The rapid advancement of large language model (LLM) technology has led to diverse applications, many of which inherently require randomness, such as stochastic decision-making, gaming, scheduling, AI agents, and cryptography-related tasks. However, the capabilities of LLMs in handling randomness, particularly in generating and utilizing random numbers effectively, remain unclear. This paper investigates the capacity of LLMs for handling tasks that involve randomness through a series of experiments. We designed a set of experiments that consider various factors that can influence an LLM's performance in tasks involving randomness, such as accessibility to external tools, types of tasks, model states (fresh vs. non-fresh), and prompting strategies. The experiments cover a range of tasks, including generating random numbers, generating random strings such as passwords, shuffling items, and evaluating the quality of randomness using entropy and the NIST randomness test-suite. Our findings reveal that while LLMs can generate outputs that exhibit some degree of randomness, their performance is inconsistent and often deviates significantly from the expected behavior. The analysis of the experimental results highlights key limitations and areas where improvement is needed for the LLMs to effectively handle tasks involving randomness

Pseudo-random number generators (PRNGs) are high-nonlinear processes, and they are key blocks in optimization of Large language models. Transformers excel at processing complex nonlinear relationships. Thus it is reasonable to generate high-quality pseudo-random numbers based on transformers. In this paper, we explore this question from both theoretical and practical perspectives, highlighting the potential benefits and implications of Transformer in PRNGs. We theoretically demonstrate that decoder-only Transformer models with Chain-of-Thought can simulate both the Linear Congruential Generator (LCG) and Mersenne Twister (MT) PRNGs. Based on this, we conclude that the log-precision decoder-only Transformer can represent non-uniform $\text{AC}^0$. Our simulative theoretical findings are validated through experiments. The random numbers generated by Transformer-based PRNGs successfully pass the majority of NIST tests, whose heat maps exhibit clear statistical randomness. Finally, we assess their capability in prediction attacks.

Machine learning (ML) frameworks rely heavily on pseudorandom number generators (PRNGs) for tasks such as data shuffling, weight initialization, dropout, and optimization. Yet, the statistical quality and reproducibility of these generators-particularly when integrated into frameworks like PyTorch, TensorFlow, and NumPy-are underexplored. In this paper, we compare the statistical quality of PRNGs used in ML frameworks (Mersenne Twister, PCG, and Philox) against their original C implementations. Using the rigorous TestU01 BigCrush test suite, we evaluate 896 independent random streams for each generator. Our findings challenge claims of statistical robustness, revealing that even generators labeled ''crush-resistant'' (e.g., PCG, Philox) may fail certain statistical tests. Surprisingly, we can observe some differences in failure profiles between the native and framework-integrated versions of the same algorithm, highlighting some implementation differences that may exist.

True Random Number Generators (TRNGs) play a fundamental role in hardware security, cryptographic systems, and data protection. In the context of Deep NeuralNetworks (DNNs), safeguarding model parameters, particularly weights, is critical to ensure the integrity, privacy, and intel-lectual property of AI systems. While software-based pseudo-random number generators are widely used, they lack the unpredictability and resilience offered by hardware-based TRNGs. In this work, we propose a novel and robust Encoding-in-Memory TRNG called EIM-TRNG that leverages the inherent physical randomness in DRAM cell behavior, particularly under RowHammer-induced disturbances, for the first time. We demonstrate how the unpredictable bit-flips generated through carefully controlled RowHammer operations can be harnessed as a reliable entropy source. Furthermore, we apply this TRNG framework to secure DNN weight data by encoding via a combination of fixed and unpredictable bit-flips. The encrypted data is later decrypted using a key derived from the probabilistic flip behavior, ensuring both data confidentiality and model authenticity. Our results validate the effectiveness of DRAM-based entropy extraction for robust, low-cost hardware security and offer a promising direction for protecting machine learning models at the hardware level.

AI-Hybrid TRNG is a deep-learning framework that extracts near-uniform entropy directly from physical noise, eliminating the need for bulky quantum devices or expensive laboratory-grade RF receivers. Instead, it relies on a low-cost, thumb-sized RF front end, plus CPU-timing jitter, for training, and then emits 32-bit high-entropy streams without any quantization step. Unlike deterministic or trained artificial intelligence random number generators (RNGs), our dynamic inner-outer network couples adaptive natural sources and reseeding, yielding truly unpredictable and autonomous sequences. Generated numbers pass the NIST SP 800-22 battery better than a CPU-based method. It also passes nineteen bespoke statistical tests for both bit- and integer-level analysis. All results satisfy cryptographic standards, while forward and backward prediction experiments reveal no exploitable biases. The model's footprint is below 0.5 MB, making it deployable on MCUs and FPGA soft cores, as well as suitable for other resource-constrained platforms. By detaching randomness quality from dedicated hardware, AI-Hybrid TRNG broadens the reach of high-integrity random number generators across secure systems, cryptographic protocols, embedded and edge devices, stochastic simulations, and server applications that need randomness.

