Common infinite-width architectures such as Neural Tangent Kernels (NTKs)
have historically shown weak performance compared to finite models. This has
been attributed to the absence of feature learning. We show that this is not
the case. In fact, we show that infinite width NTK models are able to access
richer features than finite models by selecting relevant subfeatures from their
(infinite) feature vector. In fact, we show experimentally that NTKs
under-perform traditional finite models even when feature learning is
artificially disabled. Instead, weak performance is due to the fact that
existing constructions depend on weak optimizers like SGD. We provide an
infinite width limit based on ADAM-like learning dynamics and demonstrate
empirically that the resulting models erase this performance gap.

无限宽度架构，如神经切向核 (NTK) 在过去显示出与有限模型相比较弱的性能。我们证明这并非如此，实际上，我们展示无限宽度的 NTK 模型能够通过从无限特征向量中选择相关子特征来访问更丰富的特征。事实上，我们实验性地表明，即使在关闭特征学习的情况下，NTK 仍不如传统的有限模型性能好。相反，性能不佳是因为现有的构造依赖于像 SGD 这样的弱优化器。我们提供了基于类似于 ADAM 的学习动力学的无限宽度极限，并通过实验证明生成的模型消除了性能差距。

无限宽度模型的有效性：为什么特征学习不如你想象的那样重要

Infinite Width Models That Work: Why Feature Learning Doesn't Matter as  Much as You Think

We study the problem of finite ontology mediated query answering (FOMQA), the
variant of OMQA where the represented world is assumed to be finite, and thus
only finite models of the ontology are considered. We adopt the most typical
setting with unions of conjunctive queries and ontologies expressed in
description logics (DLs). The study of FOMQA is relevant in settings that are
not finitely controllable. This is the case not only for DLs without the finite
model property, but also for those allowing transitive role declarations. When
transitive roles are allowed, evaluating queries is challenging: FOMQA is
undecidable for SHOIF and only known to be decidable for the Horn fragment of
ALCIF. We show decidability of FOMQA for three proper fragments of SOIF: SOI,
SOF, and SIF. Our approach is to characterise models relevant for deciding
finite query entailment. Relying on a certain regularity of these models, we
develop automata-based decision procedures with optimal complexity bounds.

该研究探讨了有限本体中介查询应答的问题，使用 DLs 描述逻辑中的联合，当仅考虑本体的有限模型时，研究 FOMQA 是相关的，本研究显示了 SOIF 的三个适当片段的 FOMQA 具有可决定性，这是基于模型的特定规律，开发了自动机决策程序。

具有传递角色的表达能力描述逻辑中的有限查询回答

Finite Query Answering in Expressive Description Logics with Transitive  Roles

The $\epsilon$-logic (which is called $\epsilon$E-logic in this paper) of
Kuyper and Terwijn is a variant of first order logic with the same syntax, in
which the models are equipped with probability measures and in which the
$\forall x$ quantifier is interpreted as "there exists a set $A$ of measure
$\ge 1 - \epsilon$ such that for each $x \in A$, ...." Previously, Kuyper and
Terwijn proved that the general satisfiability and validity problems for this
logic are, i) for rational $\epsilon \in (0, 1)$, respectively
$\Sigma^1_1$-complete and $\Pi^1_1$-hard, and ii) for $\epsilon = 0$,
respectively decidable and $\Sigma^0_1$-complete. The adjective "general" here
means "uniformly over all languages."
We extend these results in the scenario of finite models. In particular, we
show that the problems of satisfiability by and validity over finite models in
$\epsilon$E-logic are, i) for rational $\epsilon \in (0, 1)$, respectively
$\Sigma^0_1$- and $\Pi^0_1$-complete, and ii) for $\epsilon = 0$, respectively
decidable and $\Pi^0_1$-complete. Although partial results toward the countable
case are also achieved, the computability of $\epsilon$E-logic over countable
models still remains largely unsolved. In addition, most of the results, of
this paper and of Kuyper and Terwijn, do not apply to individual languages with
a finite number of unary predicates. Reducing this requirement continues to be
a major point of research.
On the positive side, we derive the decidability of the corresponding
problems for monadic relational languages --- equality- and function-free
languages with finitely many unary and zero other predicates. This result holds
for all three of the unrestricted, the countable, and the finite model cases.
Applications in computational learning theory, weighted graphs, and neural
networks are discussed in the context of these decidability and undecidability
results.

本文研究的是 epsilonE-logic 中关于有限模型的可满足性和有效性问题，特别是对于有理的 epsilon，结果为 Sigma^0_1 和 Pi^0_1 完备性，而对于 epsilon=0，结果为可判定，但对于可数模型的 εE 逻辑的可计算性仍然存在研究点；此外，还讨论了在计算学习理论，加权图和神经网络中的应用。