A new quantum algorithm for classical mechanics with an exponential speedup

Quantum computers promise to solve some problems exponentially faster than classical computers, but there are only a handful of examples with such a dramatic speedup, such as Shor’s factoring algorithm and quantum simulation. Of those few examples, the majority of them involve simulating physical systems that are inherently quantum mechanical — a natural application for quantum computers. But what about simulating systems that are not inherently quantum? Can quantum computers offer an exponential advantage for this?

In “Exponential quantum speedup in simulating coupled classical oscillators”, published in Physical Review X (PRX) and presented at the Symposium on Foundations of Computer Science (FOCS 2023), we report on the discovery of a new quantum algorithm that offers an exponential advantage for simulating coupled classical harmonic oscillators. These are some of the most fundamental, ubiquitous systems in nature and can describe the physics of countless natural systems, from electrical circuits to molecular vibrations to the mechanics of bridges. In collaboration with Dominic Berry of Macquarie University and Nathan Wiebe of the University of Toronto, we found a mapping that can transform any system involving coupled oscillators into a problem describing the time evolution of a quantum system. Given certain constraints, this problem can be solved with a quantum computer exponentially faster than it can with a classical computer. Further, we use this mapping to prove that any problem efficiently solvable by a quantum algorithm can be recast as a problem involving a network of coupled oscillators, albeit exponentially many of them. In addition to unlocking previously unknown applications of quantum computers, this result provides a new method of designing new quantum algorithms by reasoning purely about classical systems.

Simulating coupled oscillators

The systems we consider consist of classical harmonic oscillators. An example of a single harmonic oscillator is a mass (such as a ball) attached to a spring. If you displace the mass from its rest position, then the spring will induce a restoring force, pushing or pulling the mass in the opposite direction. This restoring force causes the mass to oscillate back and forth.

A simple example of a harmonic oscillator is a mass connected to a wall by a spring. [Image Source: Wikimedia]

Now consider coupled harmonic oscillators, where multiple masses are attached to one another through springs. Displace one mass, and it will induce a wave of oscillations to pulse through the system. As one might expect, simulating the oscillations of a large number of masses on a classical computer gets increasingly difficult.

An example system of masses connected by springs that can be simulated with the quantum algorithm.

To enable the simulation of a large number of coupled harmonic oscillators, we came up with a mapping that encodes the positions and velocities of all masses and springs into the quantum wavefunction of a system of qubits. Since the number of parameters describing the wavefunction of a system of qubits grows exponentially with the number of qubits, we can encode the information of N balls into a quantum mechanical system of only about log(N) qubits. As long as there is a compact description of the system (i.e., the properties of the masses and the springs), we can evolve the wavefunction to learn coordinates of the balls and springs at a later time with far fewer resources than if we had used a naïve classical approach to simulate the balls and springs.

We showed that a certain class of coupled-classical oscillator systems can be efficiently simulated on a quantum computer. But this alone does not rule out the possibility that there exists some as-yet-unknown clever classical algorithm that is similarly efficient in its use of resources. To show that our quantum algorithm achieves an exponential speedup over any possible classical algorithm, we provide two additional pieces of evidence.

The glued-trees problem and the quantum oracle

For the first piece of evidence, we use our mapping to show that the quantum algorithm can efficiently solve a famous problem about graphs known to be difficult to solve classically, called the glued-trees problem. The problem takes two branching trees — a graph whose nodes each branch to two more nodes, resembling the branching paths of a tree — and glues their branches together through a random set of edges, as shown in the figure below.

A visual representation of the glued trees problem. Here we start at the node labeled ENTRANCE and are allowed to locally explore the graph, which is obtained by randomly gluing together two binary trees. The goal is to find the node labeled EXIT.

The goal of the glued-trees problem is to find the exit node — the “root” of the second tree — as efficiently as possible. But the exact configuration of the nodes and edges of the glued trees are initially hidden from us. To learn about the system, we must query an oracle, which can answer specific questions about the setup. This oracle allows us to explore the trees, but only locally. Decades ago, it was shown that the number of queries required to find the exit node on a classical computer is proportional to a polynomial factor of N, the total number of nodes.

