Although personalized recommendation is not a standard logical inference problem, logical inference still helps in this task, which is shown by the results – it is clear that on both the preference prediction and the top-k recommendation tasks, NLN achieves the best performance. 0 share, Complex reasoning over text requires understanding and chaining together... One is binary Preference Prediction and the other is Top-K Recommendation. The NLN on the preference prediction tasks is trained similarly as on the simulated data (Section 4), training on the known expressions and predicting the T/F values of the unseen expressions, with the cross-entropy loss. Further experiments on real-world data show that NLN on simulated data show that NLN achieves significant performance on solving No code available yet. However, the concrete ability of logical reasoning is critical to many theoretical and practical problems. vi is the vector representation of variable vi, and T is the vector representation of logic constant T, where the vector dimension is d. AND(⋅,⋅), OR(⋅,⋅), and NOT(⋅) are three neural modules. Note that at most 10 previous interactions right before the target item are considered in our experiments. However, the behaviors of the modules are freely trained with no logical regularization. We first randomly generate n variables V={vi}, each has a value of T or F. Then these variables are used to randomly generate m boolean expressions E={ei} in disjunctive normal form (DNF) as the dataset. 0 It learns basic logical operations as neural modules, and conducts propositional logical reasoning through the network for inference. Experiments are conducted on two publicly available datasets: ∙ ML-100k Harper and Konstan (2016). It is intuitive to study whether NLN can solve the T/F values of variables. Abstract: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. share, With computers to handle more and more complicated things in variable It learns basic logical operations as neural modules, and conducts propositional logical reasoning through the network for inference. We further apply NLN on personalized recommendation tasks effortlessly and achieved excellent performance, which reveals the prospect of NLN in terms of practical tasks. Significantly better than the other models (italic ones) with, *. Neural Markov Logic Networks Giuseppe Marra Department of Information Engineering University of Florence Florence, Italy Ondˇrej Kuželka Faculty of Electrical Engineering Czech Technical University in Prague Prague, Czech Republic Abstract We introduce Neural Markov Logic Networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. McCulloch and Pitts (1943) proposed one of the first neural system for boolean logic in 1943, . A neural network is a series of algorithms that work to recognize relationships and patterns in a way that is very similar to how the human brain operates. Experiments on simulated data show that NLN achieves significant performance on solving logical equations. module is implemented by multi-layer perceptron (MLP) with one hidden layer: where Ha1∈Rd×2d,Ha2∈Rd×d,ba∈Rd are the parameters of the AND network. Each intermediate vector represents part of the logic expression, and finally, we have the vector representation of the whole logic expression e=(vi∧vj)∨¬vk. Then the interactions are sorted by time and translated to logic expressions in the way mentioned above. In: arXiv preprint In this paper, we propose Neural Logic Network (NLN), which is a dynamic neural architecture that builds the computational graph according to input logical expressions. Note that a→b=¬a∨b. Artificial Neural Network (ANN) is a computational model based on the biological neural networks of animal brains. The "POPFNN" architecture is a five-layer neural network where the layers from 1 to 5 are called: input linguistic layer, condition layer, rule layer, consequent layer, output linguistic layer. Most neural networks are developed based on fixed neural architec- tures that are … Preprints and early-stage research may not have been peer reviewed yet. In top-k evaluation, we sample 100 v− for each v+ and evaluate the rank of v+ in these 101 candidates. (2017) is Neural Collaborative Filtering, which conducts collaborative filtering with a neural network, and it is one of the state-of-the-art neural recommendation models using only the user-item interaction matrix as input. We can see that the T and F variables are clearly separated, and the accuracy of T/F values according to the two clusters is 95.9%, which indicates high accuracy of solving variables based on NLN. 0 the shape of the distribution. In this way, the model is encouraged to output the same vector representation when inputs are different forms of the same expression in terms of associativity and commutativity. This way of data partition and evaluation is usually called the Leave-One-Out setting in personalized recommendation. The three modules can be implemented by various neural structures, as long as they have the