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Logical Neural Networks
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We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, yielding resilience to inconsistent knowledge. It also enables the open-world assumption by maintaining bounds on truth values which can have probabilistic semantics, yielding resilience to incomplete knowledge.
Forward citations
Cited by 5 Pith papers
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Training, Reading, and Editing Legible Transformers
A variance-floor objective plus learned operator gates produce an end-to-end legible transformer whose crisp units are 50–184× more local to edit and can be reshaped from fan-out to fan-in circuits without quality loss.
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Enabling topography-resolving structural dynamic contact simulation
A multi-scale FE–BEM method is extended to dynamic time integration and Harmonic Balance, enabling topography-resolved contact simulation of bolted joints and load-history-dependent equilibria on the S4 Beam.
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A Comparative Study of Neurosymbolic AI Approaches to Interpretable Logical Reasoning
A comparison of two neurosymbolic designs concludes that the hybrid design, pairing an LLM with a separate symbolic solver, is the more promising path to general logical reasoning.
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Learning Interpretable Differentiable Logic Networks for Tabular Regression
A weighted sum over binary logic-rule activations lets Differentiable Logic Networks perform tabular regression with accuracy close to random forests at much lower inference cost.
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Standard Neural Computation Alone Is Insufficient for Logical Intelligence
The paper claims that standard arithmetic-based neural layers are insufficient for logical intelligence and proposes differentiable Logical Neural Units, supported only by a 20-sample toy experiment.
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