But recasting this as a problem with balls and springs, we can imagine each node as a ball and each connection between two nodes as a spring. Pluck the entrance node (the root of the first tree), and the oscillations will pulse through the trees. It only takes a time that scales with the depth of the tree — which is exponentially smaller than N — to reach the exit node. So, by mapping the glued-trees ball-and-spring system to a quantum system and evolving it for that time, we can detect the vibrations of the exit node and determine it exponentially faster than we could using a classical computer.


The second and strongest piece of evidence that our algorithm is exponentially more efficient than any possible classical algorithm is revealed by examination of the set of problems a quantum computer can solve efficiently (i.e., solvable in polynomial time), referred to as bounded-error quantum polynomial time or BQP. The hardest problems in BQP are called “BQP-complete”.

While it is generally accepted that there exist some problems that a quantum algorithm can solve efficiently and a classical algorithm cannot, this has not yet been proven. So, the best evidence we can provide is that our problem is BQP-complete, that is, it is among the hardest problems in BQP. If someone were to find an efficient classical algorithm for solving our problem, then every problem solved by a quantum computer efficiently would be classically solvable! Not even the factoring problem (finding the prime factors of a given large number), which forms the basis of modern encryption and was famously solved by Shor’s algorithm, is expected to be BQP-complete.

A diagram showing the believed relationships of the classes BPP and BQP, which are the set of problems that can be efficiently solved on a classical computer and quantum computer, respectively. BQP-complete problems are the hardest problems in BQP.

To show that our problem of simulating balls and springs is indeed BQP-complete, we start with a standard BQP-complete problem of simulating universal quantum circuits, and show that every quantum circuit can be expressed as a system of many balls coupled with springs. Therefore, our problem is also BQP-complete.

Implications and future work

This effort also sheds light on work from 2002, when theoretical computer scientist Lov K. Grover and his colleague, Anirvan M. Sengupta, used an analogy to coupled pendulums to illustrate how Grover’s famous quantum search algorithm could find the correct element in an unsorted database quadratically faster than could be done classically. With the proper setup and initial conditions, it would be possible to tell whether one of N pendulums was different from the others — the analogue of finding the correct element in a database — after the system had evolved for time that was only ~√(N). While this hints at a connection between certain classical oscillating systems and quantum algorithms, it falls short of explaining why Grover’s quantum algorithm achieves a quantum advantage.

Our results make that connection precise. We showed that the dynamics of any classical system of harmonic oscillators can indeed be equivalently understood as the dynamics of a corresponding quantum system of exponentially smaller size. In this way we can simulate Grover and Sengupta’s system of pendulums on a quantum computer of log(N) qubits, and find a different quantum algorithm that can find the correct element in time ~√(N). The analogy we discovered between classical and quantum systems can be used to construct other quantum algorithms offering exponential speedups, where the reason for the speedups is now more evident from the way that classical waves propagate.

Our work also reveals that every quantum algorithm can be equivalently understood as the propagation of a classical wave in a system of coupled oscillators. This would imply that, for example, we can in principle build a classical system that solves the factoring problem after it has evolved for time that is exponentially smaller than the runtime of any known classical algorithm that solves factoring. This may look like an efficient classical algorithm for factoring, but the catch is that the number of oscillators is exponentially large, making it an impractical way to solve factoring.

Coupled harmonic oscillators are ubiquitous in nature, describing a broad range of systems from electrical circuits to chains of molecules to structures such as bridges. While our work here focuses on the fundamental complexity of this broad class of problems, we expect that it will guide us in searching for real-world examples of harmonic oscillator problems in which a quantum computer could offer an exponential advantage.


We would like to thank our Quantum Computing Science Communicator, Katie McCormick, for helping to write this blog post.

Source: Google AI Blog

Chrome Beta for Desktop Update

The Beta channel has been updated to 120.0.6099.62 for Windows, Mac and Linux.

A partial list of changes is available in the Git log. Interested in switching release channels? Find out how. If you find a new issue, please let us know by filing a bug. The community help forum is also a great place to reach out for help or learn about common issues.

Srinivas Sista
Google Chrome

Summary report optimization in the Privacy Sandbox Attribution Reporting API

In recent years, the Privacy Sandbox initiative was launched to explore responsible ways for advertisers to measure the effectiveness of their campaigns, by aiming to deprecate third-party cookies (subject to resolving any competition concerns with the UK’s Competition and Markets Authority). Cookies are small pieces of data containing user preferences that websites store on a user’s device; they can be used to provide a better browsing experience (e.g., allowing users to automatically sign in) and to serve relevant content or ads. The Privacy Sandbox attempts to address concerns around the use of cookies for tracking browsing data across the web by providing a privacy-preserving alternative.

