Alexandre Défossez

Baptiste Rozière, Jonas Gehring, Fabian Gloeckle et al. · meta-ai

We release Code Llama, a family of large language models for code based on Llama 2 providing state-of-the-art performance among open models, infilling capabilities, support for large input contexts, and zero-shot instruction following ability for programming tasks. We provide multiple flavors to cover a wide range of applications: foundation models (Code Llama), Python specializations (Code Llama - Python), and instruction-following models (Code Llama - Instruct) with 7B, 13B, 34B and 70B parameters each. All models are trained on sequences of 16k tokens and show improvements on inputs with up to 100k tokens. 7B, 13B and 70B Code Llama and Code Llama - Instruct variants support infilling based on surrounding content. Code Llama reaches state-of-the-art performance among open models on several code benchmarks, with scores of up to 67% and 65% on HumanEval and MBPP, respectively. Notably, Code Llama - Python 7B outperforms Llama 2 70B on HumanEval and MBPP, and all our models outperform every other publicly available model on MultiPL-E. We release Code Llama under a permissive license that allows for both research and commercial use.

Alexandre Défossez, Jade Copet, Gabriel Synnaeve et al.

We introduce a state-of-the-art real-time, high-fidelity, audio codec leveraging neural networks. It consists in a streaming encoder-decoder architecture with quantized latent space trained in an end-to-end fashion. We simplify and speed-up the training by using a single multiscale spectrogram adversary that efficiently reduces artifacts and produce high-quality samples. We introduce a novel loss balancer mechanism to stabilize training: the weight of a loss now defines the fraction of the overall gradient it should represent, thus decoupling the choice of this hyper-parameter from the typical scale of the loss. Finally, we study how lightweight Transformer models can be used to further compress the obtained representation by up to 40%, while staying faster than real time. We provide a detailed description of the key design choices of the proposed model including: training objective, architectural changes and a study of various perceptual loss functions. We present an extensive subjective evaluation (MUSHRA tests) together with an ablation study for a range of bandwidths and audio domains, including speech, noisy-reverberant speech, and music. Our approach is superior to the baselines methods across all evaluated settings, considering both 24 kHz monophonic and 48 kHz stereophonic audio. Code and models are available at github.com/facebookresearch/encodec.

Jade Copet, Felix Kreuk, Itai Gat et al.

We tackle the task of conditional music generation. We introduce MusicGen, a single Language Model (LM) that operates over several streams of compressed discrete music representation, i.e., tokens. Unlike prior work, MusicGen is comprised of a single-stage transformer LM together with efficient token interleaving patterns, which eliminates the need for cascading several models, e.g., hierarchically or upsampling. Following this approach, we demonstrate how MusicGen can generate high-quality samples, both mono and stereo, while being conditioned on textual description or melodic features, allowing better controls over the generated output. We conduct extensive empirical evaluation, considering both automatic and human studies, showing the proposed approach is superior to the evaluated baselines on a standard text-to-music benchmark. Through ablation studies, we shed light over the importance of each of the components comprising MusicGen. Music samples, code, and models are available at https://github.com/facebookresearch/audiocraft

Felix Kreuk, Gabriel Synnaeve, Adam Polyak et al.

We tackle the problem of generating audio samples conditioned on descriptive text captions. In this work, we propose AaudioGen, an auto-regressive generative model that generates audio samples conditioned on text inputs. AudioGen operates on a learnt discrete audio representation. The task of text-to-audio generation poses multiple challenges. Due to the way audio travels through a medium, differentiating ``objects'' can be a difficult task (e.g., separating multiple people simultaneously speaking). This is further complicated by real-world recording conditions (e.g., background noise, reverberation, etc.). Scarce text annotations impose another constraint, limiting the ability to scale models. Finally, modeling high-fidelity audio requires encoding audio at high sampling rate, leading to extremely long sequences. To alleviate the aforementioned challenges we propose an augmentation technique that mixes different audio samples, driving the model to internally learn to separate multiple sources. We curated 10 datasets containing different types of audio and text annotations to handle the scarcity of text-audio data points. For faster inference, we explore the use of multi-stream modeling, allowing the use of shorter sequences while maintaining a similar bitrate and perceptual quality. We apply classifier-free guidance to improve adherence to text. Comparing to the evaluated baselines, AudioGen outperforms over both objective and subjective metrics. Finally, we explore the ability of the proposed method to generate audio continuation conditionally and unconditionally. Samples: https://felixkreuk.github.io/audiogen

Alexandre Défossez, Laurent Mazaré, Manu Orsini et al.

We introduce Moshi, a speech-text foundation model and full-duplex spoken dialogue framework. Current systems for spoken dialogue rely on pipelines of independent components, namely voice activity detection, speech recognition, textual dialogue and text-to-speech. Such frameworks cannot emulate the experience of real conversations. First, their complexity induces a latency of several seconds between interactions. Second, text being the intermediate modality for dialogue, non-linguistic information that modifies meaning -- such as emotion or non-speech sounds -- is lost in the interaction. Finally, they rely on a segmentation into speaker turns, which does not take into account overlapping speech, interruptions and interjections. Moshi solves these independent issues altogether by casting spoken dialogue as speech-to-speech generation. Starting from a text language model backbone, Moshi generates speech as tokens from the residual quantizer of a neural audio codec, while modeling separately its own speech and that of the user into parallel streams. This allows for the removal of explicit speaker turns, and the modeling of arbitrary conversational dynamics. We moreover extend the hierarchical semantic-to-acoustic token generation of previous work to first predict time-aligned text tokens as a prefix to audio tokens. Not only this "Inner Monologue" method significantly improves the linguistic quality of generated speech, but we also illustrate how it can provide streaming speech recognition and text-to-speech. Our resulting model is the first real-time full-duplex spoken large language model, with a theoretical latency of 160ms, 200ms in practice, and is available at https://github.com/kyutai-labs/moshi.

Alexandre Défossez, Charlotte Caucheteux, Jérémy Rapin et al.

Decoding speech from brain activity is a long-awaited goal in both healthcare and neuroscience. Invasive devices have recently led to major milestones in that regard: deep learning algorithms trained on intracranial recordings now start to decode elementary linguistic features (e.g. letters, words, spectrograms). However, extending this approach to natural speech and non-invasive brain recordings remains a major challenge. Here, we introduce a model trained with contrastive-learning to decode self-supervised representations of perceived speech from the non-invasive recordings of a large cohort of healthy individuals. To evaluate this approach, we curate and integrate four public datasets, encompassing 175 volunteers recorded with magneto- or electro-encephalography (M/EEG), while they listened to short stories and isolated sentences. The results show that our model can identify, from 3 seconds of MEG signals, the corresponding speech segment with up to 41% accuracy out of more than 1,000 distinct possibilities on average across participants, and more than 80% in the very best participants - a performance that allows the decoding of words and phrases absent from the training set. The comparison of our model to a variety of baselines highlights the importance of (i) a contrastive objective, (ii) pretrained representations of speech and (iii) a common convolutional architecture simultaneously trained across multiple participants. Finally, the analysis of the decoder's predictions suggests that they primarily depend on lexical and contextual semantic representations. Overall, this effective decoding of perceived speech from non-invasive recordings delineates a promising path to decode language from brain activity, without putting patients at risk for brain surgery.

Robin San Roman, Yossi Adi, Antoine Deleforge et al.

Deep generative models can generate high-fidelity audio conditioned on various types of representations (e.g., mel-spectrograms, Mel-frequency Cepstral Coefficients (MFCC)). Recently, such models have been used to synthesize audio waveforms conditioned on highly compressed representations. Although such methods produce impressive results, they are prone to generate audible artifacts when the conditioning is flawed or imperfect. An alternative modeling approach is to use diffusion models. However, these have mainly been used as speech vocoders (i.e., conditioned on mel-spectrograms) or generating relatively low sampling rate signals. In this work, we propose a high-fidelity multi-band diffusion-based framework that generates any type of audio modality (e.g., speech, music, environmental sounds) from low-bitrate discrete representations. At equal bit rate, the proposed approach outperforms state-of-the-art generative techniques in terms of perceptual quality. Training and, evaluation code, along with audio samples, are available on the facebookresearch/audiocraft Github page.

Chung-Ming Chien, Manu Orsini, Eugene Kharitonov et al.

Speech-to-speech language models have recently emerged to enhance the naturalness of conversational AI. In particular, full-duplex models are distinguished by their real-time interactivity, including handling of pauses, interruptions, and backchannels. However, improving their factuality remains an open challenge. While scaling the model size could address this gap, it would make real-time inference prohibitively expensive. In this work, we propose MoshiRAG, a modular approach that combines a compact full-duplex interface with selective retrieval to access more powerful knowledge sources. Our asynchronous framework enables the model to identify knowledge-demanding queries and ground its responses in external information. By leveraging the natural temporal gap between response onset and the delivery of core information, the retrieval process can be completed while maintaining a natural conversation flow. With this approach, MoshiRAG achieves factuality comparable to the best publicly released non-duplex speech language models while preserving the interactivity inherent to full-duplex systems. Moreover, our flexible design supports plug-and-play retrieval methods without retraining and demonstrates strong performance on out-of-domain mathematical reasoning tasks.

Neil Zeghidour, Eugene Kharitonov, Manu Orsini et al.

We introduce Delayed Streams Modeling (DSM), a flexible formulation for streaming, multimodal sequence-to-sequence learning. Sequence-to-sequence generation is often cast in an offline manner, where the model consumes the complete input sequence before generating the first output timestep. Alternatively, streaming sequence-to-sequence rely on learning a policy for choosing when to advance on the input stream, or write to the output stream. DSM instead models already time-aligned streams with a decoder-only language model. By moving the alignment to a pre-processing step,and introducing appropriate delays between streams, DSM provides streaming inference of arbitrary output sequences, from any input combination, making it applicable to many sequence-to-sequence problems. In particular, given text and audio streams, automatic speech recognition (ASR) corresponds to the text stream being delayed, while the opposite gives a text-to-speech (TTS) model. We perform extensive experiments for these two major sequence-to-sequence tasks, showing that DSM provides state-of-the-art performance and latency while supporting arbitrary long sequences, being even competitive with offline baselines. Code, samples and demos are available at https://github.com/kyutai-labs/delayed-streams-modeling

Alexandre Défossez, Yossi Adi, Gabriel Synnaeve

We propose DiffQ a differentiable method for model compression for quantizing model parameters without gradient approximations (e.g., Straight Through Estimator). We suggest adding independent pseudo quantization noise to model parameters during training to approximate the effect of a quantization operator. DiffQ is differentiable both with respect to the unquantized weights and the number of bits used. Given a single hyper-parameter balancing between the quantized model size and accuracy, DiffQ optimizes the number of bits used per individual weight or groups of weights, in end-to-end training. We experimentally verify that our method is competitive with STE based quantization techniques on several benchmarks and architectures for image classification, language modeling, and audio source separation. For instance, on the ImageNet dataset, DiffQ compresses a 12 layers transformer-based model by more than a factor of 8, (lower than 4 bits precision per weight on average), with a loss of 0.3% in model accuracy. Code is available at github.com/facebookresearch/diffq.

Robin San Roman, Pierre Fernandez, Alexandre Défossez et al. · meta-ai

In the rapidly evolving field of speech generative models, there is a pressing need to ensure audio authenticity against the risks of voice cloning. We present AudioSeal, the first audio watermarking technique designed specifically for localized detection of AI-generated speech. AudioSeal employs a generator/detector architecture trained jointly with a localization loss to enable localized watermark detection up to the sample level, and a novel perceptual loss inspired by auditory masking, that enables AudioSeal to achieve better imperceptibility. AudioSeal achieves state-of-the-art performance in terms of robustness to real life audio manipulations and imperceptibility based on automatic and human evaluation metrics. Additionally, AudioSeal is designed with a fast, single-pass detector, that significantly surpasses existing models in speed - achieving detection up to two orders of magnitude faster, making it ideal for large-scale and real-time applications.

Tom Labiausse, Romain Fabre, Yannick Estève et al.

Simultaneous speech translation requires translating source speech into a target language in real-time while handling non-monotonic word dependencies. Traditional approaches rely on supervised training with word-level aligned data, which is difficult to collect at scale and thus depends on synthetic alignments using language-specific heuristics that are suboptimal. We propose Hibiki-Zero, which eliminates the need for word-level alignments entirely. This fundamentally simplifies the training pipeline and enables seamless scaling to diverse languages with varying grammatical structures, removing the bottleneck of designing language-specific alignment heuristics. We first train on sentence-level aligned data to learn speech translation at high latency, then apply a novel reinforcement learning strategy using GRPO to optimize latency while preserving translation quality. Hibiki-Zero achieves state-of-the-art performance in translation accuracy, latency, voice transfer, and naturalness across five X-to-English tasks. Moreover, we demonstrate that our model can be adapted to support a new input language with less than 1000h of speech. We provide examples, model weights, inference code and we release a benchmark containing 45h of multilingual data for speech translation evaluation.

