Neural network configurations with random weights play an important role in the analysis of deep learning. They define the initial loss landscape and are closely related to kernel and random feature methods. Despite the fact that these networks are built out of random matrices, the vast and powerful machinery of random matrix theory has so far found limited success in studying them. A main obstacle in this direction is that neural networks are nonlinear, which prevents the straightforward utilization of many of the existing mathematical results. In this work, we open the door for direct applications of random matrix theory to deep learning by demonstrating that the pointwise nonlinearities typically applied in neural networks can be incorporated into a standard method of proof in random matrix theory known as the moments method.

One way to address safety risks from large language models (LLMs) is to censor dangerous knowledge from their training data. While this removes the explicit information, implicit information can remain scattered across various training documents. Could an LLM infer the censored knowledge by piecing together these implicit hints? As a step towards answering this question, we study inductive out-of-context reasoning (OOCR), a type of generalization in which LLMs infer latent information from evidence distributed across training documents and apply it to downstream tasks without in-context learning. Using a suite of five tasks, we demonstrate that frontier LLMs can perform inductive OOCR. In one experiment we finetune an LLM on a corpus consisting only of distances between an unknown city and other known cities. Remarkably, without in-context examples or Chain of Thought, the LLM can verbalize that the unknown city is Paris and use this fact to answer downstream questions. Further experiments show that LLMs trained only on individual coin flip outcomes can verbalize whether the coin is biased, and those trained only on pairs (x, f(x)) can articulate a definition of f and compute inverses. While OOCR succeeds in a range of cases, we also show that it is unreliable, particularly for smaller LLMs learning complex structures. Overall, the ability of LLMs to "connect the dots" without explicit in-context learning poses a potential obstacle to monitoring and controlling the knowledge acquired by LLMs.

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is to exploit the Bayesian approach by using Bayesian neural networks (BNN). Another shortcoming of NN is the lack of flexibility to customize different distributions for the weights and neurons according to the data, as is often done in probabilistic graphical models. To address these problems, we propose a class of probabilistic neural networks, dubbed natural-parameter networks (NPN), as a novel and lightweight Bayesian treatment of NN.

We present a new framework of applying deep neural networks (DNN) to devise a universal discrete denoiser. Unlike other approaches that utilize supervised learning for denoising, we do not require any additional training data. In such setting, while the ground-truth label, i.e., the clean data, is not available, we devise "pseudolabels" and a novel objective function such that DNN can be trained in a same way as supervised learning to become a discrete denoiser. We experimentally show that our resulting algorithm, dubbed as Neural DUDE, significantly outperforms the previous state-of-the-art in several applications with a systematic rule of choosing the hyperparameter, which is an attractive feature in practice.

Deep neural networks (DNNs) exhibit a surprising structure in their final layer known as neural collapse (NC), and a growing body of works has currently investigated the propagation of neural collapse to earlier layers of DNNs - a phenomenon called deep neural collapse (DNC). However, existing theoretical results are restricted to special cases: linear models, only two layers or binary classification. In contrast, we focus on non-linear models of arbitrary depth in multi-class classification and reveal a surprising qualitative shift. As soon as we go beyond two layers or two classes, DNC stops being optimal for the deep unconstrained features model (DUFM) - the standard theoretical framework for the analysis of collapse. The main culprit is a low-rank bias of multi-layer regularization schemes: this bias leads to optimal solutions of even lower rank than the neural collapse. We support our theoretical findings with experiments on both DUFM and real data, which show the emergence of the low-rank structure in the solution found by gradient descent.

