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Despite the empirical success of foundation models, we do not have a systematic characterization of the representations that these models learn. In this paper, we establish the contexture theory. It shows that a large class of representation learning methods can be characterized as learning from the association between the input and a context variable. Specifically, we show that many popular methods aim to approximate the top-d singular functions of the expectation operator induced by the context, in which case we say that the representation learns the contexture. We demonstrate the generality of the contexture theory by proving that representation learning within various learning paradigms—supervised, self-supervised, and manifold learning—can all be studied from such a perspective. We also prove that the representations that learn the contexture are optimal on those tasks that are compatible with the context. One important implication of the contexture theory is that once the model is large enough to approximate the top singular functions, further scaling up the model size yields diminishing returns. Therefore, scaling is not all we need, and further improvement requires better contexts. To this end, we study how to evaluate the usefulness of a context without knowing the downstream tasks. We propose a metric and show by experiments that it correlates well with the actual performance of the encoder on many real datasets. 

Abstract Stellar flares occasionally present apeak-bumplight-curve morphology, consisting of an initial impulsive phase followed by a gradual late phase. Analyzing this specific morphology can uncover the underlying physics of stellar flare dynamics, particularly the plasma heating–evaporation–condensation process. While previous studies have mainly examined peak-bump occurrences on M dwarfs, this report extends the investigation to G-, K-, and M-type stars. We utilize the flare catalog published by J. Crowley et al., encompassing 12,597 flares, detected by using Transiting Exoplanet Survey Satellite (TESS) observations. Our analysis identifies 10,142 flares with discernible classical and complex morphology, of which 197 (∼1.9%) exhibit the peak-bump feature. We delve into the statistical properties of these TESS late-phase flares, noting that both the amplitude and FWHM durations of both the peaks and bumps show positive correlations across all source-star spectral types, following a power law with indices 0.69 ± 0.09 and 1.0 ± 0.15, respectively. Additionally, a negative correlation between the flare amplitude and the effective temperature of their host stars is observed. Compared to the other flares in our sample, peak-bump flares tend to have larger and longer initial peak amplitudes and FWHM durations and possess energies ranging from 10³¹to 10³⁶erg. 

Social media platforms allow users to create polls to gather public opinion on diverse topics. However, we know little about what such polls are used for and how reliable they are, especially in significant contexts like elections. Focusing on the 2020 presidential elections in the U.S., this study shows that outcomes of election polls on Twitter deviate from election results despite their prevalence. Leveraging demographic inference and statistical analysis, we find that Twitter polls are disproportionately authored by male Republicans and exhibit a large bias towards candidate Donald Trump in comparison to mainstream polls. We investigate potential sources of biased outcomes from the point of view of inauthentic, automated, and counter-normative behavior. Using social media experiments and interviews with poll authors, we identify inconsistencies between public vote counts and those privately visible to poll authors, with the gap potentially attributable to purchased votes. We find that election polls tend to be more biased, contain more questionable votes, and attract more bots before the election day than after. We highlight and compare key factors contributing to biased poll outcomes. Finally, we identify instances of polls spreading voter fraud conspiracy theories and estimate that a couple of thousand such polls were posted in 2020. The study discusses the implications of biased election polls in the context of transparency and accountability of social media platforms. 

The central molecular zone (CMZ) of our Galaxy exhibits widespread emission from SiO and various complex organic molecules (COMs), yet the exact origin of such emission is uncertain. Here we report the discovery of a unique class of long (>0.5 pc) and narrow (<0.03 pc) filaments in the emission of SiO 5–4 and eight additional molecular lines, including several COMs, in our ALMA 1.3 mm spectral line observations toward two massive molecular clouds in the CMZ, which we name as slim filaments. However, these filaments are not detected in the 1.3 mm continuum at the 5σlevel. Their line-of-sight velocities are coherent and inconsistent with being outflows. The column densities and relative abundances of the detected molecules are statistically similar to those in protostellar outflows but different from those in dense cores within the same clouds. Turbulent pressure in these filaments dominates over self gravity and leads to hydrostatic inequilibrium, indicating that they are a different class of objects than the dense gas filaments in dynamical equilibrium ubiquitously found in nearby molecular clouds. We argue that these newly detected slim filaments are associated with parsec-scale shocks, likely arising from dynamic interactions between shock waves and molecular clouds. The dissipation of the slim filaments may replenish SiO and COMs in the interstellar medium and lead to their widespread emission in the CMZ. 

Abstract: We consider the quadratic Zakharov-Kuznetsov equation $$\partial_t u + \partial_x \Delta u + \partial_x u^2=0$$ on $$\Bbb{R}^3$$. A solitary wave solution is given by $Q(x-t,y,z)$, where $$Q$$ is the ground state solution to $$-Q+\Delta Q+Q^2=0$$. We prove the asymptotic stability of these solitary wave solutions. Specifically, we show that initial data close to $$Q$$ in the energy space, evolves to a solution that, as $$t\to\infty$$, converges to a rescaling and shift of $Q(x-t,y,z)$ in $L^2$ in a rightward shifting region $$x>\delta t-\tan\theta\sqrt{y^2+z^2}$$ for $$0\leq\theta\leq{\pi\over 3}-\delta$$.