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In programming by example, users "write" programs by generating a small number of input-output examples and asking the computer to synthesize consistent programs. We consider a challenging problem in this domain: learning regular…
Humans demonstrate a variety of interesting behavioral characteristics when performing tasks, such as selecting between seemingly equivalent optimal actions, performing recovery actions when deviating from the optimal trajectory, or…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…
Classical Bayesian persuasion assumes that senders fully understand how receivers form beliefs and make decisions--an assumption that rarely holds when receivers possess private information or exhibit non-Bayesian behavior. In this paper,…
Decision tree induction systems are being used for knowledge acquisition in noisy domains. This paper develops a subjective Bayesian interpretation of the task tackled by these systems and the heuristic methods they use. It is argued that…
Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…
We address the problem of inferring descriptions of system behavior using Linear Temporal Logic (LTL) from a finite set of positive and negative examples. Most of the existing approaches for solving such a task rely on predefined templates…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to…
A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of…
We present a Bayesian approach to machine learning with probabilistic programs. In our approach, training on available data is implemented as inference on a hierarchical model. The posterior distribution of model parameters is then used to…
We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access.…
Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…
Utilizing the hyperspace of noise-based logic, we show two string verification methods with low communication complexity. One of them is based on continuum noise-based logic. The other one utilizes noise-based logic with random telegraph…
Reinforcement learning methods can achieve significant performance but require a large amount of training data collected on the same robotic platform. A policy trained with expensive data is rendered useless after making even a minor change…
The Moore-Lewis method of "intelligent selection of language model training data" is very effective, cheap, efficient... and also has structural problems. (1) The method defines relevance by playing language models trained on the in-domain…
This paper examines some methods and ideas underlying the author's successful probabilistic learning systems(PLS), which have proven uniquely effective and efficient in generalization learning or induction. While the emerging principles are…
A network of agents attempt to learn some unknown state of the world drawn by nature from a finite set. Agents observe private signals conditioned on the true state, and form beliefs about the unknown state accordingly. Each agent may face…
We introduce a simple time-triggered protocol to achieve communication-efficient non-Bayesian learning over a network. Specifically, we consider a scenario where a group of agents interact over a graph with the aim of discerning the true…