Knowledge Editing (KE) algorithms alter models’ weights to perform targeted updates to incorrect, outdated, or otherwise unwanted factual associations.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.

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. To unravel the underlying mechanisms of stepwise inference 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. 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 trade-off 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.

Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing simple logical operations. 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 aim to assess in this paper “how capable can a transformer become?”. Specifically, we train autoregressive Transformer models on a 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) composing functions by generating intermediate outputs is more effective at generalizing to unseen compositions, compared to generating no intermediate outputs; (3) biases in the order of the compositions in the training data, results in Transformers that fail to compose some combinations of functions; and (4) the attention layers seem to select the capability to apply while the feed-forward layers execute the capability.

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.

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. Code is available at https://github.com/grasp-lyrl/picture_of_space_of_tasks.

Generalization error always improves with more in-distribution data. However, it is an open question what happens as we add out-of-distribution (OOD) data. Intuitively, if the OOD data is quite different, it seems more data would harm generalization error, though if the OOD data are sufficiently similar, much empirical evidence suggests that OOD data can actually improve generalization error. We show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the amount of OOD data. Specifically, we prove that generalization error can improve with small amounts of OOD data, and then get worse than no OOD data with larger amounts. In other words, there is value in training on small amounts of OOD data. We analytically demonstrate these results via Fisher’s Linear Discriminant on synthetic datasets, and empirically demonstrate them via deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet. 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.

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

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. In this work, we instead adopt 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 since it does not construct an explicit graph of the entire state space. 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.

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.