相关论文: Relevance in the Renormalization Group and in Info…
Computing conceptual structures, like formal concept lattices, is in the age of massive data sets a challenging task. There are various approaches to deal with this, e.g., random sampling, parallelization, or attribute extraction. A so far…
The development of diagnostic models is gaining traction in the field of psychiatric disorders. Recently, machine learning classifiers based on resting-state functional magnetic resonance imaging (rs-fMRI) have been developed to identify…
We define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric, $\g \to \lambda^2 \g$. We consider explicitly the case of a scalar field,…
Using Wilson-Polchinski renormalization group equations, we give a simple new proof of decoupling in a $\phi^4$-type scalar field theory involving two real scalar fields (one is heavy with mass $M$ and the other light). Then, to all orders…
We introduce the matrix-based Renyi's $\alpha$-order entropy functional to parameterize Tishby et al. information bottleneck (IB) principle with a neural network. We term our methodology Deep Deterministic Information Bottleneck (DIB), as…
Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and…
The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for…
The relationship according to which one physical theory encompasses the domain of empirical validity of another is widely known as "reduction." Here it is argued that one popular methodology for showing that one theory reduces to another,…
The Information Bottleneck (IB) method frequently suffers from unstable optimization, characterized by abrupt representation shifts near critical points of the IB trade-off parameter, beta. In this paper, I introduce a novel approach to…
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from…
We develop a novel method for ensuring fairness in machine learning which we term as the Renyi Fair Information Bottleneck (RFIB). We consider two different fairness constraints - demographic parity and equalized odds - for learning fair…
We illustrate the importance of mass scales and their relation in the specific case of the linear sigma model within the context of its one loop Ward identities. In the calculation it becomes apparent the delicate and essential connection…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
The selective visual attention mechanism in the human visual system (HVS) restricts the amount of information to reach visual awareness for perceiving natural scenes, allowing near real-time information processing with limited computational…
Neural collapse describes the geometry of activation in the final layer of a deep neural network when it is trained beyond performance plateaus. Open questions include whether neural collapse leads to better generalization and, if so, why…
The information bottleneck (IB) method is a feasible defense solution against adversarial attacks in deep learning. However, this method suffers from the spurious correlation, which leads to the limitation of its further improvement of…
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
An introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics is presented in the form of 6 lectures delivered to the British Universities Summer School in Theoretical…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…