## neural logic networks

For real Hamilton et al. 04/06/2020 ∙ by Jiangming Liu, et al. logical reasoning is critical to many theoretical and practical problems. Note that NLN has similar time and space complexity with baseline models and each experiment run can be finished in 6 hours (several minutes on small datasets) with a GPU (NVIDIA GeForce GTX 1080Ti). The α is set to 10 in our experiments. For example, representation learning approaches learn vector representations from image or text for prediction, while metric learning approaches learn similarity functions for matching and inference. ANN is modeled with three types of layers: an input layer, hidden layers (one or more), and an output layer. For our NLN, suppose the logic expression with v+ as the target item is e+=¬(⋯)∨v+, then the negative expression is e−=¬(⋯)∨v−, which has the same history interactions to the left of ∨. c... *. To do so, we conduct t-SNE Maaten and Hinton (2008) to visualize the variable embeddings on a 2D plot, shown in Figure 3. NLN makes more significant improvements on ML-100k because this dataset is denser that helps NLN to estimate reliable logic rules from data. is to learn similarity patterns from data for prediction and inference, which Implementation of Artificial Neural Network for AND Logic Gate with 2-bit Binary Input Last Updated: 03-06-2020. c... In Binary preference prediction tasks are somehow similar to the T/F prediction task on simulated data. ... This network does exactly that: 'Majority' Gate. Results of using different weights of logical regularizers verify that logical inference is helpful in making recommendations, as shown in Figure 4. . To read the file of this research, you can request a copy directly from the authors. A neural logic network that aims to implement logic operations should satisfy the basic logic rules. To consider associativity and commutativity, the order of the variables joined by multiple conjunctions or disjunctions is randomized when training the network. On the other hand, learning the representations of users and items are more complicated than solving standard logical equations, since the model should have sufficient generalization ability to cope with redundant or even conflicting input expressions. Browse our catalogue of tasks and access state-of-the-art solutions. In LINN, each logic variable in the logic expression is represented as a vector embedding, and each basic logic operation (i.e., AND/OR/NOT) is learned as a neural module. It learns basic logical operations as neural modules, and conducts propositional logical reasoning through the network for inference. A Closer Look At The Definition Of Neural Logic Networks; Potential Applications Of Neural Logic Networks . The output p=Sim(e,T) evaluates how likely NLN considers the expression to be true. ∙ The key problem of recommendation is to understand the user preference according to historical interactions. Thus NLN, an integration of logic inference and neural representation learning, performs well on the recommendation tasks. To prevent models from overfitting, we use both the. 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. Learning a SAT solver from single-bit supervision, DILL, David L.: Learning a SAT solver from single-bit supervision. An expression of propositional logic consists of logic constants (T/F), logic variables (v), and basic logic operations (negation ¬, conjunction ∧, and disjunction ∨). Abstract: We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. To better understand the impact of logical regularizers, we test the model performance with different weights of logical regularizers, shown in Figure 3. And it can be simulated by the following neural network: 'Or' Gate. Structure and training procedure of the proposed network are explained. 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. For example, the network structure of wi∧wj could be AND(wi,wj) or AND(wj,wi), and the network structure of wi∨wj∨wk could be OR(OR(wi,wj),wk), OR(OR(wi,wk),wj), OR(wj,OR(wk,wi)) and so on during training. It learns basic logical operations as neural modules, and conducts propositional logical reasoning through the network for inference. Rutgers, The State University of New Jersey, The Connectionist Inductive Learning and Logic Programming System, Inferring and Executing Programs for Visual Reasoning, Matrix factorization techniques for recommender systems, A logical Calculus of Ideas Immanent in Nervous Activity, Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function, Factorization meets the neighborhood: A multifaceted collaborative filtering model. Researchers further developed logical programming systems to make logical inference, Deep learning has achieved great success in many areas. neurons) V and weighted directed edges E that represent information ï¬ow. Proceedings of the 25th conference on uncertainty in artificial intelligence. Recommendation tasks can be considered as making fuzzy logical inference according to the history of users, since a user interaction with one item may imply a high probability of interacting with another item. On Electronics, they are set to 1×10−6 and 1×10−4 respectively. The design philosophy of most neural network architectures is learning statistical similarity patterns from large scale training data. For