Many browsers use differential privacy (DP) to provide privacy-preserving APIs, such as the Attribution Reporting API (ARA), that don’t rely on cookies for ad conversion measurement. ARA encrypts individual user actions and collects them in an aggregated summary report, which estimates measurement goals like the number and value of conversions (useful actions on a website, such as making a purchase or signing up for a mailing list) attributed to ad campaigns.

The task of configuring API parameters, e.g., allocating a contribution budget across different conversions, is important for maximizing the utility of the summary reports. In “Summary Report Optimization in the Privacy Sandbox Attribution Reporting API”, we introduce a formal mathematical framework for modeling summary reports. Then, we formulate the problem of maximizing the utility of summary reports as an optimization problem to obtain the optimal ARA parameters. Finally, we evaluate the method using real and synthetic datasets, and demonstrate significantly improved utility compared to baseline non-optimized summary reports.

ARA summary reports

We use the following example to illustrate our notation. Imagine a fictional gift shop called Du & Penc that uses digital advertising to reach its customers. The table below captures their holiday sales, where each record contains impression features with (i) an impression ID, (ii) the campaign, and (iii) the city in which the ad was shown, as well as conversion features with (i) the number of items purchased and (ii) the total dollar value of those items.

Impression and conversion feature logs for Du & Penc.

Mathematical model

ARA summary reports can be modeled by four algorithms: (1) Contribution Vector, (2) Contribution Bounding, (3) Summary Reports, and (4) Reconstruct Values. Contribution Bounding and Summary Reports are performed by the ARA, while Contribution Vector and Reconstruct Values are performed by an AdTech provider — tools and systems that enable businesses to buy and sell digital advertising. The objective of this work is to assist AdTechs in optimizing summary report algorithms.

The Contribution Vector algorithm converts measurements into an ARA format that is discretized and scaled. Scaling needs to account for the overall contribution limit per impression. Here we propose a method that clips and performs randomized rounding. The outcome of the algorithm is a histogram of aggregatable keys and values.

Next, the Contribution Bounding algorithm runs on client devices and enforces the contribution bound on attributed reports where any further contributions exceeding the limit are dropped. The output is a histogram of attributed conversions.

The Summary Reports algorithm runs on the server side inside a trusted execution environment and returns noisy aggregate results that satisfy DP. Noise is sampled from the discrete Laplace distribution, and to enforce privacy budgeting, a report may be queried only once.

Finally, the Reconstruct Values algorithm converts measurements back to the original scale. Reconstruct Values and Contribution Vector Algorithms are designed by the AdTech, and both impact the utility received from the summary report.

Illustrative usage of ARA summary reports, which include Contribution Vector (Algorithm A), Contribution Bounding (Algorithm C), Summary Reports (Algorithm S), and Reconstruct Values (Algorithm R). Algorithms C and S are fixed in the API. The AdTech designs A and R.

Error metrics

There are several factors to consider when selecting an error metric for evaluating the quality of an approximation. To choose a particular metric, we considered the desirable properties of an error metric that further can be used as an objective function. Considering desired properties, we have chosen 𝜏-truncated root mean square relative error (RMSRE𝜏) as our error metric for its properties. See the paper for a detailed discussion and comparison to other possible metrics.


To optimize utility as measured by RMSRE𝜏, we choose a capping parameter, C, and privacy budget, 𝛼, for each slice. The combination of both determines how an actual measurement (such as two conversions with a total value of $3) is encoded on the AdTech side and then passed to the ARA for Contribution Bounding algorithm processing. RMSRE𝜏 can be computed exactly, since it can be expressed in terms of the bias from clipping and the variance of the noise distribution. Following those steps we find out that RMSRE𝜏 for a fixed privacy budget, 𝛼, or a capping parameter, C, is convex (so the error-minimizing value for the other parameter can be obtained efficiently), while for joint variables (C, 𝛼) it becomes non-convex (so we may not always be able to select the best possible parameters). In any case, any off-the-shelf optimizer can be used to select privacy budgets and capping parameters. In our experiments, we use the SLSQP minimizer from the scipy.optimize library.

Synthetic data

Different ARA configurations can be evaluated empirically by testing them on a conversion dataset. However, access to such data can be restricted or slow due to privacy concerns, or simply unavailable. One way to address these limitations is to use synthetic data that replicates the characteristics of real data.

