Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChemical Boltzmann Machines
291
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
How smart can a micron-sized bag of chemicals be? How can an artificial or real cell make inferences about its environment? From which kinds of probability distributions can chemical reaction networks sample? We begin tackling these questions by showing four ways in which a stochastic chemical reaction network can implement a Boltzmann machine, a stochastic neural network model that can generate a wide range of probability distributions and compute conditional probabilities. The resulting models, and the associated theorems, provide a road map for constructing chemical reaction networks that exploit their native stochasticity as a computational resource. Finally, to show the potential of our models, we simulate a chemical Boltzmann machine to classify and generate MNIST digits in-silico.
rate research
Read More
Restricted Boltzmann Machines (RBMs) are a class of generative neural network that are typically trained to maximize a log-likelihood objective function. We argue that likelihood-based training strategies may fail because the objective does not sufficiently penalize models that place a high probability in regions where the training data distribution has low probability. To overcome this problem, we introduce Boltzmann Encoded Adversarial Machines (BEAMs). A BEAM is an RBM trained against an adversary that uses the hidden layer activations of the RBM to discriminate between the training data and the probability distribution generated by the model. We present experiments demonstrating that BEAMs outperform RBMs and GANs on multiple benchmarks.
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance-sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially distributed. Here we focus on mathematical models based on deterministic mass-action kinetics. These models are systems of coupled nonlinear differential equations on the positive orthant. We explain how mathematical properties of the solutions of mass-action systems are strongly related to key properties of the networks of chemical reactions that generate them, such as specif
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Boltzmann machines carry a rich structure, with connections to geometry, applied algebra, probability, statistics, machine learning, and other areas. The analysis of these models is attractive in its own right and also as a platform to combine and generalize mathematical tools for graphical models with hidden variables. This article gives an introduction to the mathematical analysis of restricted Boltzmann machines, reviews recent results on the geometry of the sets of probability distributions representable by these models, and suggests a few directions for further investigation.
The search for novel entangled phases of matter has lead to the recent discovery of a new class of ``entanglement transitions, exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free energy cost of inserting a domain wall. In this paper, we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural network-inspired variational Ansatze, we investigate under what conditions on the variational parameters these Ansatze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite size effects in finite size numerical simulations. Introducing phases with correlations decaying as $1/r^alpha$ in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent $alpha$. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