ability to approximate the logical operations. Perception and reasoning are basic human abilities that are seamlessly Specifically, we develop an iterative distillation method that transfers the structured information of … and personalized recommendation tasks. Part 1 describes the general theory of neural logic networks and their potential applications. share, The human reasoning process is seldom a one-way process from an input le... To prevent models from overfitting, we use both the. ∙ Get the latest machine learning methods with code. The α is set to 10 in our experiments. In this way, we can avoid the necessity to regularize the neural modules for distributivity and De Morgan laws. ANN is modeled with three types of layers: an input layer, hidden layers (one or more), and an output layer. NLN adopts vectors to represent logic variables, and each basic logic operation (AND/OR/NOT) is learned as a neural module based on logic regularization. To solve the problem, NLN dynamically constructs its neural architecture according to the input logical expression, which is different from many other neural networks. Bi-RNN performs better than Bi-LSTM because the forget gate in LSTM may be harmful to model the variable sequence in expressions. In the variational E-step, we infer the plausibility of LINN adopts vectors to represent logic variables, and each basic logic operation (AND/OR/NOT) is learned as a neu- Relations, Tunneling Neural Perception and Logic Reasoning through Abductive Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. Retrouvez Neural Logic Networks: A New Class of Neural Networks et des millions de livres en stock sur Amazon.fr. Further experiments on real-world data show that NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks. However, if λl is too large it will result in a drop of performance, because the expressiveness power of the model may be significantly constrained by the logical regularizers. To read the file of this research, you can request a copy directly from the authors. A pLogicNet defines the joint distribution of all possible triplets by using a Markov logic network with first-order logic, which can be efficiently optimized with the … The principles of multi-layer feed-forward neural network, radial basis function network, self-organizing map, counter-propagation neural network, recurrent neural network, deep learning neural network will be explained with appropriate numerical examples. Furthermore, the visualization of variable embeddings in different epochs are shown in Figure 6. However, its output layer, which feeds the corresponding neural predicate, needs to be normalized. We also emphasize the important role of the threshold, asserting that without it the last theorem does not hold. For example, any variable or expression w conjuncted with false should result in false w∧F=F, and a double negation should result in itself ¬(¬w)=w. Then the loss function of NLN is: where p(e+) and p(e−) are the predictions of e+ and e−, respectively, and other parts are the logic, vector length and ℓ2 regularizers as mentioned in Section 2. But note that the T/F values of the variables are invisible to the model. how the proposed bidirectional structure can be easily modified to allow ∙ Visualization of Variables. BiasedMF Koren et al. The two more successful approaches to CF are latent factor models, which directly profile both users and products, and neighborhood models, which analyze similarities between products or users. By encoding logical structure information in neural architecture, NLN can flexibly process an exponential amount of logical expressions. In NLN, variables in the logic expressions are represented as vectors, and each basic logic operation is learned as a neural module during the training process. share. Here are some examples of the generated expressions when n=100: On simulated data, λl and λℓ are set to 1×10−2 and 1×10−4 respectively. We use bold font to represent the vectors, e.g. Our main findings are that bidirectional networks outperform unidirectional ones, and Long Short Term Memory (LSTM) is much faster and also more accurate than both standard Recurrent Neural Nets (RNNs) and time-windowed Multilayer Perceptrons (MLPs). expressions. propositional logical reasoning through the network for inference. Combination of logic rules and neural networks has been considered in different contexts. In NLN, negation, conjunction, and disjunction are learned as three neural modules. be trained in an efficient way. Let ri,j=1/0 if user ui likes/dislikes item vj. Starting with the background knowledge represented by a propositional logic program, a translation algorithm is applied generating a neural network that can be trained with examples. Vector sizes of the variables in simulation data and the user/item vectors in recommendation are 64. The loss function encourages the predictions of positive interactions to be higher than the negative samples. In this work, we proposed a Neural Logic Network (NLN) framework to make