Transformers Provably Solve Parity Efficiently with Chain of Thought

This work provides the first theoretical analysis of training transformers to solve complex problems by recursively generating intermediate states, analogous to fine-tuning for chain-of-thought (CoT) reasoning. We consider training a one-layer transformer to solve the fundamental $k$-parity problem, extending the work on RNNs by Wies et al. (2023). We establish three key results: (1) any finite-precision gradient-based algorithm, without intermediate supervision, requires substantial iterations to solve parity with finite samples. (2) In contrast, when intermediate parities are incorporated into the loss function, our model can learn parity in one gradient update when aided by \emph{teacher forcing}, where ground-truth labels of the reasoning chain are provided at each generation step. (3) Even without teacher forcing, where the model must generate CoT chains end-to-end, parity can be learned efficiently if augmented data is employed to internally verify the soundness of intermediate steps. These results rigorously show that task decomposition and stepwise reasoning naturally arise from optimizing transformers with CoT; moreover, self-consistency checking can improve reasoning ability, aligning with empirical studies of CoT.

Transformers are Minimax Optimal Nonparametric In-Context Learners

In-context learning (ICL) of large language models has proven to be a surprisingly effective method of learning a new task from only a few demonstrative examples. In this paper, we study the efficacy of ICL from the viewpoint of statistical learning theory. We develop approximation and generalization error bounds for a transformer composed of a deep neural network and one linear attention layer, pretrained on nonparametric regression tasks sampled from general function spaces including the Besov space and piecewise $\gamma$-smooth class. We show that sufficiently trained transformers can achieve -- and even improve upon -- the minimax optimal estimation risk in context by encoding the most relevant basis representations during pretraining. Our analysis extends to high-dimensional or sequential data and distinguishes the \emph{pretraining} and \emph{in-context} generalization gaps. Furthermore, we establish information-theoretic lower bounds for meta-learners w.r.t. both the number of tasks and in-context examples. These findings shed light on the roles of task diversity and representation learning for ICL.

Computer Vision for Clinical Gait Analysis: A Gait Abnormality Video Dataset

Clinical gait analysis (CGA) using computer vision is an emerging field in artificial intelligence that faces barriers of accessible, real-world data, and clear task objectives. This paper lays the foundation for current developments in CGA as well as vision-based methods and datasets suitable for gait analysis. We introduce The Gait Abnormality in Video Dataset (GAVD) in response to our review of over 150 current gait-related computer vision datasets, which highlighted the need for a large and accessible gait dataset clinically annotated for CGA. GAVD stands out as the largest video gait dataset, comprising 1874 sequences of normal, abnormal and pathological gaits. Additionally, GAVD includes clinically annotated RGB data sourced from publicly available content on online platforms. It also encompasses over 400 subjects who have undergone clinical grade visual screening to represent a diverse range of abnormal gait patterns, captured in various settings, including hospital clinics and urban uncontrolled outdoor environments. We demonstrate the validity of the dataset and utility of action recognition models for CGA using pretrained models Temporal Segment Networks(TSN) and SlowFast network to achieve video abnormality detection of 94% and 92% respectively when tested on GAVD dataset. A GitHub repository https://github.com/Rahmyyy/GAVD consisting of convenient URL links, and clinically relevant annotation for CGA is provided for over 450 online videos, featuring diverse subjects performing a range of normal, pathological, and abnormal gait patterns.

A Novel Nuanced Conversation Evaluation Framework for Large Language Models in Mental Health

Understanding the conversation abilities of Large Language Models (LLMs) can help lead to its more cautious and appropriate deployment. This is especially important for safety-critical domains like mental health, where someone's life may depend on the exact wording of a response to an urgent question. In this paper, we propose a novel framework for evaluating the nuanced conversation abilities of LLMs. Within it, we develop a series of quantitative metrics developed from literature on using psychotherapy conversation analysis literature. While we ensure that our framework and metrics are transferable by researchers to relevant adjacent domains, we apply them to the mental health field. We use our framework to evaluate several popular frontier LLMs, including some GPT and Llama models, through a verified mental health dataset. Our results show that GPT4 Turbo can perform significantly more similarly to verified therapists than other selected LLMs. We conduct additional analysis to examine how LLM conversation performance varies across specific mental health topics. Our results indicate that GPT4 Turbo performs well in achieving high correlation with verified therapists in particular topics such as Parenting and Relationships. We believe our contributions will help researchers develop better LLMs that, in turn, will more positively support people's lives.

Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscape

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 attention trained on linear regression tasks. In this paper, we study the optimization of a Transformer consisting of a fully connected layer followed by a linear attention layer. The MLP acts as a common nonlinear representation or feature map, greatly enhancing the power of in-context learning. We prove in the mean-field and two-timescale limit that the infinite-dimensional loss landscape for the distribution of parameters, while highly nonconvex, becomes quite benign. We also analyze the second-order stability of mean-field dynamics and show that Wasserstein gradient flow almost always avoids saddle points. Furthermore, we establish novel methods for obtaining concrete improvement rates both away from and near critical points. This represents the first saddle point analysis of mean-field dynamics in general and the techniques are of independent interest.

Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems

In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose mean-field Langevin averaged gradient (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose mean-field Langevin anchored best response (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.

$t^3$-Variational Autoencoder: Learning Heavy-tailed Data with Student's t and Power Divergence

The variational autoencoder (VAE) typically employs a standard normal prior as a regularizer for the probabilistic latent encoder. However, the Gaussian tail often decays too quickly to effectively accommodate the encoded points, failing to preserve crucial structures hidden in the data. In this paper, we explore the use of heavy-tailed models to combat over-regularization. Drawing upon insights from information geometry, we propose $t^3$VAE, a modified VAE framework that incorporates Student's t-distributions for the prior, encoder, and decoder. This results in a joint model distribution of a power form which we argue can better fit real-world datasets. We derive a new objective by reformulating the evidence lower bound as joint optimization of KL divergence between two statistical manifolds and replacing with $\gamma$-power divergence, a natural alternative for power families. $t^3$VAE demonstrates superior generation of low-density regions when trained on heavy-tailed synthetic data. Furthermore, we show that $t^3$VAE significantly outperforms other models on CelebA and imbalanced CIFAR-100 datasets.

Hessian Based Smoothing Splines for Manifold Learning

We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius norm of the Hessian matrix. This leads to a natural definition of smoothing splines on manifolds, which minimizes square error while optimizing a global curvature penalty. The existence and uniqueness of the solution is shown by applying the theory of reproducing kernel Hilbert spaces. The minimizer is expressed as a combination of Green's functions for the biharmonic operator, and 'linear' functions of everywhere vanishing Hessian. Furthermore, we utilize the Hessian estimation procedure from the Hessian Eigenmaps algorithm to approximate the spline loss when the true manifold is unknown. This yields a particularly simple quadratic optimization algorithm for smoothing response values without needing to fit the underlying manifold. Analysis of asymptotic error and robustness are given, as well as discussion of out-of-sample prediction methods and applications.

Predicting the Popularity of Reddit Posts with AI

Social media creates crucial mass changes, as popular posts and opinions cast a significant influence on users' decisions and thought processes. For example, the recent Reddit uprising inspired by r/wallstreetbets which had remarkable economic impact was started with a series of posts on the thread. The prediction of posts that may have a notable impact will allow for the preparation of possible following trends. This study aims to develop a machine learning model capable of accurately predicting the popularity of a Reddit post. Specifically, the model is predicting the number of upvotes a post will receive based on its textual content. I experimented with three different models: a baseline linear regression model, a random forest regression model, and a neural network. I collected Reddit post data from an online data set and analyzed the model's performance when trained on a single subreddit and a collection of subreddits. The results showed that the neural network model performed the best when the loss of the models were compared. With the use of a machine learning model to predict social trends through the reaction users have to post, a better picture of the near future can be envisioned.