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In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…
We have been striving to exceed computational complexity, and in the process, we have come to realize the dilemma of classical computing, and in turn we realize that superpositioner may be a way to solve. A superpositioner is a model formed…
Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show that the spectrum of $A$ decomposes,…
We present a principled and simplified design of the projector and loss function for non-contrastive self-supervised learning based on hyperdimensional computing. We theoretically demonstrate that this design introduces an inductive bias…
A fundamental feature of human intelligence is the ability to infer high-level abstractions from low-level sensory data. An essential component of such inference is the ability to discover modularized generative mechanisms. Despite many…
In human consciousness perceptions are distinct or atomistic events despite being perceived by an apparently undivided inner observer. This paper applies both classical (Boolean) and quantum logic to analysis of the Liar paradox which is…
Self-supervised learning aims to learn a embedding space where semantically similar samples are close. Contrastive learning methods pull views of samples together and push different samples away, which utilizes semantic invariance of…
Self-supervised representation learning often uses data augmentations to induce some invariance to "style" attributes of the data. However, with downstream tasks generally unknown at training time, it is difficult to deduce a priori which…
Successive self-training on a language model's own outputs is widely characterized as a process of flattening: diversity drops, distributions narrow, and the text becomes "more like itself." We provide evidence that this characterization is…
Large language models often produce unsupported claims. We frame this as a misclassification error at the output boundary, where internally generated completions are emitted as if they were grounded in evidence. This motivates a composite…
In this study, we examine the representation learning abilities of Denoising Diffusion Models (DDM) that were originally purposed for image generation. Our philosophy is to deconstruct a DDM, gradually transforming it into a classical…
Self-supervised contrastive learning has emerged as a powerful tool in machine learning and computer vision to learn meaningful representations from unlabeled data. Meanwhile, its empirical success has encouraged many theoretical studies to…
In recent years prominent intellectuals have raised ethical concerns about the consequences of artificial intelligence. One concern is that an autonomous agent might modify itself to become "superintelligent" and, in supremely effective…
Self-supervised representation learning has shown remarkable success in a number of domains. A common practice is to perform data augmentation via hand-crafted transformations intended to leave the semantics of the data invariant. We seek…
Personalizing diffusion models using limited data presents significant challenges, including overfitting, loss of prior knowledge, and degradation of text alignment. Overfitting leads to shifts in the noise prediction distribution,…
Presented is a novel methodology for determining representational structure, which builds upon the existing Spotlight Resonance method. This new tool is used to gain insight into how discrete representations can emerge and organise in…
Self-organization of complex morphological patterns from local interactions is a fascinating phenomenon in many natural and artificial systems. In the artificial world, typical examples of such morphogenetic systems are cellular automata.…
An important development in deep learning from the earliest MLPs has been a move towards architectures with structural inductive biases which enable the model to keep distinct sources of information and routes of processing well-separated.…
The superposition hypothesis states that single neurons may participate in representing multiple features in order for the neural network to represent more features than it has neurons. In neuroscience and AI, representational alignment…
If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…