A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Compressing Recurrent Neural Network with Tensor Train

Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters and require many computational resources for training and predicting new data. This paper proposes an alternative RNN model to reduce the number of parameters significantly by representing the weight parameters based on Tensor Train (TT) format. In this paper, we implement the TT-format representation for several RNN architectures such as simple RNN and Gated Recurrent Unit (GRU). We compare and evaluate our proposed RNN model with uncompressed RNN model on sequence classification and sequence prediction tasks. Our proposed RNNs with TT-format are able to preserve the performance while reducing the number of RNN parameters significantly up to 40 times smaller.Comment: Accepted at IJCNN 201

New formats for computing with real-numbers under round-to-nearest

An edited version of this work was accepted in IEEE Transactions on computers, DOI 10.1109/TC.2015.2479623In this paper, a new family of formats to deal with real number for applications requiring round to nearest is proposed. They are based on shifting the set of exactly represented numbers which are used in conventional radix-R number systems. This technique allows performing radix complement and round to nearest without carry propagation with negligible time and hardware cost. Furthermore, the proposed formats have the same storage cost and precision as standard ones. Since conversion to conventional formats simply require appending one extra-digit to the operands, standard circuits may be used to perform arithmetic operations with operands under the new format. We also extend the features of the RN-representation system and carry out a thorough comparison between both representation systems. We conclude that the proposed representation system is generally more adequate to implement systems for computation with real number under round-to-nearest.Ministry of Education and Science of Spain under contracts TIN2013-42253-P

A grid-based ant colony algorithm for automatic 3D hose routing

Ant Colony Algorithms applied to difficult combinatorial optimization problems such as the traveling salesman problem (TSP) and the quadratic assignment problem. In this paper we propose a grid-based ant colony algorithm for automatic 3D hose routing. Algorithm uses the tessellated format of the obstacles and the generated hoses in order to detect collisions. The representation of obstacles and hoses in the tessellated format greatly helps the algorithm towards handling free-form objects and speed up the computations. The performance of the algorithm has been tested on a number of 3D models

Representation Synthesis by Probabilistic Many-Valued Logic Operation in Self-Supervised Learning

Self-supervised learning (SSL) using mixed images has been studied to learn various image representations. Existing methods using mixed images learn a representation by maximizing the similarity between the representation of the mixed image and the synthesized representation of the original images. However, few methods consider the synthesis of representations from the perspective of mathematical logic. In this study, we focused on a synthesis method of representations. We proposed a new SSL with mixed images and a new representation format based on many-valued logic. This format can indicate the feature-possession degree, that is, how much of each image feature is possessed by a representation. This representation format and representation synthesis by logic operation realize that the synthesized representation preserves the remarkable characteristics of the original representations. Our method performed competitively with previous representation synthesis methods for image classification tasks. We also examined the relationship between the feature-possession degree and the number of classes of images in the multilabel image classification dataset to verify that the intended learning was achieved. In addition, we discussed image retrieval, which is an application of our proposed representation format using many-valued logic.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

An Approach to Large Scale Radar-Based Modeling and Simulation

This research presents a method of aggregating, or reducing the resolution, of a commonly available Department of Defense (DoD) simulation. It addresses the differences between varying levels of resolution and scope used in the DoD’s hierarchy of models pyramid. A data representation that aggregates engagement-level simulation data to use at a lower resolution level, the mission-level, is presented and analyzed. Two formats of implementing this data representation are developed and compared: the rigid cylinder format and the expanding tables format. The rigid cylinder format provides an intuitive way to visualize the data and is used to develop the theory. The expanding tables format expands upon the capabilities of the rigid cylinder format and reduces the simulation time. Tests are run to show the effects of each format for various combinations of engagement-level simulation inputs. A final set of tests highlight the loss in accuracy incurred from reducing the number of samples used by the mission-level simulation. These tests culminate the work by deriving a notional scenario, applying the data cylinder representation, and exploring the realistic problem of comparing accuracy and computational constraints