A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Kernel for STL formulae enables machine learning in temporal logic.
Many software analysis methods have come to rely on machine learning approaches. Code segmentation - the process of decomposing source code into meaningful blocks - can augment these methods by featurizing code, reducing noise, and limiting the problem space. Traditionally, code segmentation has been done using syntact…
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 …
The paper explores how neural networks learn logical functions and their generalization error.
Refines neural network predictions using background knowledge for improved accuracy.
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…
Using reinforcement learning to learn control policies is a challenge when the task is complex with potentially long horizons. Ensuring adequate but safe exploration is also crucial for controlling physical systems. In this paper, we use temporal logic to facilitate specification and learning of complex tasks. We combi…
The paper explores how different network architectures learn logical functions under GOTU, finding that a min-degree-interpolator is learned.
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…
AlphaLogics mines market logic to generate interpretable alpha factors.
Unified tensor network formalism for combining neural and symbolic AI.
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives in logic programming, which is now increasingly seen to provide a declarative bac…
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…
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
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…
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. …
Boolean logic used for neural network training and inference, with convergence analysis.
It is notoriously difficult to control the behavior of reinforcement learning agents. Agents often learn to exploit the environment or reward signal and need to be retrained multiple times. The multi-objective reinforcement learning (MORL) framework separates a reward function into several objectives. An ideal MORL age…
Paper investigates differentiable fuzzy implications and their suitability for learning.
Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
Combining logic and probability has been a long stand- ing goal of AI research. Markov Logic Networks (MLNs) achieve this by attaching weights to formulas in first-order logic, and can be seen as templates for constructing features for ground Markov networks. Most techniques for learning weights of MLNs are domain-size…
Unified framework for hierarchical image classification with epistemic uncertainty.
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams, knot-logical diagrams and an arrow of reference that elucidates self-reference and G…
This study proposes a logic architecture for the high-speed and power efficiently training of a gradient boosting decision tree model of binary classification. We implemented the proposed logic architecture on an FPGA and compared training time and power efficiency with three general GBDT software libraries using CPU a…
Our interest in this paper is in the construction of symbolic explanations for predictions made by a deep neural network. We will focus attention on deep relational machines (DRMs, first proposed by H. Lodhi). A DRM is a deep network in which the input layer consists of Boolean-valued functions (features) that are defi…
Transformers learn to predict temporal logic solutions from classical solver outputs.
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…
Study logical generalization in GNNs using a new benchmark.
The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co~event. The theory of experience and chance is the theory of c…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learn…
We describe the concept of logical scaffolds, which can be used to improve the quality of software that relies on AI components. We explain how some of the existing ideas on runtime monitors for perception systems can be seen as a specific instance of logical scaffolds. Furthermore, we describe how logical scaffolds ma…
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…
Responds to comments on Bayesian Logic Regression algorithm, provides extensions and tutorial.
Tensor logic aims to unify AI types with scalable and transparent features.
PolyLUT uses polynomials to reduce FPGA latency.
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…
Logical neural networks solve mazes by filling dead ends, but not all methods generalize well.
New method uses logical relations to derive bounds and inequality constraints from causal models.
In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space R^n with n >= 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot…
Intermediate logic of all convex polyhedra is axiomatized.
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,…
This paper introduces a new reward shaping method for average-reward reinforcement learning.
ENN neural network learns logical syllogisms using Euler diagrams.
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…
Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple un…
This paper presents a stochastic logic time delay reservoir design. The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design. A novel re-seeding method is introduced to reduce the adverse effects of…
Paper uses subjective logic to estimate uncertainty in multi-armed bandit problems.