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.
Tensor logic aims to unify AI types with scalable and transparent features.
Unified tensor network formalism for combining neural and symbolic AI.
RWTNs improve NTN performance in SRL tasks.
We introduce the -simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive …
In category theory, logic and geometry cooperate with each other producing what is known under the name Synthetic Differential Geometry (SDG). The main difference between SDG and standard differential geometry is that the intuitionistic logic of SDG enforces the existence of infinitesimal objects which essentially modi…
GETF efficiently decomposes large-scale Boolean tensors.
In this paper, we study the problem of learning probabilistic logical rules for inductive and interpretable link prediction. Despite the importance of inductive link prediction, most previous works focused on transductive link prediction and cannot manage previously unseen entities. Moreover, they are black-box models …
Semantic Image Interpretation is the task of extracting a structured semantic description from images. This requires the detection of visual relationships: triples (subject,relation,object) describing a semantic relation between a subject and an object. A pure supervised approach to visual relationship detection requir…
AlphaLogics mines market logic to generate interpretable alpha factors.
Human ability at solving complex tasks is helped by priors on object and event semantics of their environment. This paper investigates the use of similar prior knowledge for transfer learning in Reinforcement Learning agents. In particular, the paper proposes to use a first-order-logic language grounded in deep neural …
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…
This paper generalizes graph representation for diverse data types.
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…
Boolean logic used for neural network training and inference, with convergence analysis.
Neural Logic Reasoning integrates deep learning and symbolic logic for better prediction tasks.
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…
Kernel for STL formulae enables machine learning in temporal logic.
Bayesian Tensor Network combines prior and data likelihood for efficient prediction and parameter estimation.
Transformers learn to predict temporal logic solutions from classical solver outputs.
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…
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 …
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…
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…
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.
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.
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…
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,…
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…
Enhances labels from unlabeled data using sample correlations.
Paper uses subjective logic to estimate uncertainty in multi-armed bandit problems.
The study examines causal razors and their logical relations, highlighting a dilemma in causal discovery.
RDLI integrates domain logic and context grounding to detect crypto anomalies under scarce labels.
AI in finance uses quantum logic for better decision-making.
Zipper logic is a graph rewrite system, consisting in only local rewrites on a class of zipper graphs. Connections with the chemlambda artificial chemistry and with knot diagrammatics based computation are explored in the article.
BOiLS optimizes circuit quality using Bayesian optimization.