A Boolean complete neural model of adaptive behavior

A multi-layered neural assembly is developed which has the capability of learning arbitrary Boolean functions. Though the model neuron is more powerful than those previously considered, assemblies of neurons are needed to detect non-linearly separable patterns. Algorithms for learning at the neuron and assembly level are described. The model permits multiple output systens to share a common memory. Learned evaluation allows sequences of actions to be organized. Computer simulations demonstrate the capabilities of the model

Synthetic associative learning in engineered multicellular consortia

Associative learning is one of the key mechanisms displayed by living organisms in order to adapt to their changing environments. It was early recognized to be a general trait of complex multicellular organisms but also found in "simpler" ones. It has also been explored within synthetic biology using molecular circuits that are directly inspired in neural network models of conditioning. These designs involve complex wiring diagrams to be implemented within one single cell and the presence of diverse molecular wires become a challenge that might be very difficult to overcome. Here we present three alternative circuit designs based on two-cell microbial consortia able to properly display associative learning responses to two classes of stimuli and displaying long and short-term memory (i. e. the association can be lost with time). These designs might be a helpful approach for engineering the human gut microbiome or even synthetic organoids, defining a new class of decision-making biological circuits capable of memory and adaptation to changing conditions. The potential implications and extensions are outlined.Comment: 5 figure

Submodular relaxation for inference in Markov random fields

In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approach (SMR) based on a Lagrangian relaxation of the initial problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR does not decompose the graph structure of the initial problem but constructs a submodular energy that is minimized within the Lagrangian relaxation. Our approach is applicable to both pairwise and high-order MRFs and allows to take into account global potentials of certain types. We study theoretical properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on Pattern Analysis and Machine Intelligenc

On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain

Learning and adaptation in physical agents

Learning and adaptation is fundamental for autonomous agents that operate in a physical world and not a computer network. The paper is providing a general framework of skills learning within behaviour logic framework of agents that communicate, sense and act in the physical world. It is advocated that playfulness can be important in learning and to improving skills of agents

Neural Networks retrieving Boolean patterns in a sea of Gaussian ones

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for associative memory. In this equivalence, weights in the former play as patterns in the latter. As Boltzmann machines usually require real weights to be trained with gradient descent like methods, while Hopfield networks typically store binary patterns to be able to retrieve, the investigation of a mixed Hebbian network, equipped with both real (e.g., Gaussian) and discrete (e.g., Boolean) patterns naturally arises. We prove that, in the challenging regime of a high storage of real patterns, where retrieval is forbidden, an extra load of Boolean patterns can still be retrieved, as long as the ratio among the overall load and the network size does not exceed a critical threshold, that turns out to be the same of the standard Amit-Gutfreund-Sompolinsky theory. Assuming replica symmetry, we study the case of a low load of Boolean patterns combining the stochastic stability and Hamilton-Jacobi interpolating techniques. The result can be extended to the high load by a non rigorous but standard replica computation argument.Comment: 16 pages, 1 figur

Verification of integer multipliers on the arithmetic bit level

One of the most severe short-comings of currently available equivalence checkers is their inability to verify integer multipliers. In this paper, we present a bit level reverse-engineering technique that can be integrated into standard equivalence checking flows. We propose a Boolean mapping algorithm that extracts a network of half adders from the gate netlist of an addition circuit. Once the arithmetic bit level representation of the circuit is obtained, equivalence checking can be performed using simple arithmetic operations. Experimental results show the promise of our approach