Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
Better neural arithmetic logic units improve cell counting model generalization.
problem Neural networks struggle with high cell counts outside training data range.
method Introduced Neural Arithmetic Logic Units (NALU) for arithmetic operations in existing architectures.
result Improved cell counting accuracy for higher numeric ranges with better generalization.
Stock prediction is a topic undergoing intense study for many years. Finance experts and mathematicians have been working on a way to predict the future stock price so as to decide to buy the stock or sell it to make profit. Stock experts or economists, usually analyze on the previous stock values using technical indic…
Boolean logic used for neural network training and inference, with convergence analysis.
problem Discrete optimization in neural networks with Boolean logic.
method Boolean logic backpropagation with convergence analysis.
result First convergence analysis for Boolean logic in neural networks.
Neural Power Unit (NPU) learns arbitrary power functions on real numbers.
problem Neural Networks struggle with generalizing beyond seen data and arithmetic operations.
method Introduces Neural Power Unit (NPU) that operates on real numbers and learns arbitrary power functions.
result NPU outperforms competitors in accuracy and sparsity on arithmetic datasets and discovers governing equations from data.
A new deep learning method using Boolean logic reduces training and inference energy.
problem High computational and energy costs in deep learning training and inference.
method Introduces Boolean weights and inputs for efficient training using Boolean logic.
result Achieves full-precision accuracy in ImageNet classification and surpasses state-of-the-art results in semantic segmentation.
Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian classifiers, DNN suffer from bad interpretability where we understand by interpr…
Deep neural networks have achieved impressive supervised classification performance in many tasks including image recognition, speech recognition, and sequence to sequence learning. However, this success has not been translated to applications like question answering that may involve complex arithmetic and logic reason…
ENN neural network learns logical syllogisms using Euler diagrams.
problem Traditional neural networks struggle with logical reasoning, especially syllogisms.
method ENN represents logical relations as Euler diagrams, optimizing syllogism structures with a novel back-propagation algorithm.
result ENN can precisely represent and reason with all 24 syllogism structures.
Geodesics on modular surface yield arithmetic 3-manifolds.
problem Understanding arithmetic properties of modular surfaces.
method Constructing geodesics and analyzing their lifts.
result Complements of canonical lifts are arithmetic 3-manifolds.
Quantum Signal Processing reduces derivative pricing quantum resource requirements.
problem Efficiently pricing financial derivatives on quantum computers.
method Quantum Signal Processing (QSP) to encode payoffs directly into quantum amplitudes.
result Significantly reduces quantum resources (T-gates and qubits) for practical derivative contracts.
Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually preserves information from the natural language side in the form of similar token…
Recent years have witnessed the great success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the ability of logical reasoning. However, the concrete ability of logical reas…
Study C-Fuchsian subgroups of non-arithmetic lattices.
problem Understand structure and fundamental domains of C-Fuchsian subgroups. method General procedure to analyze structure and show fundamental domains lie on a complex geodesic.
result Fundamental domains of C-Fuchsian subgroups lie on a complex geodesic homeomorphic to the unit disk. Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
problem Lack of cognitive reasoning in deep neural networks limits their ability to solve complex prediction tasks.
method Proposes Logic-Integrated Neural Network (LINN) that learns logical operations and conducts propositional logical reasoning.
result LINN significantly outperforms state-of-the-art recommendation models in Top-K recommendation.
NSR enables neural networks to reason with continuous numbers and extrapolate.
problem Quantitative reasoning and extrapolation in neural networks.
method Proposes Neural Status Register (NSR) for continuous number reasoning.
result NSR achieves extrapolation to numbers many orders of magnitude larger than training data.
We propose the Neural Logic Machine (NLM), a neural-symbolic architecture for both inductive learning and logic reasoning. NLMs exploit the power of both neural networks---as function approximators, and logic programming---as a symbolic processor for objects with properties, relations, logic connectives, and quantifier…
While neural networks are good at learning unspecified functions from training samples, they cannot be directly implemented in hardware and are often not interpretable or formally verifiable. On the other hand, logic circuits are implementable, verifiable, and interpretable but are not able to learn from training data …
MC-LSTM extends LSTM to conserve mass in neural networks.
problem Conservation laws in real-world systems.
method Extending LSTM's inductive bias to conserve mass.
result MC-LSTM sets new state-of-the-art for predicting peak flows.
We introduce neural Markov logic networks (NMLNs), a statistical relational learning system that borrows ideas from Markov logic. Like Markov logic networks (MLNs), NMLNs are an exponential-family model for modelling distributions over possible worlds, but unlike MLNs, they do not rely on explicitly specified first-ord…
Combining deep neural networks with structured logic rules is desirable to harness flexibility and reduce uninterpretability of the neural models. We propose a general framework capable of enhancing various types of neural networks (e.g., CNNs and RNNs) with declarative first-order logic rules. Specifically, we develop…
Transformers learn to predict temporal logic solutions from classical solver outputs.
problem Training neural networks on logic problem solutions for verification.
method Training a Transformer on generated training data from classical solvers, focusing on one solution per formula.
result Transformers can predict correct solutions to temporal logic problems, even to unseen benchmarks.
Survey of Weber's class number problem and related topics.
problem Weber's class number problem and its variants.
method Arithmetic topology, units, generalized Pell's equation, p-adic limits of class numbers. result Numerical investigation of class numbers in p-adic towers for knots and elliptic curves. Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.
problem Understanding how logical neural networks extrapolate solutions to mazes.
method Examined recurrent and implicit neural networks trained on maze-solving tasks.
result Models fail to generalize well to diverse maze sizes, suggesting limitations in learning scalable algorithms.
