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Neural algorithmic reasoning aims to capture computations with neural networks by training models to imitate the execution of classical algorithms. While common architectures are expressive enough to contain the correct model in the weight…
Understanding how the time-complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived…
This paper explores the interplay between statistics and generative artificial intelligence. Generative statistics, an integral part of the latter, aims to construct models that can generate efficiently and meaningfully new data across the…
A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable…
Artificial bee colony (ABC) algorithm has proved its importance in solving a number of problems including engineering optimization problems. ABC algorithm is one of the most popular and youngest member of the family of population based…
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is…
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
While there are many works on the applications of machine learning, not so many of them are trying to understand the theoretical justifications to explain their efficiency. In this work, overfitting control (or generalization property) in…
In this paper, we derive a new model of synaptic plasticity, based on recent algorithms for reinforcement learning (in which an agent attempts to learn appropriate actions to maximize its long-term average reward). We show that these direct…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
Recently, the use of bio-inspired learning techniques such as Hebbian learning and its closely-related Spike-Timing-Dependent Plasticity (STDP) variant have drawn significant attention for the design of compute-efficient AI systems that can…
The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a…
Characterising the intelligence of biological organisms is challenging. This work considers intelligent algorithms developed evolutionarily within neural systems. Mathematical analyses unveil a natural equivalence between canonical neural…
We propose a linear-time, single-pass, top-down algorithm for multiple testing on directed acyclic graphs (DAGs), where nodes represent hypotheses and edges specify a partial ordering in which hypotheses must be tested. The procedure is…
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactification; it also gives a representation of the limit in…
Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…
Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…
Functions of chemical composition are complex and discrete in nature making it impossible to optimize them with gradient methods. Genetic algorithms, which do not use derivative information, are used to maximize the thermal conductivity of…
This paper is concerned with the modeling and analysis of two of the most commonly used recurrent neural network models (i.e., Hopfield neural network and firing-rate neural network) with dynamic recurrent connections undergoing Hebbian…