Revisiting Dynamic Evaluation: Online Adaptation for Large Language Models

We consider the problem of online fine tuning the parameters of a language model at test time, also known as dynamic evaluation. While it is generally known that this approach improves the overall predictive performance, especially when considering distributional shift between training and evaluation data, we here emphasize the perspective that online adaptation turns parameters into temporally changing states and provides a form of context-length extension with memory in weights, more in line with the concept of memory in neuroscience. We pay particular attention to the speed of adaptation (in terms of sample efficiency),sensitivity to the overall distributional drift, and the computational overhead for performing gradient computations and parameter updates. Our empirical study provides insights on when online adaptation is particularly interesting. We highlight that with online adaptation the conceptual distinction between in-context learning and fine tuning blurs: both are methods to condition the model on previously observed tokens.

Kalman Filter for Online Classification of Non-Stationary Data

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

Optimal Preconditioning and Fisher Adaptive Langevin Sampling

We define an optimal preconditioning for the Langevin diffusion by analytically maximizing the expected squared jumped distance. This yields as the optimal preconditioning an inverse Fisher information covariance matrix, where the covariance matrix is computed as the outer product of log target gradients averaged under the target. We apply this result to the Metropolis adjusted Langevin algorithm (MALA) and derive a computationally efficient adaptive MCMC scheme that learns the preconditioning from the history of gradients produced as the algorithm runs. We show in several experiments that the proposed algorithm is very robust in high dimensions and significantly outperforms other methods, including a closely related adaptive MALA scheme that learns the preconditioning with standard adaptive MCMC as well as the position-dependent Riemannian manifold MALA sampler.

Personalized Federated Learning with Exact Stochastic Gradient Descent

In Federated Learning (FL), datasets across clients tend to be heterogeneous or personalized, and this poses challenges to the convergence of standard FL schemes that do not account for personalization. To address this, we present a new approach for personalized FL that achieves exact stochastic gradient descent (SGD) minimization. We start from the FedPer (Arivazhagan et al., 2019) neural network (NN) architecture for personalization, whereby the NN has two types of layers: the first ones are the common layers across clients, while the few final ones are client-specific and are needed for personalization. We propose a novel SGD-type scheme where, at each optimization round, randomly selected clients perform gradient-descent updates over their client-specific weights towards optimizing the loss function on their own datasets, without updating the common weights. At the final update, each client computes the joint gradient over both client-specific and common weights and returns the gradient of common parameters to the server. This allows to perform an exact and unbiased SGD step over the full set of parameters in a distributed manner, i.e. the updates of the personalized parameters are performed by the clients and those of the common ones by the server. Our method is superior to FedAvg and FedPer baselines in multi-class classification benchmarks such as Omniglot, CIFAR-10, MNIST, Fashion-MNIST, and EMNIST and has much lower computational complexity per round.

Gradient Estimation with Discrete Stein Operators

Gradient estimation -- approximating the gradient of an expectation with respect to the parameters of a distribution -- is central to the solution of many machine learning problems. However, when the distribution is discrete, most common gradient estimators suffer from excessive variance. To improve the quality of gradient estimation, we introduce a variance reduction technique based on Stein operators for discrete distributions. We then use this technique to build flexible control variates for the REINFORCE leave-one-out estimator. Our control variates can be adapted online to minimize the variance and do not require extra evaluations of the target function. In benchmark generative modeling tasks such as training binary variational autoencoders, our gradient estimator achieves substantially lower variance than state-of-the-art estimators with the same number of function evaluations.

Double Control Variates for Gradient Estimation in Discrete Latent Variable Models

Stochastic gradient-based optimisation for discrete latent variable models is challenging due to the high variance of gradients. We introduce a variance reduction technique for score function estimators that makes use of double control variates. These control variates act on top of a main control variate, and try to further reduce the variance of the overall estimator. We develop a double control variate for the REINFORCE leave-one-out estimator using Taylor expansions. For training discrete latent variable models, such as variational autoencoders with binary latent variables, our approach adds no extra computational cost compared to standard training with the REINFORCE leave-one-out estimator. We apply our method to challenging high-dimensional toy examples and training variational autoencoders with binary latent variables. We show that our estimator can have lower variance compared to other state-of-the-art estimators.

Entropy-based adaptive Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be sensitive to the choice of mass matrix used therein. We develop a gradient-based algorithm that allows for the adaptation of the mass matrix by encouraging the leapfrog integrator to have high acceptance rates while also exploring all dimensions jointly. In contrast to previous work that adapt the hyperparameters of HMC using some form of expected squared jumping distance, the adaptation strategy suggested here aims to increase sampling efficiency by maximizing an approximation of the proposal entropy. We illustrate that using multiple gradients in the HMC proposal can be beneficial compared to a single gradient-step in Metropolis-adjusted Langevin proposals. Empirical evidence suggests that the adaptation method can outperform different versions of HMC schemes by adjusting the mass matrix to the geometry of the target distribution and by providing some control on the integration time.

Sequential Changepoint Detection in Neural Networks with Checkpoints

We introduce a framework for online changepoint detection and simultaneous model learning which is applicable to highly parametrized models, such as deep neural networks. It is based on detecting changepoints across time by sequentially performing generalized likelihood ratio tests that require only evaluations of simple prediction score functions. This procedure makes use of checkpoints, consisting of early versions of the actual model parameters, that allow to detect distributional changes by performing predictions on future data. We define an algorithm that bounds the Type I error in the sequential testing procedure. We demonstrate the efficiency of our method in challenging continual learning applications with unknown task changepoints, and show improved performance compared to online Bayesian changepoint detection.

Information Theoretic Meta Learning with Gaussian Processes

We formulate meta learning using information theoretic concepts such as mutual information and the information bottleneck. The idea is to learn a stochastic representation or encoding of the task description, given by a training or support set, that is highly informative about predicting the validation set. By making use of variational approximations to the mutual information, we derive a general and tractable framework for meta learning. We particularly develop new memory-based meta learning algorithms based on Gaussian processes and derive extensions that combine memory and gradient-based meta learning. We demonstrate our method on few-shot regression and classification by using standard benchmarks such as Omniglot, mini-Imagenet and Augmented Omniglot.

Unbiased Gradient Estimation for Variational Auto-Encoders using Coupled Markov Chains

The variational auto-encoder (VAE) is a deep latent variable model that has two neural networks in an autoencoder-like architecture; one of them parameterizes the model's likelihood. Fitting its parameters via maximum likelihood is challenging since the computation of the likelihood involves an intractable integral over the latent space; thus the VAE is trained instead by maximizing a variational lower bound. Here, we develop a maximum likelihood training scheme for VAEs by introducing unbiased gradient estimators of the log-likelihood. We obtain the unbiased estimators by augmenting the latent space with a set of importance samples, similarly to the importance weighted auto-encoder (IWAE), and then constructing a Markov chain Monte Carlo (MCMC) coupling procedure on this augmented space. We provide the conditions under which the estimators can be computed in finite time and have finite variance. We demonstrate experimentally that VAEs fitted with unbiased estimators exhibit better predictive performance on three image datasets.