Related papers: Solomonoff induction
Conformal predictions make it possible to define reliable and robust learning algorithms. But they are essentially a method for evaluating whether an algorithm is good enough to be used in practice. To define a reliable learning framework…
Generalization is a central challenge for the deployment of reinforcement learning (RL) systems in the real world. In this paper, we show that the sequential structure of the RL problem necessitates new approaches to generalization beyond…
The Solecki dichotomy in descriptive set theory and the Posner-Robinson theorem in computability theory bear a superficial resemblance to each other and can sometimes be used to prove the same results, but do not have any obvious direct…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
Kobayashi introduced a uniform notion of compressibility of infinite binary sequences in terms of relative Turing computations with sub-identity use of the oracle. Kobayashi compressibility has remained a relatively obscure notion, with the…
In this paper we introduce a new method which employs the concept of "Orientation Vectors" to train a feed forward neural network and suitable for problems where large dimensions are involved and the clusters are characteristically sparse.…
The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym…
We introduce a universal approach for applying the partition rank method, an extension of Tao's slice rank polynomial method, to tensors that are not diagonal. This is accomplished by generalizing Naslund's distinctness indicator to what we…
Compositional generalization is a fundamental trait in humans, allowing us to effortlessly combine known phrases to form novel sentences. Recent works have claimed that standard seq-to-seq models severely lack the ability to compositionally…
We present arguments for the formulation of unified approach to different standard continuous inference methods from partial information. It is claimed that an explicit partition of information into a priori (prior knowledge) and a…
This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems,…
Evaluating theories in physics used to be easy. Our theories provided very distinct predictions. Experimental accuracy was so small that worrying about epistemological problems was not necessary. That is no longer the case. The…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
In most real-world reinforcement learning applications, state information is only partially observable, which breaks the Markov decision process assumption and leads to inferior performance for algorithms that conflate observations with…
Interpretation of cosmological data to determine the number and values of parameters describing the universe must not rely solely on statistics but involve physical insight. When statistical techniques such as "model selection" or…
Black box models in machine learning have demonstrated excellent predictive performance in complex problems and high-dimensional settings. However, their lack of transparency and interpretability restrict the applicability of such models in…
We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. [2016]. We study the problem of learning such a non-discriminatory…
One of the central elements of any causal inference is an object called structural causal model (SCM), which represents a collection of mechanisms and exogenous sources of random variation of the system under investigation (Pearl, 2000). An…
One of the fundamental results in computability is the existence of well-defined functions that cannot be computed. In this paper we study the effects of data representation on computability; we show that, while for each possible way of…