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Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model…

Mixtures of linear mixed models (MLMMs) are useful for clustering grouped data and can be estimated by likelihood maximization through the EM algorithm. The conventional approach to determining a suitable number of components is to compare…

Residual networks, as discrete approximations of Ordinary Differential Equations (ODEs), have inspired significant advancements in neural network design, including multistep methods, high-order methods, and multi-particle dynamical systems.…

With the attention mechanism, transformers achieve significant empirical successes. Despite the intuitive understanding that transformers perform relational inference over long sequences to produce desirable representations, we lack a…

Large language models based on the Transformer architecture have demonstrated impressive capabilities to learn in context. However, existing theoretical studies on how this phenomenon arises are limited to the dynamics of a single layer of…

Transformer-based large language models (LLMs) have demonstrated impressive capabilities in a variety of natural language processing (NLP) tasks. Nonetheless, it is challenging to deploy and fine-tune LLMs on mobile edge devices with…

We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…

Multitask learning algorithms are typically designed assuming some fixed, a priori known latent structure shared by all the tasks. However, it is usually unclear what type of latent task structure is the most appropriate for a given…

Universal Approximation Theorems establish the density of various classes of neural network function approximators in $C(K, \mathbb{R}^m)$, where $K \subset \mathbb{R}^n$ is compact. In this paper, we aim to extend these guarantees by…

We show that memory-augmented Transformers can implement the entire class of linear first-order methods (LFOMs), a class that contains gradient descent (GD) and more advanced methods such as conjugate gradient descent (CGD), momentum…

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns:…

Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which…

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its…

Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground…

In recent years, meta-reinforcement learning (meta-RL) algorithm has been proposed to improve sample efficiency in the field of decision-making and control, enabling agents to learn new knowledge from a small number of samples. However,…

Modern cryptographic methods for implementing privacy-preserving LLMs such as \gls{HE} require the LLMs to have a polynomial form. Forming such a representation is challenging because transformers include non-polynomial components, such as…

Transformers empirically perform precise probabilistic reasoning in carefully constructed ``Bayesian wind tunnels'' and in large-scale language models, yet the mechanisms by which gradient-based learning creates the required internal…

Solomonoff Induction is an optimal-in-the-limit unbounded algorithm for sequence prediction, representing a Bayesian mixture of every computable probability distribution and performing close to optimally in predicting any computable…

We study the optimization landscape of the log-likelihood function and the convergence of the Expectation-Maximization (EM) algorithm in latent Gaussian tree models, i.e. tree-structured Gaussian graphical models whose leaf nodes are…

To accelerate learning process with few samples, meta-learning resorts to prior knowledge from previous tasks. However, the inconsistent task distribution and heterogeneity is hard to be handled through a global sharing model…