Diffusion models have achieved remarkable performance in generative modeling, yet their theoretical foundations are often intricate, and the gap between mathematical formulations in papers and practical open-source implementations can be difficult to bridge. Existing tutorials primarily focus on deriving equations, offering limited guidance on how diffusion models actually operate in code. To address this, we present a concise implementation of approximately 300 lines that explains diffusion models from a code-execution perspective. Our minimal example preserves the essential components -- including forward diffusion, reverse sampling, the noise-prediction network, and the training loop -- while removing unnecessary engineering details. This technical report aims to provide researchers with a clear, implementation-first understanding of how diffusion models work in practice and how code and theory correspond. Our code and pre-trained models are available at: https://github.com/disanda/GM/tree/main/DDPM-DDIM-ClassifierFree.

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in the field of generative modeling due to its flexibility in the formulation and strong modeling power of the latent space. However, the common practice of learning latent space EBMs with non-convergent short-run MCMC for prior and posterior sampling is hindering the model from further progress; the degenerate MCMC sampling quality in practice often leads to degraded generation quality and instability in training, especially with highly multi-modal and/or high-dimensional target distributions. To remedy this sampling issue, in this paper we introduce a simple but effective diffusion-based amortization method for long-run MCMC sampling and develop a novel learning algorithm for the latent space EBM based on it. We provide theoretical evidence that the learned amortization of MCMC is a valid long-run MCMC sampler.

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $ε$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional spaces (e.g., using total variation), which limits their applications to complex data (e.g., images). To extend DCT to more types of data, a natural idea is to introduce maximum mean discrepancy (MMD), a powerful measurement of the distributional discrepancy between two complex distributions, into DCT scenarios. However, we find that MMD's value can be the same for many pairs of distributions that have different norms in the same reproducing kernel Hilbert space (RKHS), making MMD less informative when assessing the closeness levels for multiple distribution pairs. To mitigate the issue, we design a new measurement of distributional discrepancy, norm-adaptive MMD (NAMMD), which scales MMD's value using the RKHS norms of distributions. Based on the asymptotic distribution of NAMMD, we finally propose the NAMMD-based DCT to assess the closeness levels of a distribution pair. Theoretically, we prove that NAMMD-based DCT has higher test power compared to MMD-based DCT, with bounded type-I error, which is also validated by extensive experiments on many types of data (e.g., synthetic noise, real images). Furthermore, we also apply the proposed NAMMD for addressing the two-sample testing problem and find NAMMD-based two-sample test has higher test power than the MMD-based two-sample test in both theory and experiments.

To address the challenges of sim-to-real gap and sample efficiency in reinforcement learning (RL), this work studies distributionally robust Markov decision processes (RMDPs) --- optimize the worst-case performance when the deployed environment is within an uncertainty set around some nominal MDP. Despite recent efforts, the sample complexity of RMDPs has remained largely undetermined. While the statistical implications of distributional robustness in RL have been explored in some specific cases, the generalizability of the existing findings remains unclear, especially in comparison to standard RL. Assuming access to a generative model that samples from the nominal MDP, we examine the sample complexity of RMDPs using a class of generalized L_p norms as the'distance' function for the uncertainty set, under two commonly adopted sa -rectangular and s -rectangular conditions. Our results imply that RMDPs can be more sample-efficient to solve than standard MDPs using generalized L_p norms in both sa - and s -rectangular cases, potentially inspiring more empirical research.

Large Language Models (LLMs), despite their impressive capabilities, often fail to accurately repeat a single word when prompted to, and instead output unrelated text. This unexplained failure mode represents a vulnerability, allowing even end-users to diverge models away from their intended behavior. We aim to explain the causes for this phenomenon and link it to the concept of ``attention sinks'', an emergent LLM behavior crucial for fluency, in which the initial token receives disproportionately high attention scores. Our investigation identifies the neural circuit responsible for attention sinks and shows how long repetitions disrupt this circuit. We extend this finding to other non-repeating sequences that exhibit similar circuit disruptions. To address this, we propose a targeted patch that effectively resolves the issue without negatively impacting the model's overall performance. This study provides a mechanistic explanation for an LLM vulnerability, demonstrating how interpretability can diagnose and address issues, and offering insights that pave the way for more secure and reliable models.

The double hypothesis test (DHT) is a test that allows controlling Type I (producer) and Type II (consumer) errors. It is possible to say whether the batch has a defect rate, p, between 1.5 and 2%, or between 2 and 5%, or between 5 and 10%, and so on, until finding a required value for this probability. Using the two probabilities side by side, the Type I error for the lower probability distribution and the Type II error for the higher probability distribution, both can be controlled and minimized. It can be applied in the development or manufacturing process of a batch of components, or in the case of purchasing from a supplier, when the percentage of defects (p) is unknown, considering the technology and/or process available to obtain them. The power of the test is amplified by the joint application of the Limit of Successive Failures (LSF) related to the Renewal Theory. To enable the choice of the most appropriate algorithm for each application. Four distributions are proposed for the Bernoulli event sequence, including their computational efforts: Binomial, Binomial approximated by Poisson, and Binomial approximated by Gaussian (with two variants). Fuzzy logic rules are also applied to facilitate decision-making.

Transformers have become the de facto architecture for a wide range of machine learning tasks, particularly in large language models (LLMs). Despite their remarkable performance, challenges remain in training deep transformer networks, especially regarding the location of layer normalization. While Pre-Norm structures facilitate easier training due to their more prominent identity path, they often yield suboptimal performance compared to Post-Norm. In this paper, we propose $\textbf{HybridNorm}$, a straightforward yet effective hybrid normalization strategy that integrates the advantages of both Pre-Norm and Post-Norm approaches. Specifically, HybridNorm employs QKV normalization within the attention mechanism and Post-Norm in the feed-forward network (FFN) of each transformer block. This design not only stabilizes training but also enhances performance, particularly in the context of LLMs. Comprehensive experiments in both dense and sparse architectures show that HybridNorm consistently outperforms both Pre-Norm and Post-Norm approaches, achieving state-of-the-art results across various benchmarks. These findings highlight the potential of HybridNorm as a more stable and effective technique for improving the training and performance of deep transformer models. %Code will be made publicly available. Code is available at https://github.com/BryceZhuo/HybridNorm.

Speaker identity plays a significant role in human communication and is being increasingly used in societal applications, many through advances in machine learning. Speaker identity perception is an essential cognitive phenomenon that can be broadly reduced to two main tasks: recognizing a voice or discriminating between voices. Several studies have attempted to identify acoustic correlates of identity perception to pinpoint salient parameters for such a task. Unlike other communicative social signals, most efforts have yielded inefficacious conclusions. Furthermore, current neurocognitive models of voice identity processing consider the bases of perception as acoustic dimensions such as fundamental frequency, harmonics-to-noise ratio, and formant dispersion. However, these findings do not account for naturalistic speech and within-speaker variability. Representational spaces of current self-supervised models have shown significant performance in various speech-related tasks. In this work, we demonstrate that self-supervised representations from different families (e.g., generative, contrastive, and predictive models) are significantly better for speaker identification over acoustic representations. We also show that such a speaker identification task can be used to better understand the nature of acoustic information representation in different layers of these powerful networks. By evaluating speaker identification accuracy across acoustic, phonemic, prosodic, and linguistic variants, we report similarity between model performance and human identity perception. We further examine these similarities by juxtaposing the encoding spaces of models and humans and challenging the use of distance metrics as a proxy for speaker proximity. Lastly, we show that some models can predict brain responses in Auditory and Language regions during naturalistic stimuli.