On Learning Language-Invariant Representations for Universal Machine Translation

Han Zhao; Junjie Hu; Andrej Risteski

Home/Archive/arXiv

arXiv · 2008.04510

On Learning Language-Invariant Representations for Universal Machine Translation

Han Zhao·Junjie Hu·Andrej Risteski

View original source ↗Read source document ↗Export metadata ↓

Abstract

The goal of universal machine translation is to learn to translate between any pair of languages, given a corpus of paired translated documents for \emph{a small subset} of all pairs of languages. Despite impressive empirical results and an increasing interest in massively multilingual models, theoretical analysis on translation errors made by such universal machine translation models is only nascent. In this paper, we formally prove certain impossibilities of this endeavour in general, as well as prove positive results in the presence of additional (but natural) structure of data. For the former, we derive a lower bound on the translation error in the many-to-many translation setting, which shows that any algorithm aiming to learn shared sentence representations among multiple language pairs has to make a large translation error on at least one of the translation tasks, if no assumption on the structure of the languages is made. For the latter, we show that if the paired documents in the corpus follow a natural \emph{encoder-decoder} generative process, we can expect a natural notion of ``generalization'': a linear number of language pairs, rather than quadratic, suffices to learn a good representation. Our theory also explains what kinds of connection graphs between pairs of languages are better suited: ones with longer paths result in worse sample complexity in terms of the total number of documents per language pair needed. We believe our theoretical insights and implications contribute to the future algorithmic design of universal machine translation.

Explore related subjects

cs.LG cs.CL stat.ML

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Han Zhao, Junjie Hu, Andrej Risteski. 2020-08-11. On Learning Language-Invariant Representations for Universal Machine Translation. https://arxiv.org/abs/2008.04510

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG↗

arXiv2026

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG↗

arXiv2026

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG↗