We present a method for generating synthetic data responsibly through statistical modeling of real-world conversion datasets. We first perform an empirical analysis of real conversion datasets to uncover relevant characteristics for ARA. We then design a pipeline that uses this distribution knowledge to create a realistic synthetic dataset that can be customized via input parameters.

The pipeline first generates impressions drawn from a power-law distribution (step 1), then for each impression it generates conversions drawn from a Poisson distribution (step 2) and finally, for each conversion, it generates conversion values drawn from a log-normal distribution (step 3). With dataset-dependent parameters, we find that these distributions closely match ad-dataset characteristics. Thus, one can learn parameters from historical or public datasets and generate synthetic datasets for experimentation.

Overall dataset generation steps with features for illustration.

Experimental evaluation

We evaluate our algorithms on three real-world datasets (Criteo, AdTech Real Estate, and AdTech Travel) and three synthetic datasets. Criteo consists of 15M clicks, Real Estate consists of 100K conversions, and Travel consists of 30K conversions. Each dataset is partitioned into a training set and a test set. The training set is used to choose contribution budgets, clipping threshold parameters, and the conversion count limit (the real-world datasets have only one conversion per click), and the error is evaluated on the test set. Each dataset is partitioned into slices using impression features. For real-world datasets, we consider three queries for each slice; for synthetic datasets, we consider two queries for each slice.

For each query we choose the RMSRE𝝉 𝜏 value to be five times the median value of the query on the training dataset. This ensures invariance of the error metric to data rescaling, and allows us to combine the errors from features of different scales by using 𝝉 per each feature.

Scatter plots of real-world datasets illustrating the probability of observing a conversion value. The fitted curves represent best log-normal distribution models that effectively capture the underlying patterns in the data.


We compare our optimization-based algorithm to a simple baseline approach. For each query, the baseline uses an equal contribution budget and a fixed quantile of the training data to choose the clipping threshold. Our algorithms produce substantially lower error than baselines on both real-world and synthetic datasets. Our optimization-based approach adapts to the privacy budget and data.

RMSREτ for privacy budgets {1, 2, 4, 8, 16, 32, 64} for our algorithms and baselines on three real-world and three synthetic datasets. Our optimization-based approach consistently achieves lower error than baselines that use a fixed quantile for the clipping threshold and split the contribution budget equally among the queries.


We study the optimization of summary reports in the ARA, which is currently deployed on hundreds of millions of Chrome browsers. We present a rigorous formulation of the contribution budgeting optimization problem for ARA with the goal of equipping researchers with a robust abstraction that facilitates practical improvements.

Our recipe, which leverages historical data to bound and scale the contributions of future data under differential privacy, is quite general and applicable to settings beyond advertising. One approach based on this work is to use past data to learn the parameters of the data distribution, and then to apply synthetic data derived from this distribution for privacy budgeting for queries on future data. Please see the paper and accompanying code for detailed algorithms and proofs.


This work was done in collaboration with Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, and Avinash Varadarajan. We thank Akash Nadan for his help.

Source: Google AI Blog

Video mode now only show pages where video is the main content

Earlier this year, we made a change to only show video thumbnails next to results on the main Google Search results page when the video is the main content of a page. Today, we're extending this change to search results in Video mode to better connect users with the video content they're looking for (rather than having to comb through a page to find that video). This change will start rolling out today, and it could take up to a week to complete.

Google Workspace Updates Weekly Recap – December 1, 2023

3 New updates

Unless otherwise indicated, the features below are available to all Google Workspace customers, and are fully launched or in the process of rolling out. Rollouts should take no more than 15 business days to complete if launching to both Rapid and Scheduled Release at the same time. If not, each stage of rollout should take no more than 15 business days to complete.