The effectiveness of training neural networks directly impacts computational costs, resource allocation, and model development timelines in machine learning applications. An optimizer's ability to train the model adequately (in terms of trained model performance) depends on the model's initial weights. Model weight initialization schemes use pseudorandom number generators (PRNGs) as a source of randomness. We investigate whether substituting PRNGs for low-discrepancy quasirandom number generators (QRNGs) -- namely Sobol' sequences -- as a source of randomness for initializers can improve model performance. We examine Multi-Layer Perceptrons (MLP), Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and Transformer architectures trained on MNIST, CIFAR-10, and IMDB datasets using SGD and Adam optimizers. Our analysis uses ten initialization schemes: Glorot, He, Lecun (both Uniform and Normal); Orthogonal, Random Normal, Truncated Normal, and Random Uniform. Models with weights set using PRNG- and QRNG-based initializers are compared pairwise for each combination of dataset, architecture, optimizer, and initialization scheme. Our findings indicate that QRNG-based neural network initializers either reach a higher accuracy or achieve the same accuracy more quickly than PRNG-based initializers in 60% of the 120 experiments conducted. Thus, using QRNG-based initializers instead of PRNG-based initializers can speed up and improve model training.

This study investigates the application of machine learning predictors for min-entropy estimation in Random Number Generators (RNGs), a key component in cryptographic applications where accurate entropy assessment is essential for cybersecurity. Our research indicates that these predictors, and indeed any predictor that leverages sequence correlations, primarily estimate average min-entropy, a metric not extensively studied in this context. We explore the relationship between average min-entropy and the traditional min-entropy, focusing on their dependence on the number of target bits being predicted. Utilizing data from Generalized Binary Autoregressive Models, a subset of Markov processes, we demonstrate that machine learning models (including a hybrid of convolutional and recurrent Long Short-Term Memory layers and the transformer-based GPT-2 model) outperform traditional NIST SP 800-90B predictors in certain scenarios. Our findings underscore the importance of considering the number of target bits in min-entropy assessment for RNGs and highlight the potential of machine learning approaches in enhancing entropy estimation techniques for improved cryptographic security.

Pseudo-Random Number Generators (PRNGs) have become ubiquitous in machine learning technologies because they are interesting for numerous methods. The field of machine learning holds the potential for substantial advancements across various domains, as exemplified by recent breakthroughs in Large Language Models (LLMs). However, despite the growing interest, persistent concerns include issues related to reproducibility and energy consumption. Reproducibility is crucial for robust scientific inquiry and explainability, while energy efficiency underscores the imperative to conserve finite global resources. This study delves into the investigation of whether the leading Pseudo-Random Number Generators (PRNGs) employed in machine learning languages, libraries, and frameworks uphold statistical quality and numerical reproducibility when compared to the original C implementation of the respective PRNG algorithms. Additionally, we aim to evaluate the time efficiency and energy consumption of various implementations. Our experiments encompass Python, NumPy, TensorFlow, and PyTorch, utilizing the Mersenne Twister, PCG, and Philox algorithms. Remarkably, we verified that the temporal performance of machine learning technologies closely aligns with that of C-based implementations, with instances of achieving even superior performances. On the other hand, it is noteworthy that ML technologies consumed only 10% more energy than their C-implementation counterparts. However, while statistical quality was found to be comparable, achieving numerical reproducibility across different platforms for identical seeds and algorithms was not achieved.

We present a new high-level synthesis methodology for using large language model tools to generate hardware designs. The methodology uses exclusively open-source tools excluding the large language model. As a case study, we use our methodology to generate a permuted congruential random number generator design with a wishbone interface. We verify the functionality and quality of the random number generator design using large language model-generated simulations and the Dieharder randomness test suite. We document all the large language model chat logs, Python scripts, Verilog scripts, and simulation results used in the case study. We believe that our method of hardware design generation coupled with the open source silicon 130 nm design tools will revolutionize application-specific integrated circuit design. Our methodology significantly lowers the bar to entry when building domain-specific computing accelerators for the Internet of Things and proof of concept prototypes for later fabrication in more modern process nodes.

Randomness supports many critical functions in the field of machine learning (ML) including optimisation, data selection, privacy, and security. ML systems outsource the task of generating or harvesting randomness to the compiler, the cloud service provider or elsewhere in the toolchain. Yet there is a long history of attackers exploiting poor randomness, or even creating it -- as when the NSA put backdoors in random number generators to break cryptography. In this paper we consider whether attackers can compromise an ML system using only the randomness on which they commonly rely. We focus our effort on Randomised Smoothing, a popular approach to train certifiably robust models, and to certify specific input datapoints of an arbitrary model. We choose Randomised Smoothing since it is used for both security and safety -- to counteract adversarial examples and quantify uncertainty respectively. Under the hood, it relies on sampling Gaussian noise to explore the volume around a data point to certify that a model is not vulnerable to adversarial examples. We demonstrate an entirely novel attack against it, where an attacker backdoors the supplied randomness to falsely certify either an overestimate or an underestimate of robustness. We demonstrate that such attacks are possible, that they require very small changes to randomness to succeed, and that they can be hard to detect. As an example, we hide an attack in the random number generator and show that the randomness tests suggested by NIST fail to detect it. We advocate updating the NIST guidelines on random number testing to make them more appropriate for safety-critical and security-critical machine-learning applications.