This paper presents a comprehensive analysis of the growth rate of
$H$-consistency bounds (and excess error bounds) for various surrogate losses
used in classification. We prove a square-root growth rate near zero for smooth
margin-based surrogate losses in binary classification, providing both upper
and lower bounds under mild assumptions. This result also translates to excess
error bounds. Our lower bound requires weaker conditions than those in previous
work for excess error bounds, and our upper bound is entirely novel. Moreover,
we extend this analysis to multi-class classification with a series of novel
results, demonstrating a universal square-root growth rate for smooth comp-sum
and constrained losses, covering common choices for training neural networks in
multi-class classification. Given this universal rate, we turn to the question
of choosing among different surrogate losses. We first examine how
$H$-consistency bounds vary across surrogates based on the number of classes.
Next, ignoring constants and focusing on behavior near zero, we identify
minimizability gaps as the key differentiating factor in these bounds. Thus, we
thoroughly analyze these gaps, to guide surrogate loss selection, covering:
comparisons across different comp-sum losses, conditions where gaps become
zero, and general conditions leading to small gaps. Additionally, we
demonstrate the key role of minimizability gaps in comparing excess error
bounds and $H$-consistency bounds.

该论文对用于分类的各种代理损失函数的 $H$- 一致性界限（和超额误差界限）的增长率进行了全面分析。我们证明了二分类中平滑边界为基础的代理损失函数在接近零时的平方根增长率，并在温和假设下提供了上下界限。我们还将此分析扩展到多类分类，并通过一系列新颖的结果展示了平滑 comp-sum 和约束损失的普遍平方根增长率。在这个普遍率的基础上，我们研究了不同代理损失函数的选择问题，并首先考察了 $H$- 一致性界限在不同类别的代理损失函数间的变化。然后，我们通过忽略常数并关注接近零时的行为，确定了最小化差距是这些界限差异化因素的关键。因此，我们深入分析这些差距，以指导代理损失函数的选择，并涵盖：对不同的 comp-sum 损失进行比较，差距变为零的条件，以及导致小差距的一般条件。此外，我们还展示了最小化差距在比较超额误差界限和 $H$- 一致性界限中的关键作用。

一种适用于具有光滑替代损失的学习的通用增长率

A Universal Growth Rate for Learning with Smooth Surrogate Losses

This paper uses computational experiments to explore the role of exposure in
the emergence of construction grammars. While usage-based grammars are
hypothesized to depend on a learner's exposure to actual language use, the
mechanisms of such exposure have only been studied in a few constructions in
isolation. This paper experiments with (i) the growth rate of the
constructicon, (ii) the convergence rate of grammars exposed to independent
registers, and (iii) the rate at which constructions are forgotten when they
have not been recently observed. These experiments show that the lexicon grows
more quickly than the grammar and that the growth rate of the grammar is not
dependent on the growth rate of the lexicon. At the same time,
register-specific grammars converge onto more similar constructions as the
amount of exposure increases. This means that the influence of specific
registers becomes less important as exposure increases. Finally, the rate at
which constructions are forgotten when they have not been recently observed
mirrors the growth rate of the constructicon. This paper thus presents a
computational model of usage-based grammar that includes both the emergence and
the unentrenchment of constructions.

本文使用计算实验来探讨暴露在实际语言使用中对于构式语法出现的作用，并实验证明词汇表的增长速度比语法更快，而且语法的增长速度并不依赖于词汇表的增长速度。同时，面向特定寄存器的语法在暴露量增加时会收敛到更相似的结构中，这意味着随着曝光量的增加，特定寄存器的影响变得越来越不重要。最后，本文提出了一个计算模型，包括构式语法的出现和未压缩。

基于语料库的语法中曝露与出现：在 35 种语言中的计算实验

Exposure and Emergence in Usage-Based Grammar: Computational Experiments in 35 Languages

Which properties of metabolic networks can be derived solely from
stoichiometric information about the network's constituent reactions?
Predictive results have been obtained by Flux Balance Analysis (FBA), by
postulating that cells set metabolic fluxes within the allowed stoichiometry so
as to maximize their growth. Here, we generalize this framework to single cell
level using maximum entropy models from statistical physics. We define and
compute, for the core metabolism of Escherichia coli, a joint distribution over
all fluxes that yields the experimentally observed growth rate. This solution,
containing FBA as a limiting case, provides a better match to the measured
fluxes in the wild type and several mutants. We find that E. coli metabolism is
close to, but not at, the optimality assumed by FBA. Moreover, our model makes
a wide range of predictions: (i) on flux variability, its regulation, and flux
correlations across individual cells; (ii) on the relative importance of
stoichiometric constraints vs. growth rate optimization; (iii) on quantitative
scaling relations for singe-cell growth rate distributions. We validate these
scaling predictions using data from individual bacterial cells grown in a
microfluidic device at different sub-inhibitory antibiotic concentrations.
Under mild dynamical assumptions, fluctuation-response relations further
predict the autocorrelation timescale in growth data and growth rate adaptation
times following an environmental perturbation.

该研究使用统计物理学中的最大熵模型，对大肠杆菌核心代谢网络进行建模，得出了单细胞水平上代谢通量的联合分布，从而发现大肠杆菌的代谢优化接近最优但不完美，并预测了代谢网络的多个特性。