Taming AI Bots: Controllability of Neural States in Large Language Models

We tackle the question of whether an agent can, by suitable choice of prompts, control an AI bot to any state. To that end, we first introduce a formal definition of ``meaning'' that is amenable to analysis. Then, we characterize ``meaningful data'' on which large language models (LLMs) are ostensibly trained, and ``well-trained LLMs'' through conditions that are largely met by today's LLMs. While a well-trained LLM constructs an embedding space of meanings that is Euclidean, meanings themselves do not form a vector (linear) subspace, but rather a quotient space within. We then characterize the subset of meanings that can be reached by the state of the LLMs for some input prompt, and show that a well-trained bot can reach any meaning albeit with small probability. We then introduce a stronger notion of controllability as {\em almost certain reachability}, and show that, when restricted to the space of meanings, an AI bot is controllable. We do so after introducing a functional characterization of attentive AI bots, and finally derive necessary and sufficient conditions for controllability. The fact that AI bots are controllable means that an adversary could steer them towards any state. However, the sampling process can be designed to counteract adverse actions and avoid reaching undesirable regions of state space before their boundary is crossed.

Learning Capacity: A Measure of the Effective Dimensionality of a Model

We exploit a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to define a "learning capacity'' which is a measure of the effective dimensionality of a model. We show that the learning capacity is a tiny fraction of the number of parameters for many deep networks trained on typical datasets, depends upon the number of samples used for training, and is numerically consistent with notions of capacity obtained from the PAC-Bayesian framework. The test error as a function of the learning capacity does not exhibit double descent. We show that the learning capacity of a model saturates at very small and very large sample sizes; this provides guidelines, as to whether one should procure more data or whether one should search for new architectures, to improve performance. We show how the learning capacity can be used to understand the effective dimensionality, even for non-parametric models such as random forests and $k$-nearest neighbor classifiers.

The Training Process of Many Deep Networks Explores the Same Low-Dimensional Manifold

We develop information-geometric techniques to analyze the trajectories of the predictions of deep networks during training. By examining the underlying high-dimensional probabilistic models, we reveal that the training process explores an effectively low-dimensional manifold. Networks with a wide range of architectures, sizes, trained using different optimization methods, regularization techniques, data augmentation techniques, and weight initializations lie on the same manifold in the prediction space. We study the details of this manifold to find that networks with different architectures follow distinguishable trajectories but other factors have a minimal influence; larger networks train along a similar manifold as that of smaller networks, just faster; and networks initialized at very different parts of the prediction space converge to the solution along a similar manifold.

Fast Diffusion Probabilistic Model Sampling through the lens of Backward Error Analysis

Denoising diffusion probabilistic models (DDPMs) are a class of powerful generative models. The past few years have witnessed the great success of DDPMs in generating high-fidelity samples. A significant limitation of the DDPMs is the slow sampling procedure. DDPMs generally need hundreds or thousands of sequential function evaluations (steps) of neural networks to generate a sample. This paper aims to develop a fast sampling method for DDPMs requiring much fewer steps while retaining high sample quality. The inference process of DDPMs approximates solving the corresponding diffusion ordinary differential equations (diffusion ODEs) in the continuous limit. This work analyzes how the backward error affects the diffusion ODEs and the sample quality in DDPMs. We propose fast sampling through the \textbf{Restricting Backward Error schedule (RBE schedule)} based on dynamically moderating the long-time backward error. Our method accelerates DDPMs without any further training. Our experiments show that sampling with an RBE schedule generates high-quality samples within only 8 to 20 function evaluations on various benchmark datasets. We achieved 12.01 FID in 8 function evaluations on the ImageNet $128\times128$, and a $20\times$ speedup compared with previous baseline samplers.

Mesh Strikes Back: Fast and Efficient Human Reconstruction from RGB videos

Human reconstruction and synthesis from monocular RGB videos is a challenging problem due to clothing, occlusion, texture discontinuities and sharpness, and framespecific pose changes. Many methods employ deferred rendering, NeRFs and implicit methods to represent clothed humans, on the premise that mesh-based representations cannot capture complex clothing and textures from RGB, silhouettes, and keypoints alone. We provide a counter viewpoint to this fundamental premise by optimizing a SMPL+D mesh and an efficient, multi-resolution texture representation using only RGB images, binary silhouettes and sparse 2D keypoints. Experimental results demonstrate that our approach is more capable of capturing geometric details compared to visual hull, mesh-based methods. We show competitive novel view synthesis and improvements in novel pose synthesis compared to NeRF-based methods, which introduce noticeable, unwanted artifacts. By restricting the solution space to the SMPL+D model combined with differentiable rendering, we obtain dramatic speedups in compute, training times (up to 24x) and inference times (up to 192x). Our method therefore can be used as is or as a fast initialization to NeRF-based methods.