New ways to use the Google Sheets app on iOS devices 
You can now copy charts from the Google Sheets app on all iOS devices and paste them externally as images or within the same spreadsheet as a duplicate chart. In addition, you can modify text formatting using the contextual toolbar in Sheets when a keyboard is attached to iOS tablets. | Rolling out to Rapid Release and Scheduled Release domains now. | Available to all Google Workspace customers and users with personal Google Accounts. | Learn more about adding & editing a chart or graph and editing & formatting a spreadsheet
New ways to use the Google Sheets app on iOS devices

Adding ‘Admin managed apps’ category to Google Workspace Marketplace
We’re excited to announce a new featured app category in the Marketplace: Admin managed. These Enterprise apps can be installed only by a Google Workspace administrator for their organization. | Available now to all Google Workspace customers. | Learn more about Featured app categories

Bulk select in Gmail on Android and iOS devices 
We’re introducing a feature that enables you to bulk select a batch of messages in the email threadlist with one tap using the Gmail app on Android and iOS devices. After clicking the select all icon, a batch of messages will be selected, enabling you to easily perform email actions such as deleting multiple messages or marking them as “read”. | This feature is available now on Android devices and is rolling out now to Rapid Release and Scheduled Release domains on iOS devices. | Available to all Google Workspace customers and users with personal Google Accounts. 
Bulk select in Gmail on Android and iOS devices

Previous announcements

The announcements below were published on the Workspace Updates blog earlier this week. Please refer to the original blog posts for complete details.

Create shareable video presentations in Google Slides 
We’re introducing slides recordings, a new Google Slides feature that lets you easily record yourself presenting, and then share the presentation with others to view when it works for them. | Available to Google Workspace Business Standard, Business Plus, Enterprise Starter, Enterprise Essentials, Enterprise Essentials Plus, Enterprise Standard, Enterprise Plus and Education Plus only. | Learn more about slides recordings. 

The next evolution of automated data entry in Google Sheets 
Enhanced Smart Fill in Google Sheets is available for customers with the Duet AI for Google Workspace Enterprise add-on. | Learn more about enhanced smart fill

Expanding message bubbles in Google Chat to iOS devices 
In September, we introduced message bubbles in Google Chat on web and Android, enabling users to more easily differentiate incoming versus outgoing messages in the Chat message stream. This week, we’re excited to announce the expansion of message bubbles to iOS devices. | Learn more about message bubbles

Updates to the Google Drive scanner on Android & iOS devices 
We’re introducing additional enhancements to the Drive scanner on Android devices, which now powers the Google Pixel camera and includes improvements to the scanner experience when capturing content. We’re also expanding the Google Drive scanner and title suggestion feature to iOS devices. | Learn more about Drive scanner. 

Introducing a new homepage view in Google Drive 
We’ve added a new streamlined homepage for Drive called Home that makes it easier and faster for you to find files that matter most. | Learn more about Drive home

Introducing a new mobile experience for Google Chat 
We recently announced a streamlined user experience in Google Chat to help you find what you need much faster, including new features like home and mentions. Starting today, we’re excited to introduce a new bottom navigation bar within the Chat app on Android & iOS devices to help you easily access these features on mobile. | Learn more about the Chat mobile experience

Google Vault now supports Google Calendar 
Google Vault now supports Calendar, which means customers can take new actions around Calendar data. | Available to Google Workspace Business Plus, Enterprise Essentials, Enterprise Essentials Plus, Enterprise Standard, Enterprise Plus, Education Standard, Education Plus customers or customers with the Vault add-on license only. | Learn more about Vault supporting Calendar

More insights to help admins troubleshoot Google Meet hardware issues 
In 2022, we introduced several improvements for managing Google Meet hardware devices. These improvements included surfacing additional information about device issues, such as a description of the issue, when the issue was detected, and more. Now, we’re taking these improvements one step further by providing admins with even more data points. | Learn more about Google Meet hardware issues

Monitor insider risk of Google Workspace data with Chronicle 
Admins can now more seamlessly integrate their Google Workspace data with Chronicle (Google’s cloud-native Security Operations platform), to quickly detect, investigate and take action on risky activity and threats. | Available to Google Workspace Enterprise Standard and Enterprise Plus customers only. | Learn more about Chronicle

Google Classroom now supports roster import from SIS partners
Educators can now easily import students from their student information system (SIS) to Google Classroom using OneRoster. This integration saves educators time and helps make class setup much quicker. | Available to Education Plus and the Teaching and Learning Upgrade only. | Learn more about roster import. 

Completed rollouts

The features below completed their rollouts to Rapid Release domains, Scheduled Release domains, or both. Please refer to the original blog posts for additional details.

Rapid Release Domains: 
Scheduled Release Domains: 
Rapid and Scheduled Release Domains: 

For a recap of announcements in the past six months, check out What’s new in Google Workspace (recent releases).

