Rahul Ramesh

Ashwin De Silva, Rahul Ramesh, Carey E. Priebe et al.

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

Rahul Ramesh, Jialin Mao, Itay Griniasty et al.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of 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 even 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) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

Rahul Ramesh, Ekdeep Singh Lubana, Mikail Khona et al.

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities, potentially yielding a combinatorial explosion of what operations it can perform on an input. Motivated by the above, we train autoregressive Transformer models on a synthetic data-generating process that involves compositions of a set of well-defined monolithic capabilities. Through a series of extensive and systematic experiments on this data-generating process, we show that: (1) autoregressive Transformers can learn compositional structures from small amounts of training data and generalize to exponentially or even combinatorially many functions; (2) generating intermediate outputs when composing functions is more effective for generalizing to new, unseen compositions than not generating any intermediate outputs (3) biases in the order of the compositions in the training data result in Transformers that fail to compose some combinations of functions; and (4) the attention layers select which capability to apply while the feed-forward layers execute the selected capability.

Rahul Ramesh, Anthony Bisulco, Ronald W. DiTullio et al.

We show that many perception tasks, from visual recognition, semantic segmentation, optical flow, depth estimation to vocalization discrimination, are highly redundant functions of their input data. Images or spectrograms, projected into different subspaces, formed by orthogonal bases in pixel, Fourier or wavelet domains, can be used to solve these tasks remarkably well regardless of whether it is the top subspace where data varies the most, some intermediate subspace with moderate variability--or the bottom subspace where data varies the least. This phenomenon occurs because different subspaces have a large degree of redundant information relevant to the task.

Ashwin De Silva, Rahul Ramesh, Rubing Yang et al.

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10. Code at https://github.com/neurodata/prolearn.

Yansong Gao, Rahul Ramesh, Pratik Chaudhari

What is the best way to exploit extra data -- be it unlabeled data from the same task, or labeled data from a related task -- to learn a given task? This paper formalizes the question using the theory of reference priors. Reference priors are objective, uninformative Bayesian priors that maximize the mutual information between the task and the weights of the model. Such priors enable the task to maximally affect the Bayesian posterior, e.g., reference priors depend upon the number of samples available for learning the task and for very small sample sizes, the prior puts more probability mass on low-complexity models in the hypothesis space. This paper presents the first demonstration of reference priors for medium-scale deep networks and image-based data. We develop generalizations of reference priors and demonstrate applications to two problems. First, by using unlabeled data to compute the reference prior, we develop new Bayesian semi-supervised learning methods that remain effective even with very few samples per class. Second, by using labeled data from the source task to compute the reference prior, we develop a new pretraining method for transfer learning that allows data from the target task to maximally affect the Bayesian posterior. Empirical validation of these methods is conducted on image classification datasets. Code is available at https://github.com/grasp-lyrl/deep_reference_priors.

Rahul Ramesh, Pratik Chaudhari

This paper argues that continual learning methods can benefit by splitting the capacity of the learner across multiple models. We use statistical learning theory and experimental analysis to show how multiple tasks can interact with each other in a non-trivial fashion when a single model is trained on them. The generalization error on a particular task can improve when it is trained with synergistic tasks, but can also deteriorate when trained with competing tasks. This theory motivates our method named Model Zoo which, inspired from the boosting literature, grows an ensemble of small models, each of which is trained during one episode of continual learning. We demonstrate that Model Zoo obtains large gains in accuracy on a variety of continual learning benchmark problems. Code is available at https://github.com/grasp-lyrl/modelzoo_continual.

Mikail Khona, Maya Okawa, Jan Hula et al.

Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these protocols, the underlying mechanisms of stepwise inference have remained elusive. To address this, we propose to study autoregressive Transformer models on a synthetic task that embodies the multi-step nature of problems where stepwise inference is generally most useful. Specifically, we define a graph navigation problem wherein a model is tasked with traversing a path from a start to a goal node on the graph. Despite is simplicity, we find we can empirically reproduce and analyze several phenomena observed at scale: (i) the stepwise inference reasoning gap, the cause of which we find in the structure of the training data; (ii) a diversity-accuracy tradeoff in model generations as sampling temperature varies; (iii) a simplicity bias in the model's output; and (iv) compositional generalization and a primacy bias with in-context exemplars. Overall, our work introduces a grounded, synthetic framework for studying stepwise inference and offers mechanistic hypotheses that can lay the foundation for a deeper understanding of this phenomenon.

Kento Nishi, Rahul Ramesh, Maya Okawa et al.

Knowledge Editing (KE) algorithms alter models' weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations. However, recent work has shown that applying KE can adversely affect models' broader factual recall accuracy and diminish their reasoning abilities. Although these studies give insights into the potential harms of KE algorithms, e.g., performance evaluations on benchmarks, little is understood about why such destructive failures occur. Motivated by this, we define a novel synthetic task in which a Transformer is trained from scratch to internalize a "structured" knowledge graph. The structure enforces relationships between entities of the graph, such that editing a factual association has "trickling effects" on other entities (e.g., altering X's parent is Y to Z affects who X's siblings' parent is). Through evaluations of edited models on this task, we show that KE inadvertently affects representations of entities beyond the targeted one, distorting relevant structures that allow a model to infer unseen knowledge about an entity. We call this phenomenon representation shattering and demonstrate that it degrades models' factual recall and reasoning performance. We further corroborate our findings in naturalistic settings with pre-trained Llama and Mamba models as well. Overall, our work yields a precise mechanistic hypothesis to explain why KE has adverse effects on model abilities.

