The recursive teaching dimension (RTD) of a concept class $C \subseteq \{0, 1\}^n$, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of $C$ in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension. Given a concept class $C \subseteq \{0, 1\}^n$ with $VCD(C) = d$, we first show that $RTD(C)$ is at most $d 2^{d+1}$. This is the first upper bound for $RTD(C)$ that depends only on $VCD(C)$, independent of the size of the concept class $|C|$ and its~domain size $n$.

Large language models (LLMs) have rapidly advanced and demonstrated impressive capabilities.

A.1 Hyper-Parameters For all datasets, the surrogate gradient function isσ(x) = 1π arctan(π2αx) + 12, thus σ0(x) = The results on the three networks are consistent, indicating that RTD is a general sequential data augmentationmethod. We compare different surrogate functions, including Rectangular (σ0(x) = sign(|x| < 12)),ArcTan(σ0(x) = 11+(πx)2)and Constant 1(σ0(x) 1),intheSNNs on CIFAR-10. The results are shown in Tab.9. Tab.9 indicates that the choice of surrogate function has a considerable influence on the SNN's performance. Although Rectangular and Constant 1 can avoid the gradient exploding/vanishing problems in Eq.(8), they still cause lower accuracy or even make the optimization not converges.

In machine teaching, a concept is represented by (and inferred from) a small number of labeled examples.

The current version of Predify assumes that there is no gap between the encoders. One can easily override the default setting by providing all the details for a PCoder. A.3 ExecutionTime Since we used a variable number of GPUs for the different experiments, an exact execution time is hard to pinpoint. We expect that this could be further improved with a more extensive and systematic hyperparameter search. In other words, their training hyperparameters appeared to have been optimised for their predictive coding network, but not - or not as much - for their feedforward baseline.

The recursive teaching dimension (RTD) of a concept class $C \subseteq \{0, 1\}^n$, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of $C$ in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension. Given a concept class $C \subseteq \{0, 1\}^n$ with $VCD(C) = d$, we first show that $RTD(C)$ is at most $d 2^{d+1}$. This is the first upper bound for $RTD(C)$ that depends only on $VCD(C)$, independent of the size of the concept class $|C|$ and its~domain size $n$.

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In machine teaching, a concept is represented by (and inferred from) a small number of labeled examples.