“Softmax takes the raw, unbounded scores produced by a neural network and transforms them into a well-defined probability distribution...”

“If a finitely generated VI^m-module is generated in degree ≤ d and related in degree ≤ r, then its regularity is bounded above by a function of m, d, and r.”

“The paper proves that the chromatic number of $P_5$-free graphs is at most a polynomial function of the clique number.”

“The article focuses on the mathematical analysis of a chemotaxis-Navier-Stokes system.”

“The paper establishes sharp two-sided heat kernel estimates for these Markov processes.”

“Under mild assumptions, the sequence generated by the proposed algorithm is bounded and each of its cluster points is a stationary solution.”

“Dynamic multipliers can be used to guarantee the closed-loop power gain to be bounded and quantifiable.”

“The paper initiates the study of these processes, state some theorems and several intriguing conjectures found by computations of the finite Markov chain.”

“The key ingredient of our proof is the Cauchy-Schwarz inequality from probability theory.”

“The paper explains how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension.”

“The findings reveal a surprising dichotomy: while the number of samples needed to accurately tilt a bounded random vector increases polynomially in the tilt amount, it increases at a super polynomial rate for unbounded distributions.”

“GCA losses are $H$-consistent for any hypothesis set that is bounded or complete, with $H$-consistency bounds that scale more favorably as $1/\sqrt{\mathsf p_{\min}}$, offering significantly stronger theoretical guarantees in imbalanced settings.”

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“LRH reduces Max/Avg load from 1.2785 to 1.0947 and achieves 60.05 Mkeys/s, about 6.8x faster than multi-probe consistent hashing with 8 probes (8.80 Mkeys/s) while approaching its balance (Max/Avg 1.0697).”

“Any tropical circuit calculating the optimal value of a Traveling Salesperson round tour uses at least $2^{Ω(k \log \log k)}$ gates.”

“The error of approximation of the $2π$-periodic sawtooth function $(π-x)/2$, $0\leq x<2π$, by its $n$-th Fourier polynomial is shown to be bounded by arccot$((2n+1)\sin(x/2))$.”

“GPS replaces unstable extrapolation with a principled, manifold-constrained interpolation, ensuring the sampling path remains on the data manifold.”

“Hidden imagination is where unacknowledged harm incubates.”

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“The density of the chemical substance stays bounded for all time if its initial datum is bounded. This implies a significant distinction from the classical Keller--Segel system: diffusion driven by the chemical potential gradient can prevent the formation of concentration singularities.”

“YulToolkit detects the known vulnerabilities (producing a violation-triggering trace), and after applying fixes, reports no further violations within bounds.”

“SWE-Compressor reaches a 57.6% solved rate and significantly outperforms ReAct-based agents and static compression baselines, while maintaining stable and scalable long-horizon reasoning under a bounded context budget.”

“The paper investigates graphs quasi-isometric to graphs of bounded treewidth.”

“Solutions to both problems are given by the minimax designs, with appropriately chosen values of their tuning constant.”

“The paper proves that $χ\leq f(ω),$ where $f$ is a polynomial of degree $2j-2i-4.$”

“The paper proves that in the subcritical regime the cluster-size distribution has exponentially decaying tails, whereas in the supercritical regime the percolation probability grows at least linearly with respect to λ near criticality.”

“The paper focuses on 'variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation'.”

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“signals are represented as atomic measures on a signed state space, and similarity is given by a generalized Jaccard overlap of these measures.”

“The article's title suggests the paper addresses AI challenges related to fuzziness and resource limitations.”

“The article is sourced from ArXiv, indicating a pre-print submission.”

“The research focuses on Hölder-Lipschitz functions on fundamental domains of lattices in $\mathbb{R}^{d}$.”

“The article is sourced from ArXiv, indicating a research paper.”

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“Their goal is to estimate Ex∼p,y∼q[f(x,y)] to within additive error ε for a bounded function f, known to both parties.”

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“Almost Sure $\ln\ln T$ Regret for a sub-Gaussian Mixture on Unbounded Data”

“Physics-informed neural networks are used to solve inverse problems in unbounded domains.”

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“The article explores feedback vertex sets of digraphs with bounded maximum degree.”

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