We consider the memorization capabilities of multilayered \emph{sign}
perceptrons neural networks (SPNNs). A recent rigorous upper-bounding capacity
characterization, obtained in \cite{Stojnictcmspnncaprdt23} utilizing the
Random Duality Theory (RDT), demonstrated that adding neurons in a network
configuration may indeed be very beneficial. Moreover, for particular
\emph{treelike committee machines} (TCM) architectures with $d\leq 5$ neurons
in the hidden layer, \cite{Stojnictcmspnncaprdt23} made a very first
mathematically rigorous progress in over 30 years by lowering the previously
best known capacity bounds of \cite{MitchDurb89}. Here, we first establish that
the RDT bounds from \cite{Stojnictcmspnncaprdt23} scale as $\sim \sqrt{d}$ and
can not on their own \emph{universally} (over the entire range of $d$) beat the
best known $\sim \log(d)$ scaling of the bounds from \cite{MitchDurb89}. After
recognizing that the progress from \cite{Stojnictcmspnncaprdt23} is therefore
promising, but yet without a complete concretization, we then proceed by
considering the recently developed fully lifted RDT (fl RDT) as an alternative.
While the fl RDT is indeed a powerful juggernaut, it typically relies on heavy
numerical evaluations. To avoid such heavy numerics, we here focus on a
simplified, \emph{partially lifted}, variant and show that it allows for very
neat, closed form, analytical capacity characterizations. Moreover, we obtain
the concrete capacity bounds that \emph{universally} improve for \emph{any} $d$
over the best known ones of \cite{MitchDurb89}.

对多层 sign 感知器神经网络（SPNNs）的记忆能力进行研究，并通过随机对偶理论（RDT）得出的容量表征结果证明，网络配置中增加神经元确实非常有益。此外，对于隐藏层具有 d≤5 个神经元的特定树状委员会机器（TCM）结构，该研究首次在 30 多年中通过降低之前最佳已知容量界限，取得了重大数学进展。

基于提升的 RDT 的训练容量分析与单隐层树状符号感知器神经网络

\emph{Lifted} RDT based capacity analysis of the 1-hidden layer treelike  \emph{sign} perceptrons neural networks

This work investigates the application of quantum machine learning techniques
for classical and quantum communication across different qubit channel models.
By employing parameterized quantum circuits and a flexible channel noise model,
we develop a machine learning framework to generate quantum channel codes and
evaluate their effectiveness. We explore classical, entanglement-assisted, and
quantum communication scenarios within our framework. Applying it to various
quantum channel models as proof of concept, we demonstrate strong performance
in each case. Our results highlight the potential of quantum machine learning
in advancing research on quantum communication systems, enabling a better
understanding of capacity bounds under modulation constraints, various
communication settings, and diverse channel models.

本研究探讨了量子机器学习技术在经典和量子通信中的应用，证明了该技术在不同量子信道模型下的强大性能，并为量子通信系统的研究提供了新的进展，使得人们在调制约束、各种通信设置和多样化的信道模型的容量界限方面有了更好的理解。

用于学习量子信道编码的量子自编码器

Quantum Autoencoders for Learning Quantum Channel Codes

Two potential bottlenecks on the expressiveness of recurrent neural networks
(RNNs) are their ability to store information about the task in their
parameters, and to store information about the input history in their units. We
show experimentally that all common RNN architectures achieve nearly the same
per-task and per-unit capacity bounds with careful training, for a variety of
tasks and stacking depths. They can store an amount of task information which
is linear in the number of parameters, and is approximately 5 bits per
parameter. They can additionally store approximately one real number from their
input history per hidden unit. We further find that for several tasks it is the
per-task parameter capacity bound that determines performance. These results
suggest that many previous results comparing RNN architectures are driven
primarily by differences in training effectiveness, rather than differences in
capacity. Supporting this observation, we compare training difficulty for
several architectures, and show that vanilla RNNs are far more difficult to
train, yet have slightly higher capacity. Finally, we propose two novel RNN
architectures, one of which is easier to train than the LSTM or GRU for deeply
stacked architectures.

通过实验证实了，所有常见的递归神经网络在仔细训练后达到了近乎相同的任务能力和单元容量边界，而许多以前的结果比较不同的递归神经网络结构主要是由于训练效果的差异而不是由于容量的差异驱动的。同时，作者还提出了两个新的递归神经网络结构，其中一个对于深度堆叠结构的训练比 LSTM 或 GRU 更容易。