Anthony Bisulco, Rahul Ramesh, Randall Balestriero et al.

Masked Autoencoders (MAEs) have emerged as a powerful pretraining technique for vision foundation models. Despite their effectiveness, they require extensive hyperparameter tuning (masking ratio, patch size, encoder/decoder layers) when applied to novel datasets. While prior theoretical works have analyzed MAEs in terms of their attention patterns and hierarchical latent variable models, the connection between MAE hyperparameters and performance on downstream tasks is relatively unexplored. This work investigates how MAEs learn spatial correlations in the input image. We analytically derive the features learned by a linear MAE and show that masking ratio and patch size can be used to select for features that capture short- and long-range spatial correlations. We extend this analysis to non-linear MAEs to show that MAE representations adapt to spatial correlations in the dataset, beyond second-order statistics. Finally, we discuss some insights on how to select MAE hyper-parameters in practice.

Jialin Mao, Itay Griniasty, Han Kheng Teoh et al.

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.

Ashwin De Silva, Rahul Ramesh, Lyle Ungar et al.

Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences.

Arjun Manoharan, Rahul Ramesh, Balaraman Ravindran

Option discovery and skill acquisition frameworks are integral to the functioning of a Hierarchically organized Reinforcement learning agent. However, such techniques often yield a large number of options or skills, which can potentially be represented succinctly by filtering out any redundant information. Such a reduction can reduce the required computation while also improving the performance on a target task. In order to compress an array of option policies, we attempt to find a policy basis that accurately captures the set of all options. In this work, we propose Option Encoder, an auto-encoder based framework with intelligently constrained weights, that helps discover a collection of basis policies. The policy basis can be used as a proxy for the original set of skills in a suitable hierarchically organized framework. We demonstrate the efficacy of our method on a collection of grid-worlds and on the high-dimensional Fetch-Reach robotic manipulation task by evaluating the obtained policy basis on a set of downstream tasks.

Rahul Ramesh, Manan Tomar, Balaraman Ravindran

The options framework in reinforcement learning models the notion of a skill or a temporally extended sequence of actions. The discovery of a reusable set of skills has typically entailed building options, that navigate to bottleneck states. This work adopts a complementary approach, where we attempt to discover options that navigate to landmark states. These states are prototypical representatives of well-connected regions and can hence access the associated region with relative ease. In this work, we propose Successor Options, which leverages Successor Representations to build a model of the state space. The intra-option policies are learnt using a novel pseudo-reward and the model scales to high-dimensional spaces easily. Additionally, we also propose an Incremental Successor Options model that iterates between constructing Successor Representations and building options, which is useful when robust Successor Representations cannot be built solely from primitive actions. We demonstrate the efficacy of our approach on a collection of grid-worlds, and on the high-dimensional robotic control environment of Fetch.

Revanth Reddy, Rahul Ramesh, Ameet Deshpande et al.

Deep Learning has managed to push boundaries in a wide variety of tasks. One area of interest is to tackle problems in reasoning and understanding, with an aim to emulate human intelligence. In this work, we describe a deep learning model that addresses the reasoning task of question-answering on categorical plots. We introduce a novel architecture FigureNet, that learns to identify various plot elements, quantify the represented values and determine a relative ordering of these statistical values. We test our model on the FigureQA dataset which provides images and accompanying questions for scientific plots like bar graphs and pie charts, augmented with rich annotations. Our approach outperforms the state-of-the-art Relation Networks baseline by approximately $7\%$ on this dataset, with a training time that is over an order of magnitude lesser.

Sahil Sharma, Aravind Suresh, Rahul Ramesh et al.

Deep Reinforcement Learning (DRL) methods have performed well in an increasing numbering of high-dimensional visual decision making domains. Among all such visual decision making problems, those with discrete action spaces often tend to have underlying compositional structure in the said action space. Such action spaces often contain actions such as go left, go up as well as go diagonally up and left (which is a composition of the former two actions). The representations of control policies in such domains have traditionally been modeled without exploiting this inherent compositional structure in the action spaces. We propose a new learning paradigm, Factored Action space Representations (FAR) wherein we decompose a control policy learned using a Deep Reinforcement Learning Algorithm into independent components, analogous to decomposing a vector in terms of some orthogonal basis vectors. This architectural modification of the control policy representation allows the agent to learn about multiple actions simultaneously, while executing only one of them. We demonstrate that FAR yields considerable improvements on top of two DRL algorithms in Atari 2600: FARA3C outperforms A3C (Asynchronous Advantage Actor Critic) in 9 out of 14 tasks and FARAQL outperforms AQL (Asynchronous n-step Q-Learning) in 9 out of 13 tasks.