A picture of the space of typical learnable tasks

We develop a technique to analyze representations learned by deep networks when they are trained on different tasks using supervised, meta- and contrastive learning. We develop a technique to visualize such representations using an isometric embedding of the space of probabilistic models into a lower-dimensional space, i.e., one that preserves pairwise distances. We discover the following surprising phenomena that shed light upon the structure in the space of learnable tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) fine-tuning a model upon a sub-task does not change the representation much if the model was trained for a large number of epochs; (5) episodic meta-learning algorithms fit similar models eventually as that of supervised learning, even if the two traverse different trajectories during training; (6) contrastive learning methods trained on different datasets learn similar representations. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

Data drift correction via time-varying importance weight estimator

Real-world deployment of machine learning models is challenging when data evolves over time. And data does evolve over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a novel time-varying importance weight estimator that can detect gradual shifts in the distribution of data. Such an importance weight estimator allows the training method to selectively sample past data -- not just similar data from the past like a standard importance weight estimator would but also data that evolved in a similar fashion in the past. Our time-varying importance weight is quite general. We demonstrate different ways of implementing it that exploit some known structure in the evolution of data. We demonstrate and evaluate this approach on a variety of problems ranging from supervised learning tasks (multiple image classification datasets) where the data undergoes a sequence of gradual shifts of our design to reinforcement learning tasks (robotic manipulation and continuous control) where data undergoes a shift organically as the policy or the task changes.

The Value of Out-of-Distribution Data

More data helps us generalize to a task. But real datasets can contain out-of-distribution (OOD) data; this can come in the form of heterogeneity such as intra-class variability but also in the form of temporal shifts or concept drifts. We demonstrate a counter-intuitive phenomenon for such problems: generalization error of the task can be a non-monotonic function of the number of OOD samples; a small number of OOD samples can improve generalization but if the number of OOD samples is beyond a threshold, then the generalization error can deteriorate. We also show that if we know which samples are OOD, then using a weighted objective between the target and OOD samples ensures that the generalization error decreases monotonically. We demonstrate and analyze this issue using linear classifiers on synthetic datasets and medium-sized neural networks on CIFAR-10.

MammoDL: Mammographic Breast Density Estimation using Federated Learning

Assessing breast cancer risk from imaging remains a subjective process, in which radiologists employ computer aided detection (CAD) systems or qualitative visual assessment to estimate breast percent density (PD). More advanced machine learning (ML) models have become the most promising way to quantify breast cancer risk for early, accurate, and equitable diagnoses, but training such models in medical research is often restricted to small, single-institution data. Since patient demographics and imaging characteristics may vary considerably across imaging sites, models trained on single-institution data tend not to generalize well. In response to this problem, MammoDL is proposed, an open-source software tool that leverages UNet architecture to accurately estimate breast PD and complexity from digital mammography (DM). With the Open Federated Learning (OpenFL) library, this solution enables secure training on datasets across multiple institutions. MammoDL is a leaner, more flexible model than its predecessors, boasting improved generalization due to federation-enabled training on larger, more representative datasets.

Machine Learning Models Are Not Necessarily Biased When Constructed Properly: Evidence from Neuroimaging Studies

Despite the great promise that machine learning has offered in many fields of medicine, it has also raised concerns about potential biases and poor generalization across genders, age distributions, races and ethnicities, hospitals, and data acquisition equipment and protocols. In the current study, and in the context of three brain diseases, we provide experimental data which support that when properly trained, machine learning models can generalize well across diverse conditions and do not suffer from biases. Specifically, by using multi-study magnetic resonance imaging consortia for diagnosing Alzheimer's disease, schizophrenia, and autism spectrum disorder, we find that, the accuracy of well-trained models is consistent across different subgroups pertaining to attributes such as gender, age, and racial groups, as also different clinical studies. We find that models that incorporate multi-source data from demographic, clinical, genetic factors and cognitive scores are also unbiased. These models have better predictive accuracy across subgroups than those trained only with structural measures in some cases but there are also situations when these additional features do not help.