Alon Ziv, Itai Gat, Gael Le Lan et al.

We introduce MAGNeT, a masked generative sequence modeling method that operates directly over several streams of audio tokens. Unlike prior work, MAGNeT is comprised of a single-stage, non-autoregressive transformer. During training, we predict spans of masked tokens obtained from a masking scheduler, while during inference we gradually construct the output sequence using several decoding steps. To further enhance the quality of the generated audio, we introduce a novel rescoring method in which, we leverage an external pre-trained model to rescore and rank predictions from MAGNeT, which will be then used for later decoding steps. Lastly, we explore a hybrid version of MAGNeT, in which we fuse between autoregressive and non-autoregressive models to generate the first few seconds in an autoregressive manner while the rest of the sequence is being decoded in parallel. We demonstrate the efficiency of MAGNeT for the task of text-to-music and text-to-audio generation and conduct an extensive empirical evaluation, considering both objective metrics and human studies. The proposed approach is comparable to the evaluated baselines, while being significantly faster (x7 faster than the autoregressive baseline). Through ablation studies and analysis, we shed light on the importance of each of the components comprising MAGNeT, together with pointing to the trade-offs between autoregressive and non-autoregressive modeling, considering latency, throughput, and generation quality. Samples are available on our demo page https://pages.cs.huji.ac.il/adiyoss-lab/MAGNeT.

Tom Labiausse, Laurent Mazaré, Edouard Grave et al.

We introduce Hibiki, a decoder-only model for simultaneous speech translation. Hibiki leverages a multistream language model to synchronously process source and target speech, and jointly produces text and audio tokens to perform speech-to-text and speech-to-speech translation. We furthermore address the fundamental challenge of simultaneous interpretation, which unlike its consecutive counterpart, where one waits for the end of the source utterance to start translating, adapts its flow to accumulate just enough context to produce a correct translation in real-time, chunk by chunk. To do so, we introduce a weakly-supervised method that leverages the perplexity of an off-the-shelf text translation system to identify optimal delays on a per-word basis and create aligned synthetic data. After supervised training, Hibiki performs adaptive, simultaneous speech translation with vanilla temperature sampling. On a French-English simultaneous speech translation task, Hibiki demonstrates state-of-the-art performance in translation quality, speaker fidelity and naturalness. Moreover, the simplicity of its inference process makes it compatible with batched translation and even real-time on-device deployment. We provide examples as well as models and inference code.

Anne Wu, Laurent Mazaré, Neil Zeghidour et al.

We propose a novel preference alignment framework for improving spoken dialogue models on real-time conversations from user interactions. Current preference learning methods primarily focus on text-based language models, and are not directly suited to the complexities of real-time speech interactions, with richer dynamics (e.g. interruption, interjection) and no explicit segmentation between speaker turns.We create a large-scale dataset of more than 150,000 preference pairs from raw multi-turn speech conversations, annotated with AI feedback, to cover preferences over both linguistic content and temporal context variations. We leverage offline alignment methods to finetune a full-duplex autoregressive speech-to-speech model. Extensive experiments demonstrate that feedback on generic conversations can be consistently effective in improving spoken dialogue models to produce more factual, safer and more contextually aligned interactions. We deploy the finetuned model and conduct holistic human evaluations to assess the impact beyond single-turn conversations. Our findings shed light on the importance of a well-calibrated balance among various dynamics, crucial for natural real-time speech dialogue systems.

Amélie Royer, Moritz Böhle, Gabriel de Marmiesse et al.

The recent successes of Vision-Language models raise the question of how to equivalently imbue a pretrained speech model with vision understanding, an important milestone towards building a multimodal speech model able to freely converse about images. Building such a conversational Vision-Speech model brings its unique challenges: (i) paired image-speech datasets are much scarcer than their image-text counterparts, (ii) ensuring real-time latency at inference is crucial thus bringing compute and memory constraints, and (iii) the model should preserve prosodic features (e.g., speaker tone) which cannot be inferred from text alone. In this work, we introduce MoshiVis, augmenting a recent dialogue speech LLM, Moshi, with visual inputs through lightweight adaptation modules. An additional dynamic gating mechanism enables the model to more easily switch between the visual inputs and unrelated conversation topics. To reduce training costs, we design a simple one-stage, parameter-efficient fine-tuning pipeline in which we leverage a mixture of image-text (i.e., "speechless") and image-speech samples. We evaluate the model on downstream visual understanding tasks with both audio and text prompts, and report qualitative samples of interactions with MoshiVis. Our inference code will be made available, as well as the image-speech data used for audio evaluation.

Jean-Marie Lemercier, Simon Rouard, Jade Copet et al.

Music generation schemes using language modeling rely on a vocabulary of audio tokens, generally provided as codes in a discrete latent space learnt by an auto-encoder. Multi-stage quantizers are often employed to produce these tokens, therefore the decoding strategy used for token prediction must be adapted to account for multiple codebooks: either it should model the joint distribution over all codebooks, or fit the product of the codebook marginal distributions. Modelling the joint distribution requires a costly increase in the number of auto-regressive steps, while fitting the product of the marginals yields an inexact model unless the codebooks are mutually independent. In this work, we introduce an independence-promoting loss to regularize the auto-encoder used as the tokenizer in language models for music generation. The proposed loss is a proxy for mutual information based on the maximum mean discrepancy principle, applied in reproducible kernel Hilbert spaces. Our criterion is simple to implement and train, and it is generalizable to other multi-stream codecs. We show that it reduces the statistical dependence between codebooks during auto-encoding. This leads to an increase in the generated music quality when modelling the product of the marginal distributions, while generating audio much faster than the joint distribution model.

Alexandre Défossez

Source separation models either work on the spectrogram or waveform domain. In this work, we show how to perform end-to-end hybrid source separation, letting the model decide which domain is best suited for each source, and even combining both. The proposed hybrid version of the Demucs architecture won the Music Demixing Challenge 2021 organized by Sony. This architecture also comes with additional improvements, such as compressed residual branches, local attention or singular value regularization. Overall, a 1.4 dB improvement of the Signal-To-Distortion (SDR) was observed across all sources as measured on the MusDB HQ dataset, an improvement confirmed by human subjective evaluation, with an overall quality rated at 2.83 out of 5 (2.36 for the non hybrid Demucs), and absence of contamination at 3.04 (against 2.37 for the non hybrid Demucs and 2.44 for the second ranking model submitted at the competition).

Yuki Mitsufuji, Giorgio Fabbro, Stefan Uhlich et al.

Music source separation has been intensively studied in the last decade and tremendous progress with the advent of deep learning could be observed. Evaluation campaigns such as MIREX or SiSEC connected state-of-the-art models and corresponding papers, which can help researchers integrate the best practices into their models. In recent years, the widely used MUSDB18 dataset played an important role in measuring the performance of music source separation. While the dataset made a considerable contribution to the advancement of the field, it is also subject to several biases resulting from a focus on Western pop music and a limited number of mixing engineers being involved. To address these issues, we designed the Music Demixing (MDX) Challenge on a crowd-based machine learning competition platform where the task is to separate stereo songs into four instrument stems (Vocals, Drums, Bass, Other). The main differences compared with the past challenges are 1) the competition is designed to more easily allow machine learning practitioners from other disciplines to participate, 2) evaluation is done on a hidden test set created by music professionals dedicated exclusively to the challenge to assure the transparency of the challenge, i.e., the test set is not accessible from anyone except the challenge organizers, and 3) the dataset provides a wider range of music genres and involved a greater number of mixing engineers. In this paper, we provide the details of the datasets, baselines, evaluation metrics, evaluation results, and technical challenges for future competitions.

Alexandre Défossez, Léon Bottou, Francis Bach et al.

We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared norm of the objective gradient averaged over the trajectory has an upper-bound which is explicit in the constants of the problem, parameters of the optimizer, the dimension $d$, and the total number of iterations $N$. This bound can be made arbitrarily small, and with the right hyper-parameters, Adam can be shown to converge with the same rate of convergence $O(d\ln(N)/\sqrt{N})$. When used with the default parameters, Adam doesn't converge, however, and just like constant step-size SGD, it moves away from the initialization point faster than Adagrad, which might explain its practical success. Finally, we obtain the tightest dependency on the heavy ball momentum decay rate $β_1$ among all previous convergence bounds for non-convex Adam and Adagrad, improving from $O((1-β_1)^{-3})$ to $O((1-β_1)^{-1})$.

Alexandre Défossez, Nicolas Usunier, Léon Bottou et al.

