Year: 2023
Type: preprint
Abstract: It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: Comunidad de Madrid, Centres de Recerca de Catalunya, Institut de Ciències Fotòniques, National Centres of Competence in Research SwissMAP, European Commission, Generalitat de Catalunya, Universidad Complutense de Madrid, Narodowym Centrum Nauki, Ministerio de Ciencia e Innovación, Barcelona Supercomputing Center, QuantERA, Ministerio de Educación y Formación Profesional, European Climate, Infrastructure and Environment Executive Agency, HORIZON EUROPE Framework Programme, Agència de Gestió d'Ajuts Universitaris i de Recerca, European Regional Development Fund, Agencia Estatal de Investigación
Awards: G1042674429, G1175115578, G1188902550, G120905174, G121809054, G1272927172, G1325701057, G1484669290, NExt level Quantum information processing for Science and Technology, G1607002692, G1622782223, G1650125035, G1701110065, Junior Leader la Caixa Postdoctoral Fellowship Programme: Shaping the new generation of leaders in research, G1855990336, G1888088267, G1908469581, G1953887145, G1972043705, Programmable Atomic Large-scale Quantum Simulation 2 - SGA1, G2064873908, G2074861924, G210041235, G2105798022, G2236380367, G2262748287, G2290189609, G2309174360, G2325688492, G2355262757, G2374945988, G2425719011, G2575991346, G2601397997, G2660406951, G2674018141, G2719595533, G2744780120, G2763573136, G279363373, G2871827553, G288263039, G2967504892, G2988934680, G3005324705, G300979063, G3020228430, G3261693824, G3302599245, G34346518, G3480869486, G348919436, G357246561, G363809202, G3639969887, G3674674691, G3681454997, G3690828678, G3798495387, G379951279, G3886156397, G391183672, G3917310960, G3939077204, G396237826, G4042783231, G408490004, G410571670, G4233400527, G4239348134, G425668148, G430777504, G434337789, G4359800586, G4391008399, G4493332189, G451917667, G4630312626, G4680432388, G4727238542, G480488906, G4886082077, G488842982, G490073602, G4920849106, G4962956970, G5065677113, G5080475149, G5195188938, G531036588, G5421974903, G5539308778, G5805502524, G5845768719, G5852091828, G5967599077, G5971291011, G6275411036, Structured electric-dipole-based chirality, G6327674822, G6366812625, G6482940084, G6656126374, G6731467812, G6743926034, G69051668, G704744937, G7048927246, G7084143925, G712370837, G7226647862, G7327758667, G7425137858, G7521977119, G773280237, G7861065020, G8118709007, G8180681537, G8283979283, G8370579132, G853839195, G8546142835, G8637226926, Optical Topologic Logic, G8665153912, G8684520763, G8959349008, G897484643, G929308097, G99296377
OpenAlex ID: W4387929093