Neural collapse (N C) is a phenomenon observed in classification tasks where top-layer representations collapse into their class means, which become equinorm, equiangular and aligned with the classifiers. These behaviours -- associated with generalization and robustness -- would manifest under specific conditions: models are trained towards zero loss, with noise-free labels belonging to balanced classes, which do not outnumber the model's hidden dimension. Recent studies have explored N C in the absence of one or more of these conditions to extend and capitalize on the associated benefits of ideal geometries. Language modelling presents a curious frontier, as training by token prediction constitutes a classification task where none of the conditions exist: the vocabulary is imbalanced and exceeds the embedding dimension; different tokens might correspond to similar contextual embeddings; and large language models (LLMs) in particular are typically only trained for a few epochs. This paper empirically investigates the impact of scaling the architectures and training of causal language models (CLMs) on their progression towards N C. We find that N C properties that develop with scale (and regularization) are linked to generalization. Moreover, there is evidence of some relationship between N C and generalization independent of scale. Our work thereby underscores the generality of N C as it extends to the novel and more challenging setting of language modelling. Downstream, we seek to inspire further research on the phenomenon to deepen our understanding of LLMs -- and neural networks at large -- and improve existing architectures based on N C-related properties.

Genetic variants (GVs) are defined as differences in the DNA sequences among individuals and play a crucial role in diagnosing and treating genetic diseases. The rapid decrease in next generation sequencing cost, analogous to Moore's Law, has led to an exponential increase in the availability of patient-level GV data. This growth poses a challenge for clinicians who must efficiently prioritize patientspecific GVs and integrate them with existing genomic databases to inform patient management. To addressing the interpretation of GVs, genomic foundation models (GFMs) have emerged. However, these models lack standardized performance assessments, leading to considerable variability in model evaluations. This poses the question: How effectively do deep learning methods classify unknown GVs and align them with clinically-verified GVs? We argue that representation learning, which transforms raw data into meaningful feature spaces, is an effective approach for addressing both indexing and classification challenges. We introduce a large-scale genetic variant dataset, named GV-Rep, featuring variable-length contexts and detailed annotations, designed for deep learning models to learn GV representations across various traits, diseases, tissue types, and experimental contexts. Our contributions are three-fold: (i) Construction of a comprehensive dataset with 7 million records, each labeled with characteristics of the corresponding variants, alongside additional data from 17,548 gene knockout tests across 1,107 cell types, 1,808 variant combinations, and 156 unique clinically-verified GVs from real-world patients.

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs). Existing works have shown the insufficiency of Principal Component Analysis (PCA) straightforwardly applied on the features of DNNs in detecting OoD data from In-Distribution (InD) data. The failure of PCA suggests that the network features residing in OoD and InD are not well separated by simply proceeding in a linear subspace, which instead can be resolved through proper non-linear mappings. In this work, we leverage the framework of Kernel PCA (KPCA) for OoD detection, and seek suitable non-linear kernels that advocate the separability between InD and OoD data in the subspace spanned by the principal components. Besides, explicit feature mappings induced from the devoted taskspecific kernels are adopted so that the KPCA reconstruction error for new test samples can be efficiently obtained with large-scale data. Extensive theoretical and empirical results on multiple OoD data sets and network structures verify the superiority of our KPCA detector in efficiency and efficacy with state-of-the-art detection performance.

We analyze the error rates of the Hamiltonian Monte Carlo algorithm with leapfrog integrator for Bayesian neural network inference.

Deployed machine learning systems require some mechanism to detect out-ofdistribution (OOD) inputs. Existing research mainly focuses on one type of distribution shift: detecting samples from novel classes, absent from the training set. However, real-world systems encounter a broad variety of anomalous inputs, and the OOD literature neglects this diversity. This work categorizes five distinct types of distribution shifts and critically evaluates the performance of recent OOD detection methods on each of them. We publicly release our benchmark under the name BROAD (Benchmarking Resilience Over Anomaly Diversity). We find that while these methods excel in detecting novel classes, their performances are inconsistent across other types of distribution shifts. In other words, they can only reliably detect unexpected inputs that they have been specifically designed to expect. As a first step toward broad OOD detection, we learn a Gaussian mixture generative model for existing detection scores, enabling an ensemble detection approach that is more consistent and comprehensive for broad OOD detection, with improved performances over existing methods. We release code to build BROAD to facilitate a more comprehensive evaluation of novel OOD detectors.