Few-shot multi-class industrial anomaly detection identifies diverse defects across multiple categories using a single unified model and limited normal samples. Although vision-language models offer strong generalization, modeling multiple distinct category manifolds concurrently without actual anomalous data causes feature space collapse and cross-class interference. Consequently, existing methods often fail to balance scalability and precision, leading to either isolated single-class retraining or excessively loose decision margins. To address this limitation, we present a one-for-all learning framework called ABounD that unites semantic concept anchoring with geometric boundary optimization. This method employs two lightweight mechanisms to resolve multi-class ambiguity. First, the Dynamic Concept Fusion module generates class-adaptive semantic anchors via query-aware hierarchical calibration, disentangling overlapping category concepts. Second, using these anchors, the Adversarial Boundary Forging module constructs a tight, class-tailored decision margin by synthesizing adversarial boundary-level fence features to prevent cross-class boundary blurring. Optimized in a single sta
Recent discoveries of apparent large-scale features in the structure of the universe, extending over many hundreds of megaparsecs, have been claimed to contradict the large-scale isotropy and homogeneity foundational to the standard ($Λ$CDM) cosmological model. We explicitly test and refute this conjecture using FLAMINGO-10K, a new and very large cosmological simulation of the growth of structure in a $Λ$CDM context. Applying the same methods used in the observations, we show that patterns like the "Giant Arc", supposedly in tension with the standard model, are, in fact, common and expected in a $Λ$CDM universe. We also show that their reported significant overdensities are an algorithmic artefact and unlikely to reflect any underlying structure.
The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical knowledge. However, we demonstrate that, when methodically questioned, large language models (LLMs) often display and demonstrate significant inconsistencies in their knowledge. Computationally, the basic aspects of the conceptualization of a given domain can be represented as Is-A hierarchies in a knowledge graph (KG) or ontology, together with a few properties or axioms that enable straightforward reasoning. We show that even simple ontologies can be used to reveal conceptual inconsistencies across several LLMs. We also propose strategies that domain experts can use to evaluate and improve the coverage of key domain concepts in LLMs of various sizes. In particular, we have been able to significantly enhance the performance of LLMs of various sizes with openly available weights using simple knowledge-graph (KG) based prompting strategies.
It is proved that given any prime ideal $\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\mathfrak{p}$-local $\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3.
"You promised me that you would never take power in your name
We present a topological analysis of the temperature fluctuation maps from the \emph{Planck 2020} Data release 4 (DR4) based on the \texttt{NPIPE} data processing pipeline. For comparison, we also present the topological characteristics of the maps from \emph{Planck 2018} Data release 3 (DR3). We perform our analysis in terms of the homology characteristics of the maps, invoking relative homology to account for analysis in the presence of masks. We perform our analysis for a range of smoothing scales spanning sub- and super-horizon scales corresponding to $FWHM = 5', 10', 20', 40', 80', 160', 320', 640'$. Our main result indicates a significantly anomalous behavior of the loops in the observed maps compared to simulations that are modeled as isotopic and homogeneous Gaussian random fields. Specifically, we observe a $4σ$ deviation between the observation and simulations in the number of loops at $FWHM = 320'$ and $FWHM = 640'$, corresponding to super-horizon scales of $5$ degrees and larger. In addition, we also notice a mildly significant deviation at $2σ$ for all the topological descriptors for almost all the scales analyzed. Our results show a consistency across different data r
Nobody knows how language works, but many theories abound. Transformers are a class of neural networks that process language automatically with more success than alternatives, both those based on neural computations and those that rely on other (e.g. more symbolic) mechanisms. Here, I highlight direct connections between the transformer architecture and certain theoretical perspectives on language. The empirical success of transformers relative to alternative models provides circumstantial evidence that the linguistic approaches that transformers embody should be, at least, evaluated with greater scrutiny by the linguistics community and, at best, considered to be the currently best available theories.
Linear mode-connectivity (LMC) (or lack thereof) is one of the intriguing characteristics of neural network loss landscapes. While empirically well established, it unfortunately still lacks a proper theoretical understanding. Even worse, although empirical data points are abound, a systematic study of when networks exhibit LMC is largely missing in the literature. In this work we aim to close this gap. We explore how LMC is affected by three factors: (1) architecture (sparsity, weight-sharing), (2) training strategy (optimization setup) as well as (3) the underlying dataset. We place particular emphasis on minimal but non-trivial settings, removing as much unnecessary complexity as possible. We believe that our insights can guide future theoretical works on uncovering the inner workings of LMC.
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the fragments are relatively long, and typically no fragment appears more than once, the scaling of the failure probability of maximum likelihood reconstruction algorithm is exactly determined for perfect reconstruction and bounded for partial reconstruction. Second, the regime in which the fragments are relatively short and repeating fragments abound is characterized. A trade-off is stated between the fraction of fragments that cannot be adequately reconstructed vs. the distortion level allowed for the reconstruction of each fragment, while still allowing vanishing failure probability
Weak structures abound in higher category theory, but are often suitably equivalent to stricter structures that are easier to understand. We extend strictification for tricategories and trihomomorphisms to trinatural transformations, trimodifications and perturbations. Along the way we distinguish between the operational coherences, which are possible to strictify, and the coherences on globular inputs, which remain weak. We introduce generalised path objects for $\mathbf{Gray}$-categories, which help reduce proofs in the three-dimensional setting to known results. Upon closing the resulting semi-strict trinatural transformations under composition, we state the hom-triequivalences of what we expect to be a `semi-strictification tetra-adjunction'.
A closed subgroup $G\subset_uU_N^+$ is called easy when its associated Tannakian category $C_{kl}=Hom(u^{\otimes k},u^{\otimes l})$ appears from a category of partitions, $C=span(D)$ with $D=(D_{kl})\subset P$, via the standard implementation of partitions as linear maps. The examples abound, and the main known subgroups $G\subset U_N^+$ are either easy, or not far from being easy. We discuss here the basic theory, examples and known classification results for the easy quantum groups $G\subset U_N^+$, as well as various generalizations of the formalism, known as super-easiness theories, and the unification problem for them.
Cooperation in multi-agent learning (MAL) is a topic at the intersection of numerous disciplines, including game theory, economics, social sciences, and evolutionary biology. Research in this area aims to understand both how agents can coordinate effectively when goals are aligned and how they may cooperate in settings where gains from working together are possible but possibilities for conflict abound. In this paper we provide an overview of the fundamental concepts, problem settings and algorithms of multi-agent learning. This encompasses reinforcement learning, multi-agent sequential decision-making, challenges associated with multi-agent cooperation, and a comprehensive review of recent progress, along with an evaluation of relevant metrics. Finally we discuss open challenges in the field with the aim of inspiring new avenues for research.
We introduce the notion of free decomposition spaces: they are simplicial spaces freely generated by their inert maps. We show that left Kan extension along the inclusion $j \colon Δ_{\operatorname{inert}} \to Δ$ takes general objects to Möbius decomposition spaces and general maps to CULF maps. We establish an equivalence of $\infty$-categories $\mathbf{PrSh}(Δ_{\operatorname{inert}}) \simeq \mathbf{Decomp}_{/B\mathbb{N}}$. Although free decomposition spaces are rather simple objects, they abound in combinatorics: it seems that all comultiplications of deconcatenation type arise from free decomposition spaces. We give an extensive list of examples, including quasi-symmetric functions.
Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further complicating issues, changepoint conclusions are not robust to small perturbations in assumptions; for example, allowing for a trend or correlation in the series can drastically change conclusions. This paper is a review of the changepoint topic, with an emphasis on illuminating the models and techniques that allow the scientist to make reliable conclusions. Pitfalls to avoid are demonstrated via actual applications. The discourse begins by narrating the salient statistical features of most climate time series. Thereafter, single and multiple changepoint problems are considered. Several pitfalls are discussed en route and good practices are recommended. While the majority of our applications involve temperature series, other settings are mentioned.
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is possible and develop tests that can confidently reject the null hypothesis that data is independent and identically distributed and have high power for (some) exchangeable distributions. We will make no structural assumptions on the underlying sample space. One potential application is in Deep Learning, where data is often scraped from the whole internet, with duplications abound, which can render data non-iid and test-set evaluation prone to give wrong answers.
Invaginations are partial enclosures formed by surfaces. Typically formed by biological membranes; they abound in nature. In this paper, we consider fundamentally different structures: elastically stabilized invaginations. Focusing on spherical invaginations formed by elastic membranes, we carried out experiments and mathematical modeling to understand the stress and strain fields underlying stable structures. Friction plays a key role in stabilization, and consequently the required force balance is an inequality. Using a novel scheme, we were able to find stable solutions of the balance equations for different models of elasticity, with reasonable agreement with experiments.
While the Bekenstein-Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein-Hawking entropy.
One of the greatest achievements of twentieth century physics is the discovery of a very close link between the microcosm and the macrocosm. This follows from the two basic principles of quantum mechanics and relativity, the uncertainty principle and the mass energy equivalence, along with the standard big bang model of cosmology. As we probe deeper into the microcosm we encounter states of higher mass and energy, which were associated with the early history of the universe. Thus discovery of the atomic nucleus followed by the nuclear particles, quarks & gluons and finally the $W$ & $Z$ bosons have recreated in the laboratory the forms of matter that abounded in the very early universe. This has helped us to trace back the history of the universe to within a few picoseconds of its creation. Finally the discovery of the Higgs and supersymmetric particles will help to solve the mystry of the invisible matter, which abound throughout the universe today, as relics of that early history.
Luttinger's contributions abound in different parts of many-body physics. Here I review the ones that appear when one uses the Renormalization Group (RG) to study the subject: the Luttinger Liquid, Luttinger's Theorem (on the volume of the Fermi surface) and the Kohn-Luttinger Theorem on the superconducting instability of all metals as one approaches absolute zero.
The relativistic extension of non-relativistic hydrodynamics suffers from notorious difficulties. In non-relativistic hydrodynamics where difficulties also abound, it has proved a useful supplement to study lattice models which can imitate viscous fluid flow. In this paper we construct a relativistic spacetime lattice and construct a dynamics of points, thus a relativistic cellular automaton over it, to model relativistic fluid flow. A simple example is also explicitly studied, and some numerical results with figures are shown in the last section.