Chrome Dev for Desktop Update

The Dev channel has been updated to 121.0.6156.3 for Windows, Mac and Linux.

A partial list of changes is available in the Git log. Interested in switching release channels? Find out how. If you find a new issue, please let us know by filing a bug. The community help forum is also a great place to reach out for help or learn about common issues.

Daniel Yip
Google Chrome

Unsupervised speech-to-speech translation from monolingual data

Speech-to-speech translation (S2ST) is a type of machine translation that converts spoken language from one language to another. This technology has the potential to break down language barriers and facilitate communication between people from different cultures and backgrounds.

Previously, we introduced Translatotron 1 and Translatotron 2, the first ever models that were able to directly translate speech between two languages. However they were trained in supervised settings with parallel speech data. The scarcity of parallel speech data is a major challenge in this field, so much that most public datasets are semi- or fully-synthesized from text. This adds additional hurdles to learning translation and reconstruction of speech attributes that are not represented in the text and are thus not reflected in the synthesized training data.

Here we present Translatotron 3, a novel unsupervised speech-to-speech translation architecture. In Translatotron 3, we show that it is possible to learn a speech-to-speech translation task from monolingual data alone. This method opens the door not only to translation between more language pairs but also towards translation of the non-textual speech attributes such as pauses, speaking rates, and speaker identity. Our method does not include any direct supervision to target languages and therefore we believe it is the right direction for paralinguistic characteristics (e.g., such as tone, emotion) of the source speech to be preserved across translation. To enable speech-to-speech translation, we use back-translation, which is a technique from unsupervised machine translation (UMT) where a synthetic translation of the source language is used to translate texts without bilingual text datasets. Experimental results in speech-to-speech translation tasks between Spanish and English show that Translatotron 3 outperforms a baseline cascade system.

Translatotron 3

Translatotron 3 addresses the problem of unsupervised S2ST, which can eliminate the requirement for bilingual speech datasets. To do this, Translatotron 3’s design incorporates three key aspects:

  1. Pre-training the entire model as a masked autoencoder with SpecAugment, a simple data augmentation method for speech recognition that operates on the logarithmic mel spectogram of the input audio (instead of the raw audio itself) and is shown to effectively improve the generalization capabilities of the encoder.
  2. Unsupervised embedding mapping based on multilingual unsupervised embeddings (MUSE), which is trained on unpaired languages but allows the model to learn an embedding space that is shared between the source and target languages.
  3. A reconstruction loss based on back-translation, to train an encoder-decoder direct S2ST model in a fully unsupervised manner.

The model is trained using a combination of the unsupervised MUSE embedding loss, reconstruction loss, and S2S back-translation loss. During inference, the shared encoder is utilized to encode the input into a multilingual embedding space, which is subsequently decoded by the target language decoder.


Translatotron 3 employs a shared encoder to encode both the source and target languages. The decoder is composed of a linguistic decoder, an acoustic synthesizer (responsible for acoustic generation of the translation speech), and a singular attention module, like Translatotron 2. However, for Translatotron 3 there are two decoders, one for the source language and another for the target language. During training, we use monolingual speech-text datasets (i.e., these data are made up of speech-text pairs; they are not translations).


The encoder has the same architecture as the speech encoder in the Translatotron 2. The output of the encoder is split into two parts: the first part incorporates semantic information whereas the second part incorporates acoustic information. By using the MUSE loss, the first half of the output is trained to be the MUSE embeddings of the text of the input speech spectrogram. The latter half is updated without the MUSE loss. It is important to note that the same encoder is shared between source and target languages. Furthermore, the MUSE embedding is multilingual in nature. As a result, the encoder is able to learn a multilingual embedding space across source and target languages. This allows a more efficient and effective encoding of the input, as the encoder is able to encode speech from both languages into a common embedding space, rather than maintaining a separate embedding space for each language.


Like Translatotron 2, the decoder is composed of three distinct components, namely the linguistic decoder, the acoustic synthesizer, and the attention module. To effectively handle the different properties of the source and target languages, however, Translatotron 3 has two separate decoders, for the source and target languages.