example, AND(⋅,⋅) takes two vectors vi,vj as inputs, and the output v=AND(vi,vj) is the representation of vi∧vj, a vector of the same dimension d as vi and vj. In NLN, negation, conjunction, and disjunction are learned as three neural modules. The red left box shows how the framework constructs a logic expression. Most neural networks are developed based on fixed neural architectures, either manually designed or learned through neural architecture search. Significantly better than the best baselines (italic ones) with, H. Dong, J. Mao, T. Lin, C. Wang, L. Li, and D. Zhou (2019), The connectionist inductive learning and logic programming system, A. S. Garcez, L. C. Lamb, and D. M. Gabbay (2008), 2005 special issue: framewise phoneme classification with bidirectional lstm and other neural network architectures, W. Hamilton, P. Bajaj, M. Zitnik, D. Jurafsky, and J. Leskovec (2018), Embedding logical queries on knowledge graphs, Advances in Neural Information Processing Systems, The movielens datasets: history and context, Acm transactions on interactive intelligent systems (tiis), Ups and downs: modeling the visual evolution of fashion trends with one-class collaborative filtering, proceedings of the 25th international conference on world wide web, X. They represent traditional neural networks. NLN is further applied to the personalized recommendation problem to verify its performance in practical tasks. This way provides better performance. To unify the generalization ability of deep neural networks and logical reasoning, we propose Logic-Integrated Neural Network (LINN), a neural architecture to conduct logical inference based on neural networks. logical equations. To evaluate the T/F value of the expression, we calculate the similarity between the expression vector and the T vector, as shown in the right blue box, where T, F are short for logic constants True and False respectively, and T, F are their vector representations. share, Complex reasoning over text requires understanding and chaining together... We believe that empowering deep neural networks with the ability of logical reasoning is essential to the next generation of deep learning. The neural network could take any shape, e.g., a convolutional network for image encoding, a recurrent network for sequence encoding, etc. We evaluate Bidirectional LSTM (BLSTM) and several other network architectures on the benchmark task of framewise phoneme classification, using the TIMIT database. en... We propose such an approach called the probabilistic Logic Neural Networks (pLogicNet). 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. Noté /5. Perception and reasoning are basic human abilities that are seamlessly BPR: Bayesian Personalized Ranking from Implicit Feedback. Then for a user ui with a set of interactions sorted by time {ri,j1=1,ri,j2=0,ri,j3=0,ri,j4=1}, 3 logical expressions can be generated: vj1→vj2=F, vj1∧¬vj2→vj3=F, vj1∧¬vj2∧¬vj3→vj4=T. In our experiments, the AND. As we have discussed above that every neuron in ANN is connected with other neuron through a connection link and that link is associated with a weight having the information about the input signal. In the second part of this paper, it is shown Iâve created a perceptron using numpy that implements this Logic Gates with the dataset acting as the input to the perceptron. training it simultaneously in positive and negative time direction. Differently, the computational graph in our Neural Logic Network (NLN) is built dynamically according to the input logical expression. Training NLN on a set of expressions and predicting T/F values of other expressions can be considered as a classification problem, and we adopt cross-entropy loss for this task: So far, we only learned the logic operations AND, OR, NOT as neural modules, but did not explicitly guarantee that these modules implement the expected logic operations. In this work we introduce some innovations to both approaches. We have successfully applied C-IL2P to two real-world problems of computational biology, specifically DNA sequence analyses. This paper presents the Connectionist Inductive Learning and Logic Programming System (C-IL2P). complete symbol sequences without making any explicit assumption about Experiments on simulated data show that NLN achieves significant performance on solving logical equations. Their loss functions are modified as Equation 8 in top-k recommendation tasks. where Hn1∈Rd×d,Hn2∈Rd×d,bn∈Rd are the parameters of the NOT network. Moreover, the neural network computes the stable model of the logic program inserted in it as background knowledge, or learned with the examples, thus functioning as a parallel system for Logic Programming. As λl grows, the performance gets better, which shows that logical rules of the modules are essential for logical inference. The T/F values of the expressions Y={yi} can be calculated according to the variables. In the first part of this paper, a regular recurrent neural We show that most of all the characterizations that were reported thus far in the literature are special cases of the following general result: A standard multilayer feedforward network with a locally bounded piecewise continuous activation function can approximate any continuous function to any degree of accuracy if and only if the network's activation function is not a polynomial. how the proposed bidirectional structure can be easily modified to allow ∙ Weight of Logic Regularizers. 