Related papers: Instantons in self-organizing logic gates
Deficiency in expressive power of the first-order logic has led to developing its numerous extensions by fixed point operators, such as Least Fixed-Point (LFP), inflationary fixed-point (IFP), partial fixed-point (PFP), etc. These logics…
Self-attention mechanisms have made striking state-of-the-art (SOTA) progress in various sequence learning tasks, standing on the multi-headed dot product attention by attending to all the global contexts at different locations. Through a…
LLMs often exhibit Aha moments such as self-correction after tokens like "Wait," yet the underlying mechanism remains unclear. Standard LLMs collapse mainly through silent divergence, where trajectories drift from the correct answer yet…
In this work, we introduce Contextual Analog Logic with Multimodality (CALM). CALM unites symbolic reasoning with neural generation, enabling systems to make context-sensitive decisions grounded in real-world multi-modal data. Background:…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
Spiking neural networks (SNNs) promise energy-efficient artificial intelligence on neuromorphic hardware but struggle with tasks requiring both fast adaptation and long-term memory, especially in continual learning. We propose Local…
In quantum logic operations, information is carried by the wavefunction rather than the energy distribution. Therefore, the relative phase is essential. Abelian and non-Abelian phases can be emulated in classical waves using passive coupled…
Today, almost all information processing is performed using electronic logic circuits operating with up to several gigahertz frequency. All-optical logic, however, that holds the promise to allow up to three orders of magnitude higher speed…
According to the positive energy conjecture of Horowitz and Myers, there is a specific supergravity solution, AdS soliton, which has minimum energy among all asymptotically locally AdS solutions with the same boundary conditions. Related to…
We develop a computation model for solving Boolean networks that implements wires through quantum ground-state computation and implements gates through identities following from angular momentum algebra and statistics. The gates are static…
Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With…
Instantons, localised saddle points of the action, play an important role in describing non-perturbative aspects of quantum field theories, for example vacuum decay or violation of conservation laws associated with anomalous symmetries.…
Instanton processes are present in a variety of quantum field theories relevant to high energy as well as condensed matter physics. While they have led to important theoretical insights and physical applications, their underlying features…
New computing technologies are being sought near the end of CMOS transistor scaling, meanwhile superconducting digital, i.e., single-flux quantum (SFQ), logic allows incredibly efficient gates which are relevant to the impending transition.…
While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving…
We present an introduction to the use of noncommutative geometry for gauge theories with emphasis on a construction of instantons for a class of four dimensional toric noncommutative manifolds. These instantons are solutions of self-duality…
In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the…
This article provides an explicit construction for a family of singular instantons on S^4 S^2 with arbitrary real holonomy parameter \alpha. This family includes the original \alpha = 1/4, c_2 = 3/2 solution discovered by P. Forgacs, Z.…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating…