Brain foundation models (BFMs) are self-supervised Transformers pretrained on fMRI data. We posit that these models should capture each subject's cognitive performance from their fMRI signal. Yet across three state-of-the-art BFMs and every readout we test, they predict cognition worse than a linear regression from the $\sim$80K parameters of the functional connectivity matrix (FC). The gap widens with scale: BrainLM's 650M model predicts cognition worse than its 111M. We attribute this to a \textbf{variance allocation problem}: BFM pretraining captures the variance components that dominate fMRI but not the higher-order structure that predicts cognition. Our per-cumulant analysis of the reconstructed signal shows that the second-order covariance is partially preserved, while the third-order co-skewness tensor is largely destroyed. To recover what BFMs lose, we design a linear pipeline that projects the fMRI signal into the subspace that best preserves its co-skewness and computes FC there. This \textbf{exceeds raw FC and every pretrained BFM} on every dataset and parcellation we test, outperforming prior state-of-the-art under controlled evaluation \textbf{with no pretraining and n
Introductory physics instruction emphasizes fluency with routine problem-solving procedures. However, even when applying these procedures, students frequently encounter challenges. This paper investigates how students navigate such moments when answering qualitative E&M problems in interviews. Students frequently noted they had partially forgotten a key equation on a problem involving RC circuits. We present focal cases that show how coherence-seeking approaches were employed to overcome this problem-solving challenge. In attempts to reconstruct these equations, participants were guided by identifying and chaining qualitative dependencies and seeking coherence between qualitative and mathematical understanding of the physical system. These moments of forgetting and reconstructing equations are a useful site for studying broader physics learning goals. While prior work investigates the use of mathematical sensemaking by examining how students respond to explicit prompts, our cases illustrate how students can spontaneously use mathematical sensemaking strategies. We reflect on these cases to consider how such adaptive reasoning can be a target for instruction and assessment.
Risk-based authentication (RBA) is used in online services to protect user accounts from unauthorized takeover. RBA commonly uses contextual features that indicate a suspicious login attempt when the characteristic attributes of the login context deviate from known and thus expected values. Previous research on RBA and anomaly detection in authentication has mainly focused on the login process. However, recent attacks have revealed vulnerabilities in other parts of the authentication process, specifically in the account recovery function. Consequently, to ensure comprehensive authentication security, the use of anomaly detection in the context of account recovery must also be investigated. This paper presents the first study to investigate risk-based account recovery (RBAR) in the wild. We analyzed the adoption of RBAR by five prominent online services (that are known to use RBA). Our findings confirm the use of RBAR at Google, LinkedIn, and Amazon. Furthermore, we provide insights into the different RBAR mechanisms of these services and explore the impact of multi-factor authentication on them. Based on our findings, we create a first maturity model for RBAR challenges. The goal o
Detection and recognition of text from scans and other images, commonly denoted as Optical Character Recognition (OCR), is a widely used form of automated document processing with a number of methods available. Yet OCR systems still do not achieve 100% accuracy, requiring human corrections in applications where correct readout is essential. Advances in machine learning enabled even more challenging scenarios of text detection and recognition "in-the-wild" - such as detecting text on objects from photographs of complex scenes. While the state-of-the-art methods for in-the-wild text recognition are typically evaluated on complex scenes, their performance in the domain of documents is typically not published, and a comprehensive comparison with methods for document OCR is missing. This paper compares several methods designed for in-the-wild text recognition and for document text recognition, and provides their evaluation on the domain of structured documents. The results suggest that state-of-the-art methods originally proposed for in-the-wild text detection also achieve competitive results on document text detection, outperforming available OCR methods. We argue that the application
We present a robotic system that watches a human using a Kinect v2 RGB-D sensor, detects what he forgot to do while performing an activity, and if necessary reminds the person using a laser pointer to point out the related object. Our simple setup can be easily deployed on any assistive robot. Our approach is based on a learning algorithm trained in a purely unsupervised setting, which does not require any human annotations. This makes our approach scalable and applicable to variant scenarios. Our model learns the action/object co-occurrence and action temporal relations in the activity, and uses the learned rich relationships to infer the forgotten action and the related object. We show that our approach not only improves the unsupervised action segmentation and action cluster assignment performance, but also effectively detects the forgotten actions on a challenging human activity RGB-D video dataset. In robotic experiments, we show that our robot is able to remind people of forgotten actions successfully.
A conjecture formulated by Henri Poincare in 1912 suggests that Max Planck's elementary quantum of action constitutes an authentic "atom of motion". When the conjecture is implemented, the resulting entity, the xon, becomes "the string string theorists forgot to notice". If a string exists in Nature, then string theoretical research should be pursued.
The past a few years have witnessed the great success of large language models, demonstrating powerful capabilities in comprehending textual data and generating human-like languages. Large language models achieve success by being trained on vast amounts of textual data, including online sources with copyrighted content and user-generated knowledge. However, this comes at a cost: the potential risk of exposing users' privacy and violating copyright protections. Thus, to safeguard individuals' "right to be forgotten", there has been increasing interests in machine unlearning -- the process of removing information carried by particular training samples from a model while not deteriorating its predictive quality. This is a challenging task due to the black-box nature of language models. Most existing studies focus on mitigating the impact of those forgot samples upon a model's outputs, and do not explicitly consider the geometric distributions of samples in the latent space of a model. To address this issue, we propose a machine unlearning framework, named Deep Contrastive Unlearning for fine-Tuning (DeepCUT) language models. Our proposed model achieves machine unlearning by directly o
Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets, providing a more realistic setting for image recognition. Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LegoGCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback Leibler divergence to encou
Motivated by the relative differential geometry, where the Euclidean normal vector of hypersurfaces is generalized by a relative normalization, we introduce anisotropic area measures of convex bodies, constructed with respect to a gauge body. Together with the anisotropic curvature measures, they are special cases of the newly introduced anisotropic support measures. We show that a convex body in ${\mathbb R}^n$, for which the anisotropic area measure of some order $k\in\{0,\dots,n-2\}$ is proportional to the area measure of order $n-1$, must be a $k$-tangential body of the gauge body.
User engagement on social media platforms is influenced by historical context, time constraints, and reward-driven interactions. This study presents an agent-based simulation approach that models user interactions, considering past conversation history, motivation, and resource constraints. Utilizing German Twitter data on political discourse, we fine-tune AI models to generate posts and replies, incorporating sentiment analysis, irony detection, and offensiveness classification. The simulation employs a myopic best-response model to govern agent behavior, accounting for decision-making based on expected rewards. Our results highlight the impact of historical context on AI-generated responses and demonstrate how engagement evolves under varying constraints.
In this paper we revisit the remainder terms of $L^p$-Hardy inequalities for magnetic $p$-Laplacians. In particular, we will give an integral representation of the sharp constant for a crucial algebraic inequality established by C. Cazacu, D. Krejčiřík, N. Lam, and A. Laptev.
In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the dimensions of the closed strata, which are isomorphic to the closure of certain fine Deligne-Lusztig varieties for a product of unitary and general linear groups. We also describe the incidence relations of the stratification by using Bruhat-Tits indices, which are related to the Bruhat-Tits building of an underlying $p$-adic unitary group.
In this comment, we point out a series of errors made by Senjaya in your paper (2024) \cite{Senjaya}. In particular, these errors involved the Dirac equation in the 3+1 dimensional Schwarzschild spacetime, tetrad field, curved gamma matrices, and the time-independent Dirac equation written in terms of the inner/scalar product between the gamma matrices and the orbital angular momentum (i.e., $\vecγ\cdot\vec{L}$). Besides, the strange/peculiar thing about all this is that even Senjaya \cite{Senjaya} citing Collas and Klein \cite{Collas}, where the (mathematical) formalism is correct, everything indicates that he ``ignored'' or ``forgot'' to use such formalism in your paper. Therefore, using Ref. \cite{Collas}, we show here the correct form of the errors made by Senjaya \cite{Senjaya}.
In 1933, Karol Borsuk asked whether each bounded set in the $n$-dimensional Euclidean space can be divided into $n$+1 parts of smaller diameter. Because it would not make sense otherwise, one usually assumes that he just forgot to require that the whole set contains at least two points. The hypothesis that the answer to that question is positive became famous under the name \emph{Borsuk's conjecture}. Counterexamples are known for any $n\ge 64$, since 2013. Let $Λ$ be the (original, unscaled) Leech lattice, a now very well-known infinite discrete vector set in the 24-dimensional Euclidean space. The smallest norm of nonzero vectors in $Λ$ is $\sqrt{32}$. Let $M$ be the set of the 196560 vectors in $Λ$ having this norm. For each $x \in M$, $-x$ is in $M$. Let $H$ be the set of all subsets of $M$ that for each $x$ in $M$ contain either $x$ or $-x$. Each element of $H$ has the same diameter $d = \sqrt{96}$. For dimensions $n<24$ one can analogously construct respective $M_n$ and $H_n$ from laminated $n$-dimensional sublattices $Λ_n$ of $Λ$. For uniformity, let $Λ_{24}=Λ$, $M_{24} = M$ and $H_{24} = H$. If $M_n$ is divisible into at most $n+1$ parts of diameter below $d$ then this a
In this document we consider an exact sequence of group varieties $e\to N\to G\to Q\to e$ over an algebraically closed field. We show that for $l eq \mathrm{char}(k)$ a prime there exists an isomorphism of graded $\mathbb{Q}_l$-algebras $\mathrm{H}_{\text{ét}}^*(G,\mathbb{Q}_l)\cong \mathrm{H}_{\text{ét}}^*(N,\mathbb{Q}_l)\otimes_{\mathbb{Q}_l}\mathrm{H}_{\text{ét}}^*(Q,\mathbb{Q}_l)$ that is compatible with pullback homomorphisms $f^*$ of endomorphisms $f:G\to G$ that stabilize $N$.
Recent years have witnessed a rise in interest in the geometrical trinity of General Relativity and its extensions. This interest has been fuelled by novel insights into the nature of gravity, the possibility to address computational and conceptual questions -- such as the determination of black hole entropy or the definition of gravitational energy-momentum -- from a new perspective. In particular, $f(Q)$ gravity has also inspired numerous works on black holes, wormholes, and cosmology. In the latter case, $f(Q)$ models have the potential to elucidate phenomena in both early and late-time cosmology without necessitating the inclusion of dark energy, the inflaton field, or dark matter. Particularly noteworthy is the role of $f(Q)$ theories in addressing cosmological tensions, presenting exciting possibilities for reshaping our understanding of gravity and its manifestations in cosmology. The emergence of intriguing new black hole solutions and the potential existence of wormhole solutions suggest the presence of novel physics within the realm of strong gravity. These phenomena have become increasingly measurable only in recent times, opening up exciting avenues for further explorat
A variant of the Gauss curvature flow for closed and convex hypersurfaces is considered. We reveal that if the initial hypersurface is pinched enough, then this property is preserved. Furthermore, based on some structure assumptions on the speed function of the shrinking flow, we show that the flow converges to a sphere. This may generalize the result of B. Chow\cite{CW85} to the possible non-homogeneous curvature flows.
In this paper, we prove that if $u$ is a solution to the Liouville equation \begin{align} \label{scalliouville} Δu+e^{2u} =0 \quad \mbox{in $\mathbb{R}^2$,} \end{align}then the diameter of $\mathbb{R}^2$ under the conformal metric $g=e^{2u}δ$ is bounded below by $π$. Here $δ$ is the Euclidean metric in $\mathbb{R}^2$. Moreover, we explicitly construct a family of solutions such that the corresponding diameters of $\mathbb{R}^2$ range over $[π,2π)$. We also discuss supersolutions. We show that if $u$ is a supersolution and $\int_{\mathbb{R}^2} e^{2u} dx<\infty$, then the diameter of $\mathbb{R}^2$ under the metric $e^{2u}δ$ is less than or equal to $2π$. For radial supersolutions, we use both analytical and geometric approaches to prove some inequalities involving conformal lengths and areas of disks in $\mathbb{R}^2$. We also discuss the connection of the above results with the sphere covering inequality in the case of Gaussian curvature bounded below by $1$. Higher dimensional generalizations are also discussed.
In this paper, we define the notion of exterior isoclinism of crossed modules. Functions for computing with these structures have been written using the GAP computational discrete algebra programming language