Two part training

The training methodology consists of two parts: (1) auto-encoding with reconstruction and (2) a back-translation term. In the first part, the network is trained to auto-encode the input to a multilingual embedding space using the MUSE loss and the reconstruction loss. This phase aims to ensure that the network generates meaningful multilingual representations. In the second part, the network is further trained to translate the input spectrogram by utilizing the back-translation loss. To mitigate the issue of catastrophic forgetting and enforcing the latent space to be multilingual, the MUSE loss and the reconstruction loss are also applied in this second part of training. To ensure that the encoder learns meaningful properties of the input, rather than simply reconstructing the input, we apply SpecAugment to encoder input at both phases. It has been shown to effectively improve the generalization capabilities of the encoder by augmenting the input data.

Training objective

During the back-translation training phase (illustrated in the section below), the network is trained to translate the input spectrogram to the target language and then back to the source language. The goal of back-translation is to enforce the latent space to be multilingual. To achieve this, the following losses are applied:

  • MUSE loss: The MUSE loss measures the similarity between the multilingual embedding of the input spectrogram and the multilingual embedding of the back-translated spectrogram.
  • Reconstruction loss: The reconstruction loss measures the similarity between the input spectrogram and the back-translated spectrogram.

In addition to these losses, SpecAugment is applied to the encoder input at both phases. Before the back-translation training phase, the network is trained to auto-encode the input to a multilingual embedding space using the MUSE loss and reconstruction loss.

MUSE loss

To ensure that the encoder generates multilingual representations that are meaningful for both decoders, we employ a MUSE loss during training. The MUSE loss forces the encoder to generate such a representation by using pre-trained MUSE embeddings. During the training process, given an input text transcript, we extract the corresponding MUSE embeddings from the embeddings of the input language. The error between MUSE embeddings and the output vectors of the encoder is then minimized. Note that the encoder is indifferent to the language of the input during inference due to the multilingual nature of the embeddings.

The training and inference in Translatotron 3. Training includes the reconstruction loss via the auto-encoding path and employs the reconstruction loss via back-translation.

Audio samples

Following are examples of direct speech-to-speech translation from Translatotron 3:

Spanish-to-English (on Conversational dataset)

Input (Spanish)
TTS-synthesized reference (English)   
Translatotron 3 (English)

Spanish-to-English (on CommonVoice11 Synthesized dataset)

Input (Spanish)
TTS-synthesized reference (English)   
Translatotron 3 (English)

Spanish-to-English (on CommonVoice11 dataset)

Input (Spanish)
TTS reference (English)
Translatotron 3 (English)   


To empirically evaluate the performance of the proposed approach, we conducted experiments on English and Spanish using various datasets, including the Common Voice 11 dataset, as well as two synthesized datasets derived from the Conversational and Common Voice 11 datasets.

The translation quality was measured by BLEU (higher is better) on ASR (automatic speech recognition) transcriptions from the translated speech, compared to the corresponding reference translation text. Whereas, the speech quality is measured by the MOS score (higher is better). Furthermore, the speaker similarity is measured by the average cosine similarity (higher is better).

Because Translatotron 3 is an unsupervised method, as a baseline we used a cascaded S2ST system that is combined from ASR, unsupervised machine translation (UMT), and TTS (text-to-speech). Specifically, we employ UMT that uses the nearest neighbor in the embedding space in order to create the translation.

Translatotron 3 outperforms the baseline by large margins in every aspect we measured: translation quality, speaker similarity, and speech quality. It particularly excelled on the conversational corpus. Moreover, Translatotron 3 achieves speech naturalness similar to that of the ground truth audio samples (measured by MOS, higher is better).

Translation quality (measured by BLEU, where higher is better) evaluated on three Spanish-English corpora.
Speech similarity (measured by average cosine similarity between input speaker and output speaker, where higher is better) evaluated on three Spanish-English corpora.
Mean-opinion-score (measured by average MOS metric, where higher is better) evaluated on three Spanish-English corpora.

Future work

As future work, we would like to extend the work to more languages and investigate whether zero-shot S2ST can be applied with the back-translation technique. We would also like to examine the use of back-translation with different types of speech data, such as noisy speech and low-resource languages.


The direct contributors to this work include Eliya Nachmani, Alon Levkovitch, Yifan Ding, Chulayutsh Asawaroengchai, Heiga Zhen, and Michelle Tadmor Ramanovich. We also thank Yu Zhang, Yuma Koizumi, Soroosh Mariooryad, RJ Skerry-Ryan, Neil Zeghidour, Christian Frank, Marco Tagliasacchi, Nadav Bar, Benny Schlesinger and Yonghui Wu.

Source: Google AI Blog