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A highly accurate but overconfident model is ill-suited for deployment in critical applications such as healthcare and autonomous driving. The classification outcome should reflect a high uncertainty on ambiguous in-distribution samples…
We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to the deformed Leibniz rule…
Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from…
We prove sharp spectral transition in the arithmetics of phase between localization and singular continuous spectrum for Diophantine almost Mathieu operators. We also determine exact exponential asymptotics of eigenfunctions and of…
Self-supervised learning is a powerful paradigm for representation learning on unlabelled images. A wealth of effective new methods based on instance matching rely on data-augmentation to drive learning, and these have reached a rough…
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras.…
Supersymmetry breaking by the quantum deformation of a classical moduli space is considered. A simple, non-chiral, renormalizable model is presented to illustrate this mechanism. The well known, chiral, $SU(3) \times SU(2)$ model and its…
Intrinsic self-correction in Large Language Models (LLMs) frequently fails in open-ended reasoning tasks due to ``hallucination snowballing,'' a phenomenon in which models recursively justify early errors during free-text reflection. While…
Artificial organisms are computer programs that self-replicate, mutate, compete and evolve. How do these lifelike information-processing behaviours could arise in diverse far-from-equilibrium physical systems remains an open question. Here,…
We propose a model for demonstrating spontaneous emergence of collective intelligent behavior from selfish individual agents. Agents' behavior is modeled using our proposed selfish algorithm ($SA$) with three learning mechanisms: reinforced…
Training Transformers on algorithmic tasks frequently demonstrates an intriguing abrupt learning phenomenon: an extended performance plateau followed by a sudden, sharp improvement. This work investigates the underlying mechanisms for such…
Self-Supervised Learning (SSL) methods harness the concept of semantic invariance by utilizing data augmentation strategies to produce similar representations for different deformations of the same input. Essentially, the model captures the…
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane.…
We introduce a set of image transformations that can be used as corruptions to evaluate the robustness of models as well as data augmentation mechanisms for training neural networks. The primary distinction of the proposed transformations…
The need for transparency of predictive systems based on Machine Learning algorithms arises as a consequence of their ever-increasing proliferation in the industry. Whenever black-box algorithmic predictions influence human affairs, the…
A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can…
Many leading self-supervised methods for unsupervised representation learning, in particular those for embedding image features, are built on variants of the instance discrimination task, whose optimization is known to be prone to…