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Recent language models generate false but plausible-sounding text with surprising frequency. Such “hallucinations” are an obstacle to the usability of language-based AI systems and can harm people who rely upon their outputs. This work shows that there is an inherent statistical lower-bound on the rate that pretrained language models hallucinate certain types of facts, having nothing to do with the transformer LM architecture or data quality. For “arbitrary” facts whose veracity cannot be determined from the training data, we show that hallucinations must occur at a certain rate for language models that satisfy a statistical calibration condition appropriate for generative language models. Specifically, if the maximum probability of any fact is bounded, we show that the probability of generating a hallucination is close to the fraction of facts that occur exactly once in the training data (a “Good-Turing” estimate), even assuming ideal training data without errors. One conclusion is that models pretrained to be sufficiently good predictors (i.e., calibrated) may require post-training to mitigate hallucinations on the type of arbitrary facts that tend to appear once in the training set. However, our analysis also suggests that there is no statistical reason that pretraining will lead to hallucination on facts that tend to appear more than once in the training data (like references to publications such as articles and books, whose hallucinations have been particularly notable and problematic) or on systematic facts (like arithmetic calculations). Therefore, different architectures and learning algorithms may mitigate these latter types of hallucinations. 

An assembly is a large population of neurons whose synchronous firing represents a memory, concept, word, and other cognitive category. Assemblies are believed to provide a bridge between high-level cognitive phenomena and low-level neural activity. Recently, a computational system called the \emph{Assembly Calculus} (AC), with a repertoire of biologically plausible operations on assemblies, has been shown capable of simulating arbitrary space-bounded computation, but also of simulating complex cognitive phenomena such as language, reasoning, and planning. However, the mechanism whereby assemblies can mediate {\em learning} has not been known. Here we present such a mechanism, and prove rigorously that, for simple classification problems defined on distributions of labeled assemblies, a new assembly representing each class can be reliably formed in response to a few stimuli from the class; this assembly is henceforth reliably recalled in response to new stimuli from the same class. Furthermore, such class assemblies will be distinguishable as long as the respective classes are reasonably separated — for example, when they are clusters of similar assemblies, or more generally separable with margin by a linear threshold function. To prove these results, we draw on random graph theory with dynamic edge weights to estimate sequences of activated vertices, yielding strong generalizations of previous calculations and theorems in this field over the past five years. These theorems are backed up by experiments demonstrating the successful formation of assemblies which represent concept classes on synthetic data drawn from such distributions, and also on MNIST, which lends itself to classification through one assembly per digit. Seen as a learning algorithm, this mechanism is entirely online, generalizes from very few samples, and requires only mild supervision — all key attributes of learning in a model of the brain. We argue that this learning mechanism, supported by separate sensory pre-processing mechanisms for extracting attributes, such as edges or phonemes, from real world data, can be the basis of biological learning in cortex. 

In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We consider the setting where all target tasks can be represented in the span of a small number of unknown linear or nonlinear features of the input data. We propose a lifelong learning algorithm that maintains and refines the internal feature representation. We prove that for any desired accuracy on all tasks, the dimension of the representation remains close to that of the underlying representation. The resulting sample complexity improves significantly on existing bounds. In the setting of linear features, our algorithm is provably efficient and the sample complexity for input dimension d, m tasks with k features up to error ϵ is O~(dk1.5/ϵ+km/ϵ). We also prove a matching lower bound for any lifelong learning algorithm that uses a single task learner as a black box. We complement our analysis with an empirical study, including a heuristic lifelong learning algorithm for deep neural networks. Our method performs favorably on challenging realistic image datasets compared to state-of-the-art continual learning methods. 

The success of gradient descent in ML and especially for learning neural networks is remarkable and robust. In the context of how the brain learns, one aspect of gradient descent that appears biologically difficult to realize (if not implausible) is that its updates rely on feedback from later layers to earlier layers through the same connections. Such bidirected links are relatively few in brain networks, and even when reciprocal connections exist, they may not be equi-weighted. Random Feedback Alignment (Lillicrap et al., 2016), where the backward weights are random and fixed, has been proposed as a bio-plausible alternative and found to be effective empirically. We investigate how and when feedback alignment (FA) works, focusing on one of the most basic problems with layered structure n×m, the goal is to find a low rank factorization Zn×rWr×m that minimizes the error ∥ZW−Y∥F. Gradient descent solves this problem optimally. We show that FA finds the optimal solution when r≥rank(Y). We also shed light on how FA works. It is observed empirically that the forward weight matrices and (random) feedback matrices come closer during FA updates. Our analysis rigorously derives this phenomenon and shows how it facilitates convergence of FA*, a closely related variant of FA. We also show that FA can be far from optimal when r