This paper investigates the information encoded in the embeddings of large language models (LLMs). We conduct simulations to analyze the representation entropy and discover a power law relationship with model sizes. Building upon this observation, we propose a theory based on (conditional) entropy to elucidate the scaling law phenomenon. Furthermore, we delve into the auto-regressive structure of LLMs and examine the relationship between the last token and previous context tokens using information theory and regression techniques. Specifically, we establish a theoretical connection between the information gain of new tokens and ridge regression. Additionally, we explore the effectiveness of Lasso regression in selecting meaningful tokens, which sometimes outperforms the closely related attention weights. Finally, we conduct controlled experiments, and find that information is distributed across tokens, rather than being concentrated in specific "meaningful" tokens alone.

This study examined the use of voice recognition technology in perioperative services (Periop) to enable Periop staff to record workflow milestones using mobile technology. The use of mobile technology to improve patient flow and quality of care could be facilitated if such voice recognition technology could be made robust. The goal of this experiment was to allow the Periop staff to provide care without being interrupted with data entry and querying tasks. However, the results are generalizable to other situations where an engineering manager attempts to improve communication performance using mobile technology. This study enhanced Google's voice recognition capability by using post-processing classifiers (i.e., bag-of-sentences, support vector machine, and maximum entropy). The experiments investigated three factors (original phrasing, reduced phrasing, and personalized phrasing) at three levels (zero training repetition, 5 training repetitions, and 10 training repetitions). Results indicated that personal phrasing yielded the highest correctness and that training the device to recognize an individual's voice improved correctness as well. Although simplistic, the bag-of-sentences classifier significantly improved voice recognition correctness. The classification efficiency of the maximum entropy and support vector machine algorithms was found to be nearly identical. These results suggest that engineering managers could significantly enhance Google's voice recognition technology by using post-processing techniques, which would facilitate its use in health care and other applications.

This survey paper provides a comprehensive analysis of big data algorithms in recommendation systems, addressing the lack of depth and precision in existing literature. It proposes a two-pronged approach: a thorough analysis of current algorithms and a novel, hierarchical taxonomy for precise categorization. The taxonomy is based on a tri-level hierarchy, starting with the methodology category and narrowing down to specific techniques. Such a framework allows for a structured and comprehensive classification of algorithms, assisting researchers in understanding the interrelationships among diverse algorithms and techniques. Covering a wide range of algorithms, this taxonomy first categorizes algorithms into four main analysis types: User and Item Similarity-Based Methods, Hybrid and Combined Approaches, Deep Learning and Algorithmic Methods, and Mathematical Modeling Methods, with further subdivisions into sub-categories and techniques. The paper incorporates both empirical and experimental evaluations to differentiate between the techniques. The empirical evaluation ranks the techniques based on four criteria. The experimental assessments rank the algorithms that belong to the same category, sub-category, technique, and sub-technique. Also, the paper illuminates the future prospects of big data techniques in recommendation systems, underscoring potential advancements and opportunities for further research in this field

We study the problem of online uncertainty quantification, such as that encountered in time-series forecasting. Our goal is to produce a prediction set at each time, based on all previous information, that contain the true label with a specified coverage probability. Such prediction sets are useful to the point of being requirements in many sequential problems, including medicine [Robinson, 1978], robotics [Lindemann et al., 2023], finance [Mykland, 2003], and epidemiology [Cramer et al., 2022]. Given this broad utility, it comes as no surprise that prediction sets have been studied for approximately one hundred years (and possibly more; see Section 1.1 of Tian et al. [2022]).

