well as the effect the training optimizer has on such compression techniques. Finally, we show how morphological networks can be employed to guarantee monotonicity and present a softened version of a known architecture, based on Maslov Dequantization, which alleviates issues of gradient propagation associated with its "hard" counterparts and moderately improves performance.

show abstract

Maxpolynomial Division with Application To Neural Network Simplification

Cited by 8 publications

References 15 publications

Annolog: A Query Processing Framework for Modelling and Reasoning with Annotated Data

Annolog: A Query Processing Framework for Modelling and Reasoning with Annotated Data

Tropical Geometry and Machine Learning

Advances in Morphological Neural Networks: Training, Pruning and Enforcing Shape Constraints

Contact Info

Product

Resources

About