Tensor logic aims to unify AI types with scalable and transparent features.
problem Lack of a unified AI programming language with scalability and transparency.
method Introduces tensor logic, a new AI language based on tensor equations.
result Tensor logic enables key AI forms like transformers, formal reasoning, and graphical models.
Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise to another dimension for network optimization, and in this paper, we study the o…
Study logical generalization in GNNs using a new benchmark.
problem Understanding how GNNs adapt to new logical tasks.
method Developed GraphLog benchmark suite for logical tasks, evaluated GNNs in supervised, pretraining, and continual learning settings.
result Logical diversity during training affects GNNs' ability to generalize.
The paper explores how different network architectures learn logical functions under GOTU, finding that a min-degree-interpolator is learned.
problem Learning logical functions with a focus on generalization on the unseen.
method Study of different network architectures trained by SGD under GOTU.
result For sparse functions and certain network models, a min-degree-interpolator is learned on the unseen.
Method integrates logical rules into neural multi-hop reasoning for drug repurposing.
problem Capturing long-range dependencies in biomedical data.
method Combines logical rules with neural multi-hop reasoning using reinforcement learning.
result Our method outperforms baseline methods in drug repurposing tasks.
This paper shows neural networks can solve complex graph problems efficiently.
problem Solving exact maximum flow computation and minimum spanning tree problems.
method Introduces Max-Affine Arithmetic Programs and shows equivalence to neural networks.
result Two combinatorial optimization problems can be solved with polynomial-size neural networks.
It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a mystery of GNN-based solvers for more complex predicate logic formulae. In this work,…
Effectively combining logic reasoning and probabilistic inference has been a long-standing goal of machine learning: the former has the ability to generalize with small training data, while the latter provides a principled framework for dealing with noisy data. However, existing methods for combining the best of both w…
We revisit fuzzy neural network with a cornerstone notion of generalized hamming distance, which provides a novel and theoretically justified framework to re-interpret many useful neural network techniques in terms of fuzzy logic. In particular, we conjecture and empirically illustrate that, the celebrated batch normal…
Enhances neural networks with logical knowledge for better performance.
problem Improving neural network performance with logical knowledge.
method Integrating logical knowledge into neural networks through a new final layer with learnable clause weights.
result KENN outperforms other methods in collective classification tasks with relational data.
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent knowledge graph embedding methods. A principled logic rule-based approach is th…
Unified tensor network formalism for combining neural and symbolic AI.
problem Combining neural and symbolic AI approaches remains a challenge.
method Introduces a tensor network formalism capturing sparsity principles.
result Unified treatment identifies tensor network contractions as a fundamental inference class.
Dual neural network architecture improves accuracy and interpretability.
problem Improving neural network interpretability and accuracy.
method Stacked recurrent and feedforward layers, binary activation function.
result Binary activation leads to simpler, more interpretable models with higher accuracy.
AI in finance uses quantum logic for better decision-making.
problem Improving financial decision-making models using AI.
method Application of quantum logic in machine learning techniques.
result Advantages of quantum-inspired neural networks in finance.
The paper explores how neural networks learn logical functions and their generalization error.
problem Learning logical functions with neural networks and understanding generalization error.
method Gradient descent on neural networks, analyzing noise-stability and Boolean influence.
result Gradient descent on certain neural architectures tends to favor low-degree representations, impacting generalization error.
Refines neural network predictions using background knowledge for improved accuracy.
problem Compensate for lack of labeled data in neural networks.
method Introduces differentiable refinement functions and Iterative Local Refinement (ILR) algorithm to refine predictions efficiently and accurately.
result ILR finds competitive results in MNIST addition task and refines predictions on complex SAT formulas.
Transformer struggles with arithmetic length but improves with explicit structure encoding.
problem Transformers fail to generalize length in arithmetic tasks.
method Explicitly encoding structural symmetries via modified number formatting and custom positional encodings.
result Transformer can generalize up to 50-digit numbers without additional data.
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of performance and energy efficiency. In the first part of this paper, the behaviour of …
Paper investigates differentiable fuzzy implications and their suitability for learning.
problem Analyzing differentiable fuzzy implications and their suitability for learning.
method Investigates the properties of fuzzy implications in a differentiable setting and introduces a new family of fuzzy implications.
result Various fuzzy implications are unsuitable for differentiable learning, and a new family of fuzzy implications is introduced.
New bounds on diameters and generators for specific lattices and graphs.
problem Finding bounds on diameters and generators for arithmetic lattices and Ramanujan graphs.
method Analyzing arithmetic lattices from Eichler orders in quaternion algebras, applying techniques to definite quaternion algebras.
result Bounds on diameters and generators for arithmetic lattices and Ramanujan graphs.
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal analysis and sparse learning proble…
Transformer models improve arithmetic accuracy with number decomposition.
problem Transformer models struggle with arithmetic operations without decomposition.
method Fine-tuning models with a pipeline that decomposes numbers into units, tens, etc.
result Accuracy increased by 63% in five-digit addition tasks.
We propose a method for efficient training of Q-functions for continuous-state Markov Decision Processes (MDPs) such that the traces of the resulting policies satisfy a given Linear Temporal Logic (LTL) property. LTL, a modal logic, can express a wide range of time-dependent logical properties (including "safety") that…
Combines neural networks and STL for multi-class time-series classification.
problem Lack of interpretability in neural networks for time-series data.
method Proposes a method that uses neural networks to classify time-series data using STL specifications, introducing margin for multi-class classification and STL-based attributes for interpretability.
result Evaluations show improved interpretability and performance compared to state-of-the-art baselines.