Deep reinforcement learning methods exhibit impressive performance on a range of tasks but still struggle on hard exploration tasks in large environments with sparse rewards. To address this, intrinsic rewards can be generated using forward model prediction errors that decrease as the environment becomes known, and incentivize an agent to explore novel states. While prediction-based intrinsic rewards can help agents solve hard exploration tasks, they can suffer from catastrophic forgetting and actually increase at visited states. We first examine the conditions and causes of catastrophic forgetting in grid world environments. We then propose a new method FARCuriosity, inspired by how humans and animals learn. The method depends on fragmentation and recall: an agent fragments an environment based on surprisal, and uses different local curiosity modules (prediction-based intrinsic reward functions) for each fragment so that modules are not trained on the entire environment. At each fragmentation event, the agent stores the current module in long-term memory (LTM) and either initializes a new module or recalls a previously stored module based on its match with the current state. With fragmentation and recall, FARCuriosity achieves less forgetting and better overall performance in games with varied and heterogeneous environments in the Atari benchmark suite of tasks. Thus, this work highlights the problem of catastrophic forgetting in prediction-based curiosity methods and proposes a solution.
Animals and robots navigate through environments by building and refining maps of the space. These maps enable functions including navigating back to home, planning, search, and foraging. In large environments, exploration of the space is a hard problem: agents can become stuck in local regions. Here, we use insights from neuroscience to propose and apply the concept of Fragmentation-and-Recall (FarMap), with agents solving the mapping problem by building local maps via a surprisal-based clustering of space, which they use to set subgoals for spatial exploration. Agents build and use a local map to predict their observations; high surprisal leads to a ``fragmentation event'' that truncates the local map. At these events, the recent local map is placed into long-term memory (LTM), and a different local map is initialized. If observations at a fracture point match observations in one of the stored local maps, that map is recalled (and thus reused) from LTM. The fragmentation points induce a natural online clustering of the larger space, forming a set of intrinsic potential subgoals that are stored in LTM as a topological graph. Agents choose their next subgoal from the set of near and far potential subgoals from within the current local map or LTM, respectively. Thus, local maps guide exploration locally, while LTM promotes global exploration. We evaluate FarMap on complex procedurally-generated spatial environments to demonstrate that this mapping strategy much more rapidly covers the environment (number of agent steps and wall clock time) and is more efficient in active memory usage, without loss of performance.
The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images $<$ few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.
Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data undersampled) regime. This drop in test error flies against classical learning theory on overfitting and has arguably underpinned the success of large models in machine learning. This non-monotonic behavior of test loss depends on the number of data, the dimensionality of the data and the number of model parameters. Here, we briefly describe double descent, then provide an explanation of why double descent occurs in an informal and approachable manner, requiring only familiarity with linear algebra and introductory probability. We provide visual intuition using polynomial regression, then mathematically analyze double descent with ordinary linear regression and identify three interpretable factors that, when simultaneously all present, together create double descent. We demonstrate that double descent occurs on real data when using ordinary linear regression, then demonstrate that double descent does not occur when any of the three factors are ablated. We use this understanding to shed light on recent observations in nonlinear models concerning superposition and double descent. Code is publicly available.
Recent works have examined how deep neural networks, which can solve a variety of difficult problems, incorporate the statistics of training data to achieve their success. However, existing results have been established only in limited settings. In this work, we derive the layerwise weight dynamics of infinite-width neural networks with nonlinear activations trained by gradient descent. We show theoretically that weight updates are aligned with input correlations from intermediate layers weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment result allows us to formulate backpropagation-free learning rules, named Align-zero and Align-ada, that theoretically achieve the same alignment as backpropagation. Finally, we test these learning rules on benchmark problems in feedforward and recurrent neural networks and demonstrate, in wide networks, comparable performance to backpropagation.
Recent works have developed several methods of defending neural networks against adversarial attacks with certified guarantees. However, these techniques can be computationally costly due to the use of certification during training. We develop a new regularizer that is both more efficient than existing certified defenses, requiring only one additional forward propagation through a network, and can be used to train networks with similar certified accuracy. Through experiments on MNIST and CIFAR-10 we demonstrate improvements in training speed and comparable certified accuracy compared to state-of-the-art certified defenses.
Recent works have empirically shown that there exist adversarial examples that can be hidden from neural network interpretability (namely, making network interpretation maps visually similar), or interpretability is itself susceptible to adversarial attacks. In this paper, we theoretically show that with a proper measurement of interpretation, it is actually difficult to prevent prediction-evasion adversarial attacks from causing interpretation discrepancy, as confirmed by experiments on MNIST, CIFAR-10 and Restricted ImageNet. Spurred by that, we develop an interpretability-aware defensive scheme built only on promoting robust interpretation (without the need for resorting to adversarial loss minimization). We show that our defense achieves both robust classification and robust interpretation, outperforming state-of-the-art adversarial training methods against attacks of large perturbation in particular.
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us to propose a general and efficient framework, CNN-Cert, that is capable of certifying robustness on general convolutional neural networks. Our framework is general -- we can handle various architectures including convolutional layers, max-pooling layers, batch normalization layer, residual blocks, as well as general activation functions; our approach is efficient -- by exploiting the special structure of convolutional layers, we achieve up to 17 and 11 times of speed-up compared to the state-of-the-art certification algorithms (e.g. Fast-Lin, CROWN) and 366 times of speed-up compared to the dual-LP approach while our algorithm obtains similar or even better verification bounds. In addition, CNN-Cert generalizes state-of-the-art algorithms e.g. Fast-Lin and CROWN. We demonstrate by extensive experiments that our method outperforms state-of-the-art lower-bound-based certification algorithms in terms of both bound quality and speed.