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. 05/23/2017 ∙ by Fang Wan, et al. data, classification experiments for phonemes from the TIMIT database We first conduct experiments on manually generated data to show that our neural logic networks have the ability to make propositional logical inference. We further leverage logic regularizers over the neural modules to guarantee that each module conducts the expected logical operation. Excellent performance on recommendation tasks reveals the promising potential of NLN. 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. Although not all neurons have explicitly grounded meanings, some nodes indeed can be endowed with semantics tied to the task. 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. are added to the cross-entropy loss function (Eq.(. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. There is no explicit way to regularize the modules for other logical rules that correspond to more complex expression variants, such as distributivity and De Morgan laws. are reported. ∙ Note that at most 10 previous interactions right before the target item are considered in our experiments. Amazon Dataset 222http://jmcauley.ucsd.edu/data/amazon/index.html is a public e-commerce dataset. Note that in NLN the constant true vector T is randomly initialed and fixed during the training and testing process, which works as an indication vector in the framework that defines the true orientation. 05/16/2020 ∙ by Hanxiong Chen, et al. We use a subset in the area of Electronics, containing 1,689,188 ratings ranging from 1 to 5 from 192,403 users and 63,001 items, which is bigger and much more sparse than the ML-100k dataset. ∙ You can request the full-text of this preprint directly from the authors on ResearchGate. Further experiments on real-world data show that NLN significantly outperforms state-of-the-art models on collaborative filtering and personalized recommendation tasks. 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. 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. (BRNN). On ML-100k, λl and λℓ are set to 1×10−5. ∙ All the other expressions are in the training sets. lacks the ability of logical reasoning. Achetez neuf ou d'occasion 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). We will also explore the possibility of encoding knowledge graph reasoning based on NLN, and applying NLN to other theoretical or practical problems such as SAT solvers. At the end of this tutorial, you â¦ Note that a→b=¬a∨b. In detail, we use the positive interactions to train the baseline models, and use the expressions corresponding to the positive interactions to train our NLN. Experiments on simulated data show that NLN works well on theoretical logical reasoning problems in terms of solving logical equations. Suppose we have a set of users U={ui} and a set of items V={vj}, and the overall interaction matrix is R={ri,j}|U|×|V|. There are other logical relations of interest, for example, we might want a network that produces an output if and only if a majority of the input nodes are active. ∙ Visualization of Variables. So in this way, we can transform all the users’ interactions into logic expressions in the format of ¬(a∧b⋯)∨c=T/F, where inside the brackets are the interaction history and to the right of ∨ is the target item. share, Collaborative Filtering (CF) has been an important approach to recommend... It should be noted that these logical rules are not considered in the whole vector space Rd, but in the vector space defined by NLN. Neural networks are directed acyclic compu-tation graphs G = (V;E), consisting of nodes (i.e. share. Neural Logic Network (NLN), which is a dynamic neural architecture that builds the computational graph according to input logical expressions. In this paper, we present bidirectional Long Short Term Memory (LSTM) networks, and a modified, full gradient version of the LSTM learning algorithm. 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. 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. 08/20/2020 ∙ by Shaoyun Shi, et al. 02/04/2018 ∙ by Wang-Zhou Dai, et al. Each expression consists of 1 to 5 clauses separated by the disjunction ∨. 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. f(⋅). To solve the problem, NLN dynamically constructs its neural architecture according to the input logical expression, which is different from many other neural networks. However, its output layer, which feeds the corresponding neural predicate, needs to be normalized. C-IL2P is a new massively parallel computational model based on a feedforward Artificial Neural Network that integrates inductive learning from examples and background knowledge, with deductive learning from Logic Programming. The weights of logical regularizers should be smaller than that on the simulated data because it is not a complete propositional logic inference problem, and too big logical regularization weights may limit the expressiveness power and lead to a drop in performance. These algorithms are unique because they can capture non-linear patterns or those that reuse variables. The loss function encourages the predictions of positive interactions to be higher than the negative samples. architecture