In this work, we provide a large-scale empirical study of the scaling properties of multilingual neural machine translation models. We examine how increases in the model size affect the model performance and investigate the role of the individual language pair weights on the scaling behavior. We find that these weights only affect the multiplicative factor of the scaling law, and in particular, the scaling exponent is unaffected by them. Through a novel joint scaling law formulation, we compute the effective number of parameters allocated to each language pair and examine the role of language similarity in the scaling behavior of our models. We find little evidence that language similarity has any impact. In contrast, ``direction'' of the multilinguality plays a significant role, with models translating from multiple languages into English having a larger number of effective parameters per task than their reversed counterparts. Finally, we leverage our observations to predict the performance of multilingual models trained with any language weighting at any scale, greatly reducing efforts required for language balancing in large multilingual models. Our findings apply to both in-domain and out-of-domain test sets and to multiple evaluation metrics, such as ChrF and BLEURT.

The rapid scaling of language models is motivating research using low-bitwidth quantization. In this work, we propose a novel binarization technique for Transformers applied to machine translation (BMT), the first of its kind. We identify and address the problem of inflated dot-product variance when using one-bit weights and activations. Specifically, BMT leverages additional LayerNorms and residual connections to improve binarization quality. Experiments on the WMT dataset show that a one-bit weight-only Transformer can achieve the same quality as a float one, while being 16$\times$ smaller in size. One-bit activations incur varying degrees of quality drop, but mitigated by the proposed architectural changes. We further conduct a scaling law study using production-scale translation datasets, which shows that one-bit weight Transformers scale and generalize well in both in-domain and out-of-domain settings. Implementation in JAX/Flax will be open sourced.

In this paper, we empirically study the optimization dynamics of multi-task learning, particularly focusing on those that govern a collection of tasks with significant data imbalance. We present a simple yet effective method of pre-training on high-resource tasks, followed by fine-tuning on a mixture of high/low-resource tasks. We provide a thorough empirical study and analysis of this method's benefits showing that it achieves consistent improvements relative to the performance trade-off profile of standard static weighting. We analyze under what data regimes this method is applicable and show its improvements empirically in neural machine translation (NMT) and multi-lingual language modeling.

In this work, we study the effect of varying the architecture and training data quality on the data scaling properties of Neural Machine Translation (NMT). First, we establish that the test loss of encoder-decoder transformer models scales as a power law in the number of training samples, with a dependence on the model size. Then, we systematically vary aspects of the training setup to understand how they impact the data scaling laws. In particular, we change the following (1) Architecture and task setup: We compare to a transformer-LSTM hybrid, and a decoder-only transformer with a language modeling loss (2) Noise level in the training distribution: We experiment with filtering, and adding iid synthetic noise. In all the above cases, we find that the data scaling exponents are minimally impacted, suggesting that marginally worse architectures or training data can be compensated for by adding more data. Lastly, we find that using back-translated data instead of parallel data, can significantly degrade the scaling exponent.

Natural language understanding and generation models follow one of the two dominant architectural paradigms: language models (LMs) that process concatenated sequences in a single stack of layers, and encoder-decoder models (EncDec) that utilize separate layer stacks for input and output processing. In machine translation, EncDec has long been the favoured approach, but with few studies investigating the performance of LMs. In this work, we thoroughly examine the role of several architectural design choices on the performance of LMs on bilingual, (massively) multilingual and zero-shot translation tasks, under systematic variations of data conditions and model sizes. Our results show that: (i) Different LMs have different scaling properties, where architectural differences often have a significant impact on model performance at small scales, but the performance gap narrows as the number of parameters increases, (ii) Several design choices, including causal masking and language-modeling objectives for the source sequence, have detrimental effects on translation quality, and (iii) When paired with full-visible masking for source sequences, LMs could perform on par with EncDec on supervised bilingual and multilingual translation tasks, and improve greatly on zero-shot directions by facilitating the reduction of off-target translations.

Recent research has proposed a series of specialized optimization algorithms for deep multi-task models. It is often claimed that these multi-task optimization (MTO) methods yield solutions that are superior to the ones found by simply optimizing a weighted average of the task losses. In this paper, we perform large-scale experiments on a variety of language and vision tasks to examine the empirical validity of these claims. We show that, despite the added design and computational complexity of these algorithms, MTO methods do not yield any performance improvements beyond what is achievable via traditional optimization approaches. We highlight alternative strategies that consistently yield improvements to the performance profile and point out common training pitfalls that might cause suboptimal results. Finally, we outline challenges in reliably evaluating the performance of MTO algorithms and discuss potential solutions.

For a certain scaling of the initialization of stochastic gradient descent (SGD), wide neural networks (NN) have been shown to be well approximated by reproducing kernel Hilbert space (RKHS) methods. Recent empirical work showed that, for some classification tasks, RKHS methods can replace NNs without a large loss in performance. On the other hand, two-layers NNs are known to encode richer smoothness classes than RKHS and we know of special examples for which SGD-trained NN provably outperform RKHS. This is true even in the wide network limit, for a different scaling of the initialization. How can we reconcile the above claims? For which tasks do NNs outperform RKHS? If covariates are nearly isotropic, RKHS methods suffer from the curse of dimensionality, while NNs can overcome it by learning the best low-dimensional representation. Here we show that this curse of dimensionality becomes milder if the covariates display the same low-dimensional structure as the target function, and we precisely characterize this tradeoff. Building on these results, we present the spiked covariates model that can capture in a unified framework both behaviors observed in earlier works. We hypothesize that such a latent low-dimensional structure is present in image classification. We numerically test this hypothesis by showing that specific perturbations of the training distribution degrade the performances of RKHS methods much more significantly than NNs.

Naive mean field variational methods are the state of-the-art approach to inference in topic modeling. We show that these methods suffer from an instability that can produce misleading conclusions. Namely, for certain regimes of the model parameters, variational inference outputs a non-trivial decomposition into topics. However -for the same parameter values- the data contain no actual information about the true topic decomposition, and the output of the algorithm is uncorrelated with it. In particular, the estimated posterior mean is wrong, and estimated credible regions do not achieve the nominal coverage. We discuss how this instability is remedied by more accurate mean field approximations.

To understand the dynamics of training in deep neural networks, we study the evolution of the Hessian eigenvalue density throughout the optimization process. In non-batch normalized networks, we observe the rapid appearance of large isolated eigenvalues in the spectrum, along with a surprising concentration of the gradient in the corresponding eigenspaces. In a batch normalized network, these two effects are almost absent. We give a theoretical rationale to partially explain these phenomena. As part of this work, we adapt advanced tools from numerical linear algebra that allow scalable and accurate estimation of the entire Hessian spectrum of ImageNet-scale neural networks; this technique may be of independent interest in other applications.

We study the supervised learning problem under either of the following two models: (1) Feature vectors xi are d-dimensional Gaussian and responses are yi = f_*(xi) for f* an unknown quadratic function; (2) Feature vectors xi are distributed as a mixture of two d-dimensional centered Gaussians, and yi's are the corresponding class labels. We use two-layers neural networks with quadratic activations, and compare three different learning regimes: the random features (RF) regime in which we only train the second-layer weights; the neural tangent (NT) regime in which we train a linearization of the neural network around its initialization; the fully trained neural network (NN) regime in which we train all the weights in the network. We prove that, even for the simple quadratic model of point (1), there is a potentially unbounded gap between the prediction risk achieved in these three training regimes, when the number of neurons is smaller than the ambient dimension. When the number of neurons is larger than the number of dimensions, the problem is significantly easier and both NT and NN learning achieve zero risk.