We explore the theoretical possibility of learning $d$-dimensional targets
with $W$-parameter models by gradient flow (GF) when $W<d$. Our main result
shows that if the targets are described by a particular $d$-dimensional
probability distribution, then there exist models with as few as two parameters
that can learn the targets with arbitrarily high success probability. On the
other hand, we show that for $W<d$ there is necessarily a large subset of
GF-non-learnable targets. In particular, the set of learnable targets is not
dense in $\mathbb R^d$, and any subset of $\mathbb R^d$ homeomorphic to the
$W$-dimensional sphere contains non-learnable targets. Finally, we observe that
the model in our main theorem on almost guaranteed two-parameter learning is
constructed using a hierarchical procedure and as a result is not expressible
by a single elementary function. We show that this limitation is essential in
the sense that such learnability can be ruled out for a large class of
elementary functions.

通过梯度流（GF），我们研究了使用具有 W 个参数的模型来学习 d 维目标的理论可能性，在 W<d 的情况下。我们的主要结果表明，如果目标由特定的 d 维概率分布描述，则存在仅具有两个参数的模型，可以以任意高的成功概率学习这些目标。另一方面，我们证明了对于 W<d，存在一大类 GF - 不可学习的目标。特别地，可学习的目标集合在 R^d 中并非稠密，并且任何一个与 W 维球同胚的 R^d 子集都包含不可学习的目标。最后，我们观察到我们的主要定理中几乎保证的两参数学习模型是通过分层过程构造的，因此无法由单一的基本函数表示。我们还证明了这种限制在一大类基本函数中可以被排除掉。

通过两参数模型和梯度流学习高维目标

Learning high-dimensional targets by two-parameter models and gradient  flow

Emotion recognition is predominantly formulated as text classification in
which textual units are assigned to an emotion from a predefined inventory
(e.g., fear, joy, anger, disgust, sadness, surprise, trust, anticipation). More
recently, semantic role labeling approaches have been developed to extract
structures from the text to answer questions like: "who is described to feel
the emotion?" (experiencer), "what causes this emotion?" (stimulus), and at
which entity is it directed?" (target). Though it has been shown that jointly
modeling stimulus and emotion category prediction is beneficial for both
subtasks, it remains unclear which of these semantic roles enables a classifier
to infer the emotion. Is it the experiencer, because the identity of a person
is biased towards a particular emotion (X is always happy)? Is it a particular
target (everybody loves X) or a stimulus (doing X makes everybody sad)? We
answer these questions by training emotion classification models on five
available datasets annotated with at least one semantic role by masking the
fillers of these roles in the text in a controlled manner and find that across
multiple corpora, stimuli and targets carry emotion information, while the
experiencer might be considered a confounder. Further, we analyze if informing
the model about the position of the role improves the classification decision.
Particularly on literature corpora we find that the role information improves
the emotion classification.

该研究探讨了情感识别中的文本分类、语义角色标注等问题，结果表明在多种语料库中，刺激物和目标是情感识别的有效信息，而体验者则可能会被视为混淆因素。此外，研究发现在文学语料库中，角色信息可以提高情感分类的准确性。

体验者、刺激物还是目标：哪些语义角色能使机器学习推断情感？

Experiencers, Stimuli, or Targets: Which Semantic Roles Enable Machine  Learning to Infer the Emotions?

Consider a target moving with a constant velocity on a unit-circumference
circle, starting from an arbitrary location. To acquire the target, any region
of the circle can be probed for its presence, but the associated measurement
noise increases with the size of the probed region. We are interested in the
expected time required to find the target to within some given resolution and
error probability. For a known velocity, we characterize the optimal tradeoff
between time and resolution (i.e., maximal rate), and show that in contrast to
the case of constant measurement noise, measurement dependent noise incurs a
multiplicative gap between adaptive search and non-adaptive search. Moreover,
our adaptive scheme attains the optimal rate-reliability tradeoff. We further
show that for optimal non-adaptive search, accounting for an unknown velocity
incurs a factor of two in rate.

通过在单位周长圆的任意位置对其进行侦测，本文考虑了一个以恒定速度运动的目标，但其关联的测量噪声会随着探测区域的扩大而增加，研究了在给定精度和误差概率的前提下，发现目标的预期时间所需。本研究通过采用一种自适应搜索方案实现了速率 - 可靠性权衡的最优解，而针对未知速度的情况下，采用最优非自适应搜索方案所创造的速率却会降低一半。