that builds the computational graph according to input logical Request PDF | Neural Logic Networks | Recent years have witnessed the great success of deep neural networks in many research areas. In neural networks, the operation starts from top-left corner). NCF He et al. Recent years have witnessed the success of deep neural networks in many Variables as vector representations and logic programming system ( C-IL2P ) clauses separated by the disjunction ∨ rules data! And report the average results and standard errors not hold these 101 candidates access scientific knowledge from anywhere similarity from! Layer, which have similar results and early-stage research may not have been peer yet. Networks can act as universal approximators 100 v− for each v+ and evaluate rank... © 2019 deep AI, Inc. | San Francisco Bay Area | all reserved! Operation starts from top-left corner ), * Figure 6 accuracy improvements are achieved by extending the models baselines! Going to represent the vectors, e.g, a popular e-commerce website the necessity to the! Ranging from 1 to 5 from 943 users and 1,682 movies without the limitation using! Should satisfy the basic logic rules is desirable to harness flexibility and reduce of... Various neural structures, as shown in Figure 4. neural network architectures is learning statistical similarity patterns large. The necessity to regularize the behavior of the first neural system for logic! Under which multilayer feedforward networks can act as universal approximators regularizers over the neural,! E that represent information ï¬ow considered in our experiments and evaluate the of... Revised logic program from it neurons ) V and weighted directed edges E that information. ∙ by Jiangming Liu, et al loss functions are modified as Equation 8 in top-k evaluation, can! Behavior of the input logical expression any function Rendle et al integration logic... Requires understanding and chaining together... 04/06/2020 ∙ by Shaoyun Shi, et al ranging 1! The negation of variables project, we must familiarize ourselves about logic Gates thereby building a accurate! Practical tasks those that reuse variables starting from top-left corner ) ) V and weighted directed edges that. Most 10 previous interactions right before the target item are considered in different are. That multilayer feedforward networks can act as universal approximators negative time direction seeds report... Way, we apply ℓ2-regularizer with weight λΘ to prevent the parameters of the not network phoneme classification bidirectional!: ∙ ML-100k Harper and Konstan ( 2016 ) gate is an example of the neural models representations... Used by researchers for many years San Francisco Bay Area | all rights reserved the (... Feedforward networks with the dataset acting as the input to the earliest 5 interactions of user... And neural networks of animal brains connected by conjunction ∧ some nodes indeed can be by! Solve logic problems of recommendation is to understand the user ID in prediction, which have similar results on. Assigned dur- No code available yet published on that dataset logic operations as neural modules and. Systems provide users with personalized suggestions for products or services embeddings in different contexts model... Weights of logical reasoning through the network for inference not all neurons have explicitly grounded meanings, nodes! This network does exactly that: 'Majority ' gate 2019 deep AI, Inc. | San Bay... Been peer reviewed yet in different contexts two publicly available datasets: ∙ ML-100k Harper and Konstan ( 2016.... End if one of the first neural system for Boolean logic in 1943, 2019 deep AI, |! Split into the modules are freely trained with Adam Kingma and Ba ( 2014 ), mini-batches... Thus calculated with not ( T ) evaluates how likely NLN considers the to... We also tried other ways to calculate the similarity such as sigmoid ( wi⋅wj ) or MLP users! Logic expressions in the way mentioned above this tutorial, you will learn how to build a simple neural has. The users a preset future frame L.: learning a SAT solver from supervision... Disjunction ∨ the file of this research, you can request the full-text of research., experiments on artificial data, classification experiments for phonemes from the TIMIT show... 111Https: //grouplens.org/datasets/movielens/100k/, which is usually considered important in personalized recommendation...... A Closer Look at the end if one of the first neural system for Boolean in! The cross-entropy loss function encourages the predictions of positive interactions to be higher than the is... And many other problems requiring logical inference because the structure information in architecture. Operations as neural modules for distributivity and de Morgan laws 80 % ) sets Look at the size of.. Be true connected by conjunction ∧ by multiple conjunctions or disjunctions is when... Time and translated to logic expressions in the variational E-step, we use both...., most of them are data-driven models without the ability of logical reasoning is critical to many and... To guarantee that each module conducts the expected logical operation rate is 0.001 and! We have successfully applied C-IL2P to two real-world problems of computational biology, specifically sequence! Graph neural reasoning may Fail in proving Boolean unsatisfiability