logical inference with deep neural networks. training it simultaneously in positive and negative time direction. embedded logical queries on knowledge graphs into vectors. (2009) is a traditional recommendation method based on matrix factorization. efficient estimation of the conditional posterior probability of Achetez neuf ou d'occasion This way provides better performance. As λl grows, the performance gets better, which shows that logical rules of the modules are essential for logical inference. We also conducted experiments on many other fixed or variational lengths of expressions, which have similar results. where ri are the logic regularizers in Table 1. The design philosophy of most neural network architectures is learning statistical similarity patterns from large scale training data. A neural logic network that aims to implement logic operations should satisfy the basic logic rules. Recent years have witnessed the great success of deep neural networks in many research areas. With the help of logic regularizers, the modules in NLN learn to perform expected logic operations, and finally, NLN achieves the best performance and significantly outperforms NLN-Rl. Comparisons with the results obtained by some of the main neural, symbolic, and hybrid inductive learning systems, using the same domain knowledge, show the effectiveness of C-IL2P. For the remaining data, the last two expressions of every user are distributed into the validation sets and test sets respectively (Test sets are preferred if there remains only one expression of the user). In The key problem of recommendation is to understand the user preference according to historical interactions. 05/16/2020 ∙ by Hanxiong Chen, et al. On Electronics, they are set to 1×10−6 and 1×10−4 respectively. Neural Logic Network (NLN), which is a dynamic neural architecture that builds the computational graph according to input logical expressions. ... SVD++ Koren (2008) is also based on matrix factorization but it considers the history implicit interactions of users when predicting, which is one of the best traditional recommendation models. ∙ f(⋅). It should be noted that except for the logical regularizers listed above, a propositional logical system should also satisfy other logical rules such as the associativity, commutativity and distributivity of AND/OR/NOT operations. We have successfully applied C-IL2P to two real-world problems of computational biology, specifically DNA sequence analyses. However, traditional symbolic reasoning methods for logical inference are mostly hard rule-based reasoning, which may require significant manual efforts in rule development, and may only have very limited generalization ability to unseen data. The equations of laws are translated into the modules and variables in our neural logic network as logical regularizers. To ensure that the output is formatted between 0 and 1, we scale the cosine similarity by multiplying a value. 0 08/20/2020 ∙ by Shaoyun Shi, et al. The methods are tested on the Netflix data. 31 Experiments on simulated data show that NLN works well on theoretical logical reasoning problems in terms of solving logical equations. Recently there are several works using deep neural networks to solve logic problems. is to learn similarity patterns from data for prediction and inference, which Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. ∙ Weight of Logical Regularizers. This paper presents the Connectionist Inductive Learning and Logic Programming System (C-IL2P). complete symbol sequences without making any explicit assumption about The poor performance of Bi-RNN and Bi-LSTM verifies that traditional neural networks that ignore the logical structure of expressions do not have the ability to conduct logical inference. Structure and training procedure of the proposed network are explained. Thus it is possible to leverage neural modules to approximate the negation, conjunction, and disjunction operations. The fuzzification of the inputs and the defuzzification of the outputs are respectively performed by the input linguistic and output linguistic layers while the fuzzy inference is collectively performed by the rule, condition and … In particular, we learn logic variables as vector representations and logic operations as neural modules regularized by logical rules. 10/17/2019 ∙ by Shaoyun Shi, et al. Part 2 discusses a new logic called Neural Logic which attempts to emulate more closely the logical thinking process of human. In the first part of this paper, a regular recurrent neural Fuzzy logic is largely used An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. We hope that our work provides insights on developing neural networks for logical inference. However, logical reasoning is an important ability of human intelligence, and it is critical to many theoretical problems such as solving logical equations, as well as practical tasks such as medical decision support systems, legal assistants, and collaborative reasoning in personalized recommender systems.