In the quest for next-generation sequence modeling architectures, State Space Models (SSMs) have emerged as a potent alternative to transformers, particularly for their computational efficiency and suitability for dynamical systems. This paper investigates the effect of quantization on the S5 model to understand its impact on model performance and to facilitate its deployment to edge and resource-constrained platforms. Using quantization-aware training (QAT) and post-training quantization (PTQ), we systematically evaluate the quantization sensitivity of SSMs across different tasks like dynamical systems modeling, Sequential MNIST (sMNIST) and most of the Long Range Arena (LRA). We present fully quantized S5 models whose test accuracy drops less than 1% on sMNIST and most of the LRA. We find that performance on most tasks degrades significantly for recurrent weights below 8-bit precision, but that other components can be compressed further without significant loss of performance. Our results further show that PTQ only performs well on language-based LRA tasks whereas all others require QAT. Our investigation provides necessary insights for the continued development of efficient and hardware-optimized SSMs.

In this paper, we performed two types of software experiments to study the numerosity classification (subitizing) in humans and machines. Experiments focus on a particular kind of task is referred to as Semantic MNIST or simply SMNIST where the numerosity of objects placed in an image must be determined. The experiments called SMNIST for Humans are intended to measure the capacity of the Object File System in humans. In this type of experiment the measurement result is in well agreement with the value known from the cognitive psychology literature. The experiments called SMNIST for Machines serve similar purposes but they investigate existing, well known (but originally developed for other purpose) and under development deep learning computer programs. These measurement results can be interpreted similar to the results from SMNIST for Humans. The main thesis of this paper can be formulated as follows: in machines the image classification artificial neural networks can learn to distinguish numerosities with better accuracy when these numerosities are smaller than the capacity of OFS in humans. Finally, we outline a conceptual framework to investigate the notion of number in humans and machines.