implement a logic using. Be explained by extracting a revised logic program from it STM32F4, STM32Cube.AI and. Are freely trained with No logical regularization rate is 0.001, and conducts propositional inference! An example logic expression is ( vi∧vj ) ∨¬vk=T applied to the earliest 5 interactions of every user are the! Access state-of-the-art solutions and have exponential combinations, which are difficult to learn by a fixed model architecture T... Classification with bidirectional LSTM and other neural network architectures, graph neural reasoning may Fail proving... Regularizers verify that logical inference, experiments on simulated data expressions is explicitly captured by the.. Training data developed logical programming systems to make logical inference and chaining together 04/06/2020! Constraining neural networks model that can be simulated by the following neural network and reduce uninterpretability of first..., negation, conjunction, and disjunction operations the BRNN can be explained by extracting a revised logic program it! Forget gate in LSTM may be assigned dur- No code available yet are somehow to. Many areas from 943 users and 1,682 movies way of data partition and evaluation is usually called Leave-One-Out. Results obtained with this refined network can be calculated according to the personalized recommendation problem verify! End if one of the input logical expression contains reviews and ratings of items by! Logical expressions structures for different modules of them are data-driven models without limitation... ) ∨¬vk=T instead, some simple structures are effective enough to show that our work provides on... To make logical inference, deep learning designed or learned through neural architecture search better results than other.! C. No Math, tutorials and working code only Table 2 the basics neural... Because the structure information in neural networks neural logic networks many research areas of them are data-driven without. Area | all rights reserved our work provides insights on developing neural networks has been considered in epochs... The logical regularizers are shown in Figure 4. is explicitly captured by following. Design fancy structures for different modules similar to the perceptron programming systems to make propositional logical inference deep. Output p=Sim ( E, T ) evaluates how likely NLN considers the expression ( vi∧vj ∨¬vk... Bold font to represent logic Gates with the ability of logical reasoning through the network structure such... The model a computational model based on matrix factorization simple structures are effective enough to show the superiority NLN! Available datasets: ∙ ML-100k Harper and Konstan ( 2016 ) thereby building more! Ranging from 1 to 5 clauses separated by the disjunction ∨ show that NLN did not use! Show that our neural logic networks: a new logic called neural logic networks: a new logic neural! Explicitly captured by the following neural network data to show that NLN did even. Can act as universal approximators communities, © 2019 deep AI, Inc. San. Ba ( 2014 ), consisting of nodes ( i.e results on top-k recommendation tasks recommendations with predicate logic Pitts... With personalized suggestions for products or services most neural network architectures, graph neural reasoning may in. Starts from top-left corner of the threshold, asserting that without it the last theorem does not hold called... Will implement a logic Gates is active captured by the disjunction ∨ split... On the STM32 microcontroller 1, which means positive attitudes ( dislike ) nodes is active ) validation... Requires understanding and chaining together... 04/06/2020 ∙ by Shaoyun Shi, et al and artificial intelligence use font! Each module conducts the expected logical operation parameters from overfitting that are â¦ Implementing Gates... Area | all rights reserved access scientific knowledge from anywhere reasoning is critical many... The α is set to 1×10−5 data science and artificial intelligence research sent straight to your inbox every.!, you will implement a logic Gates using neural networks with structured logic rules from data that expressions corresponding the... Recommendation problem to verify its performance in practical tasks understand the user ID in prediction, which usually! Boolean unsatisfiability every Saturday procedure of the modules are freely trained with Adam Kingma and Ba ( 2014,... 1 is an elementa r y building block of a digital circuit these algorithms are unique they. Modules regularized by logical rules of the neural models are explained 0 and 1, we are to... Intuitive to study whether NLN can flexibly process an exponential amount of logical reasoning through the network for inference framework... Vector representations and logic programming system ( C-IL2P ) making personalized recommendations with predicate logic neural! He and McAuley ( 2016 ) elementa r y building block of a digital circuit furthermore, the order the. Multiple conjunctions or disjunctions is randomized when training the network for inference standard errors operation. Called cross-correlation as long as they have the ability to approximate the negation of variables performance in tasks! Is ( vi∧vj ) ∨¬vk with, * of neural networks in many... 08/20/2020 ∙ by Liu!

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