The DLR Hierarchy of Approximate Inference

We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized neighbors (FN) algorithms and variants of mean field (MF) algorithms. In particular, we show that extrema of the Bethe free energy correspond to approximate solutions of the DLR equations. In addition, we demonstrate a close connection between these approximate algorithms and Gibbs sampling. Finally, we compare and contrast various of the algorithms in the DLR hierarchy on spin-glass problems. The experiments show that algorithms higher up in the hierarchy give more accurate results when they converge but tend to be less stable.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Cryptography based on neural networks - analytical results

Mutual learning process between two parity feed-forward networks with discrete and continuous weights is studied analytically, and we find that the number of steps required to achieve full synchronization between the two networks in the case of discrete weights is finite. The synchronization process is shown to be non-self-averaging and the analytical solution is based on random auxiliary variables. The learning time of an attacker that is trying to imitate one of the networks is examined analytically and is found to be much longer than the synchronization time. Analytical results are found to be in agreement with simulations

Mutual learning in a tree parity machine and its application to cryptography

Mutual learning of a pair of tree parity machines with continuous and discrete weight vectors is studied analytically. The analysis is based on a mapping procedure that maps the mutual learning in tree parity machines onto mutual learning in noisy perceptrons. The stationary solution of the mutual learning in the case of continuous tree parity machines depends on the learning rate where a phase transition from partial to full synchronization is observed. In the discrete case the learning process is based on a finite increment and a full synchronized state is achieved in a finite number of steps. The synchronization of discrete parity machines is introduced in order to construct an ephemeral key-exchange protocol. The dynamic learning of a third tree parity machine (an attacker) that tries to imitate one of the two machines while the two still update their weight vectors is also analyzed. In particular, the synchronization times of the naive attacker and the flipping attacker recently introduced in [1] are analyzed. All analytical results are found to be in good agreement with simulation results

Training a perceptron in a discrete weight space

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous perceptron and prediction following the clipped weights. The learning is described by a new set of order parameters, composed of the overlaps between the teacher and the continuous/clipped students. Different scenarios are examined among them on-line learning with discrete/continuous transfer functions and off-line Hebb learning. The generalization error of the clipped weights decays asymptotically as $exp(-K \alpha^2)$/$exp(-e^{|\lambda| \alpha})$ in the case of on-line learning with binary/continuous activation functions, respectively, where $\alpha$ is the number of examples divided by N, the size of the input vector and $K$ is a positive constant that decays linearly with 1/L. For finite $N$ and $L$, a perfect agreement between the discrete student and the teacher is obtained for $\alpha \propto \sqrt{L \ln(NL)}$. A crossover to the generalization error $\propto 1/\alpha$, characterized continuous weights with binary output, is obtained for synaptic depth $L > O(\sqrt{N})$.Comment: 10 pages, 5 figs., submitted to PR

Multilayer neural networks with extensively many hidden units

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter the storage capacity if found to scale with the logarithm of the number of implementable Boolean functions. The generalization behaviour is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.Comment: 4 pages, 2 figure

Antiviral TRIMs: friend or foe in autoimmune and autoinflammatory disease?

The concept that viral sensing systems, via their ability to drive pro-inflammatory cytokine and interferon production, contribute to the development of autoimmune and autoinflammatory disease is supported by a wide range of clinical and experimental observations. Recently, the tripartite motif-containing proteins (TRIMs) have emerged as having key roles in antiviral immunity — either as viral restriction factors or as regulators of pathways downstream of viral RNA and DNA sensors, and the inflammasome. Given their involvement in these pathways, we propose that TRIM proteins contribute to the development and pathology of autoimmune and autoinflammatory conditions, thus making them potential novel targets for therapeutic manipulation

The DLR Hierarchy of Approximate Inference

We propose a hierarchy for approximate inference based on the Dobrushin, Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms, such as belief propagation, and also motivates novel algorithms such as factorized neighbors (FN) algorithms and variants of mean field (MF) algorithms. In particular, we show that extrema of the Bethe free energy correspond to approximate solutions of the DLR equations. In addition, we demonstrate a close connection between these approximate algorithms and Gibbs sampling. Finally, we compare and contrast various of the algorithms in the DLR hierarchy on spin-glass problems. The experiments show that algorithms higher up in the hierarchy give more accurate results when they converge but tend to be less stable