Source separation for music is the task of isolating contributions, or stems, from different instruments recorded individually and arranged together to form a song. Such components include voice, bass, drums and any other accompaniments.Contrarily to many audio synthesis tasks where the best performances are achieved by models that directly generate the waveform, the state-of-the-art in source separation for music is to compute masks on the magnitude spectrum. In this paper, we compare two waveform domain architectures. We first adapt Conv-Tasnet, initially developed for speech source separation,to the task of music source separation. While Conv-Tasnet beats many existing spectrogram-domain methods, it suffersfrom significant artifacts, as shown by human evaluations. We propose instead Demucs, a novel waveform-to-waveform model,with a U-Net structure and bidirectional LSTM.Experiments on the MusDB dataset show that, with proper data augmentation, Demucs beats allexisting state-of-the-art architectures, including Conv-Tasnet, with 6.3 SDR on average, (and up to 6.8 with 150 extra training songs, even surpassing the IRM oracle for the bass source).Using recent development in model quantization, Demucs can be compressed down to 120MBwithout any loss of accuracy.We also provide human evaluations, showing that Demucs benefit from a large advantagein terms of the naturalness of the audio. However, it suffers from some bleeding,especially between the vocals and other source.

Alexandre Défossez, Nicolas Usunier, Léon Bottou et al.

We study the problem of source separation for music using deep learning with four known sources: drums, bass, vocals and other accompaniments. State-of-the-art approaches predict soft masks over mixture spectrograms while methods working on the waveform are lagging behind as measured on the standard MusDB benchmark. Our contribution is two fold. (i) We introduce a simple convolutional and recurrent model that outperforms the state-of-the-art model on waveforms, that is, Wave-U-Net, by 1.6 points of SDR (signal to distortion ratio). (ii) We propose a new scheme to leverage unlabeled music. We train a first model to extract parts with at least one source silent in unlabeled tracks, for instance without bass. We remix this extract with a bass line taken from the supervised dataset to form a new weakly supervised training example. Combining our architecture and scheme, we show that waveform methods can play in the same ballpark as spectrogram ones.

Alexandre Défossez, Neil Zeghidour, Nicolas Usunier et al.

Recent progress in deep learning for audio synthesis opens the way to models that directly produce the waveform, shifting away from the traditional paradigm of relying on vocoders or MIDI synthesizers for speech or music generation. Despite their successes, current state-of-the-art neural audio synthesizers such as WaveNet and SampleRNN suffer from prohibitive training and inference times because they are based on autoregressive models that generate audio samples one at a time at a rate of 16kHz. In this work, we study the more computationally efficient alternative of generating the waveform frame-by-frame with large strides. We present SING, a lightweight neural audio synthesizer for the original task of generating musical notes given desired instrument, pitch and velocity. Our model is trained end-to-end to generate notes from nearly 1000 instruments with a single decoder, thanks to a new loss function that minimizes the distances between the log spectrograms of the generated and target waveforms. On the generalization task of synthesizing notes for pairs of pitch and instrument not seen during training, SING produces audio with significantly improved perceptual quality compared to a state-of-the-art autoencoder based on WaveNet as measured by a Mean Opinion Score (MOS), and is about 32 times faster for training and 2, 500 times faster for inference.

Alexandre Défossez, Francis Bach

We study a new aggregation operator for gradients coming from a mini-batch for stochastic gradient (SG) methods that allows a significant speed-up in the case of sparse optimization problems. We call this method AdaBatch and it only requires a few lines of code change compared to regular mini-batch SGD algorithms. We provide a theoretical insight to understand how this new class of algorithms is performing and show that it is equivalent to an implicit per-coordinate rescaling of the gradients, similarly to what Adagrad methods can do. In theory and in practice, this new aggregation allows to keep the same sample efficiency of SG methods while increasing the batch size. Experimentally, we also show that in the case of smooth convex optimization, our procedure can even obtain a better loss when increasing the batch size for a fixed number of samples. We then apply this new algorithm to obtain a parallelizable stochastic gradient method that is synchronous but allows speed-up on par with Hogwild! methods as convergence does not deteriorate with the increase of the batch size. The same approach can be used to make mini-batch provably efficient for variance-reduced SG methods such as SVRG.

Alexandre Défossez, Francis Bach

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis leads to new insights into stochastic approximation algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the generalization error may be divided into a variance term which is decaying as O(1/n), independently of the step-size $γ$, and a bias term that decays as O(1/$γ$ 2 n 2); (c) when allowing non-uniform sampling, the choice of a good sampling density depends on whether the variance or bias terms dominate. In particular, when the variance term dominates, optimal sampling densities do not lead to much gain, while when the bias term dominates, we can choose larger step-sizes that leads to significant improvements.