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Léon Bottou, Bernhard Schölkopf

Many believe that Large Language Models (LLMs) open the era of Artificial Intelligence (AI). Some see opportunities while others see dangers. Yet both proponents and opponents grasp AI through the imagery popularised by science fiction. Will the machine become sentient and rebel against its creators? Will we experience a paperclip apocalypse? Before answering such questions, we should first ask whether this mental imagery provides a good description of the phenomenon at hand. Understanding weather patterns through the moods of the gods only goes so far. The present paper instead advocates understanding LLMs and their connection to AI through the imagery of Jorge Luis Borges, a master of 20th century literature, forerunner of magical realism, and precursor to postmodern literature. This exercise leads to a new perspective that illuminates the relation between language modelling and artificial intelligence.

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Alexandre Ramé, Kartik Ahuja, Jianyu Zhang, Matthieu Cord, Léon Bottou, David Lopez-Paz

Foundation models are redefining how AI systems are built. Practitioners now follow a standard procedure to build their machine learning solutions: download a copy of a foundation model, and fine-tune it using some in-house data about the target task of interest. Consequently, the Internet is swarmed by a handful of foundation models fine-tuned on many diverse tasks. Yet, these individual fine-tunings often lack strong generalization and exist in isolation without benefiting from each other. In our opinion, this is a missed opportunity, as these specialized models contain diverse features. Based on this insight, we propose model recycling, a simple strategy that leverages multiple fine-tunings of the same foundation model on diverse auxiliary tasks, and repurposes them as rich and diverse initializations for the target task. Specifically, model recycling fine-tunes in parallel each specialized model on the target task, and then averages the weights of all target fine-tunings into a final model. Empirically, we show that model recycling maximizes model diversity by benefiting from diverse auxiliary tasks, and achieves a new state of the art on the reference DomainBed benchmark for out-of-distribution generalization. Looking forward, model recycling is a contribution to the emerging paradigm of updatable machine learning where, akin to open-source software development, the community collaborates to incrementally and reliably update machine learning models.

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Jianyu Zhang, Léon Bottou

Does the dominant approach to learn representations (as a side effect of optimizing an expected cost for a single training distribution) remain a good approach when we are dealing with multiple distributions. Our thesis is that such scenarios are better served by representations that are "richer" than those obtained with a single optimization episode. This is supported by a collection of empirical results obtained with an apparently na\"ive ensembling technique: concatenating the representations obtained with multiple training episodes using the same data, model, algorithm, and hyper-parameters, but different random seeds. These independently trained networks perform similarly. Yet, in a number of scenarios involving new distributions, the concatenated representation performs substantially better than an equivalently sized network trained from scratch. This proves that the representations constructed by multiple training episodes are in fact different. Although their concatenation carries little additional information about the training task under the training distribution, it becomes substantially more informative when tasks or distributions change. Meanwhile, a single training episode is unlikely to yield such a redundant representation because the optimization process has no reason to accumulate features that do not incrementally improve the training performance.

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Jianyu Zhang, David Lopez-Paz, Léon Bottou

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. In order to escape this dilemma, we propose to first construct a rich representation (RFC) containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. RFC is constructed in a succession of training episodes. During each step of the discovery phase, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During the synthesis phase, we use knowledge distillation to force the network to simultaneously develop all the features identified during the discovery phase. RFC consistently helps six OoD methods achieve top performance on challenging invariant training benchmarks, ColoredMNIST (Arjovsky et al., 2020). Furthermore, on the realistic Camelyon17 task, our method helps both OoD and ERM methods outperform earlier compatable results by at least $5\%$, reduce standard deviation by at least $4.1\%$, and makes hyperparameter tuning and model selection more reliable.

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Agnieszka Słowik, Léon Bottou

Machine learning systems based on minimizing average error have been shown to perform inconsistently across notable subsets of the data, which is not exposed by a low average error for the entire dataset. In consequential social and economic applications, where data represent people, this can lead to discrimination of underrepresented gender and ethnic groups. Given the importance of bias mitigation in machine learning, the topic leads to contentious debates on how to ensure fairness in practice (data bias versus algorithmic bias). Distributionally Robust Optimization (DRO) seemingly addresses this problem by minimizing the worst expected risk across subpopulations. We establish theoretical results that clarify the relation between DRO and the optimization of the same loss averaged on an adequately weighted training dataset. The results cover finite and infinite number of training distributions, as well as convex and non-convex loss functions. We show that neither DRO nor curating the training set should be construed as a complete solution for bias mitigation: in the same way that there is no universally robust training set, there is no universal way to setup a DRO problem and ensure a socially acceptable set of results. We then leverage these insights to provide a mininal set of practical recommendations for addressing bias with DRO. Finally, we discuss ramifications of our results in other related applications of DRO, using an example of adversarial robustness. Our results show that there is merit to both the algorithm-focused and the data-focused side of the bias debate, as long as arguments in favor of these positions are precisely qualified and backed by relevant mathematics known today.

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Alexandre Défossez, Léon Bottou, Francis Bach, Nicolas Usunier

We provide a simple proof of the convergence of the optimization algorithms Adam and Adagrad with the assumptions of smooth gradients and almost sure uniform bound on the $\ell_\infty$ norm of the gradients. This work builds on the techniques introduced by Ward et al. (2019) and extends them to the Adam optimizer. 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 and the total number of iterations N. This bound can be made arbitrarily small. In particular, Adam with a learning rate $\alpha=1/\sqrt{N}$ and a momentum parameter on squared gradients $\beta_2=1 - 1/N$ achieves the same rate of convergence $O(\ln(N)/\sqrt{N})$ as Adagrad. Thus, it is possible to use Adam as a finite horizon version of Adagrad, much like constant step size SGD can be used instead of its asymptotically converging decaying step size version.

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Alexandre Défossez, Nicolas Usunier, Léon Bottou, Francis Bach

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 first show that an adaptation of Conv-Tasnet (Luo \& Mesgarani, 2019), a waveform-to-waveform model for source separation for speech, significantly beats the state-of-the-art on the MusDB dataset, the standard benchmark of multi-instrument source separation. Second, we observe that Conv-Tasnet follows a masking approach on the input signal, which has the potential drawback of removing parts of the relevant source without the capacity to reconstruct it. We propose Demucs, a new waveform-to-waveform model, which has an architecture closer to models for audio generation with more capacity on the decoder. Experiments on the MusDB dataset show that Demucs beats previously reported results in terms of signal to distortion ratio (SDR), but lower than Conv-Tasnet. Human evaluations show that Demucs has significantly higher quality (as assessed by mean opinion score) than Conv-Tasnet, but slightly more contamination from other sources, which explains the difference in SDR. Additional experiments with a larger dataset suggest that the gap in SDR between Demucs and Conv-Tasnet shrinks, showing that our approach is promising.

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Zhengdao Chen, Jianyu Zhang, Martin Arjovsky, Léon Bottou

We propose Symplectic Recurrent Neural Networks (SRNNs) as learning algorithms that capture the dynamics of physical systems from observed trajectories. An SRNN models the Hamiltonian function of the system by a neural network and furthermore leverages symplectic integration, multiple-step training and initial state optimization to address the challenging numerical issues associated with Hamiltonian systems. We show SRNNs succeed reliably on complex and noisy Hamiltonian systems. We also show how to augment the SRNN integration scheme in order to handle stiff dynamical systems such as bouncing billiards.

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Alexandre Défossez, Nicolas Usunier, Léon Bottou, Francis Bach

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.

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Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, David Lopez-Paz

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

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