A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive performance. However, in order to optimally plan maintenance operations, it is also important to quantify the uncertainty inherent to the predictions. This issue can be addressed by turning standard frequentist neural networks into Bayesian neural networks, which are naturally capable of providing confidence intervals around the estimates. Several methods exist for training those models. Researchers have focused mostly on parametric variational inference and sampling-based techniques, which notoriously suffer from limited approximation power and large computational burden, respectively. In this work, we use Stein variational gradient descent, a recently proposed algorithm for approximating intractable distributions that overcomes the drawbacks of the aforementioned techniques. In particular, we show through experimental studies on simulated run-to-failure turbofan engine degradation data that Bayesian deep learning models trained via Stein variational gradient descent consistently outperform with respect to convergence speed and predictive performance both the same models trained via parametric variational inference and their frequentist counterparts trained via backpropagation. Furthermore, we propose a method to enhance performance based on the uncertainty information provided by the Bayesian models. We release the source code at https://github.com/lucadellalib/bdl-rul-svgd.

Large language models have emerged as a versatile tool but are challenging to apply to tasks lacking large inference budgets and large in-domain training sets. This work formalizes these constraints and distinguishes four important variables: the pretraining budget (for training before the target domain is known), the specialization budget (for training after the target domain is known), the inference budget, and the in-domain training set size. Across these settings, we compare different approaches from the machine learning literature. Limited by inference cost, we find better alternatives to the standard practice of training very large vanilla transformer models. In particular, we show that hyper-networks and mixture of experts have better perplexity for large pretraining budgets, while small models trained on importance sampled datasets are attractive for large specialization budgets.

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate $1/\textit{width}$ but at late time exhibit a rate $\textit{width}^{-c}$, where $c$ depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already exist interpretable semi-parametric regression methods for large-scale applications that take into account non-linearity in the data, the complexity of the models is still often limited. One of the main challenges is the absence of interactions in these models, which are left out for the sake of better interpretability but also due to impractical computational costs. To overcome this limitation, we propose a new approach using a factorization method to derive a highly scalable higher-order tensor product spline model. Our method allows for the incorporation of all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We further develop a meaningful penalization scheme and examine the induced optimization problem. We conclude by evaluating the predictive and estimation performance of our method.

The existence of "lottery tickets" arXiv:1803.03635 at or near initialization raises the tantalizing question of whether large models are necessary in deep learning, or whether sparse networks can be quickly identified and trained without ever training the dense models that contain them. However, efforts to find these sparse subnetworks without training the dense model ("pruning at initialization") have been broadly unsuccessful arXiv:2009.08576. We put forward a theoretical explanation for this, based on the model's effective parameter count, $p_\text{eff}$, given by the sum of the number of non-zero weights in the final network and the mutual information between the sparsity mask and the data. We show the Law of Robustness of arXiv:2105.12806 extends to sparse networks with the usual parameter count replaced by $p_\text{eff}$, meaning a sparse neural network which robustly interpolates noisy data requires a heavily data-dependent mask. We posit that pruning during and after training outputs masks with higher mutual information than those produced by pruning at initialization. Thus two networks may have the same sparsities, but differ in effective parameter count based on how they were trained. This suggests that pruning near initialization may be infeasible and explains why lottery tickets exist, but cannot be found fast (i.e. without training the full network). Experiments on neural networks confirm that information gained during training may indeed affect model capacity.

The potential harms of the under-representation of minorities in training data, particularly in multi-modal settings, is a well-recognized concern. While there has been extensive effort in detecting such under-representation, resolution has remained a challenge. With recent advancements in generative AI, large language models and foundation models have emerged as versatile tools across various domains. In this paper, we propose Chameleon, a system that efficiently utilizes these tools to augment a data set with a minimal addition of synthetically generated tuples, in order to enhance the coverage of the under-represented groups. Our system follows a rejection sampling approach to ensure the generated tuples have a high quality and follow the underlying distribution. In order to minimize the rejection chance of the generated tuples, we propose multiple strategies for providing a guide for the foundation model. Our experiment results, in addition to confirming the efficiency of our proposed algorithms, illustrate the effectiveness of our approach, as the unfairness of the model in a downstream task significantly dropped after data repair using Chameleon.