Alex Tang

Pranjal Awasthi, Alex Tang, Aravindan Vijayaraghavan

We provide a convergence analysis of gradient descent for the problem of agnostically learning a single ReLU function with moderate bias under Gaussian distributions. Unlike prior work that studies the setting of zero bias, we consider the more challenging scenario when the bias of the ReLU function is non-zero. Our main result establishes that starting from random initialization, in a polynomial number of iterations gradient descent outputs, with high probability, a ReLU function that achieves an error that is within a constant factor of the optimal error of the best ReLU function with moderate bias. We also provide finite sample guarantees, and these techniques generalize to a broader class of marginal distributions beyond Gaussians.

Alex Tang, M. Emrullah Ildiz, Batin Kurt et al.

Selective State-Space Models (SSMs) such as Mamba have emerged as an alternative architecture to self-attention based transformers in sequence modeling tasks. Recent works have demonstrated the use of transformers in some filtering and output prediction tasks via in-context learning. In this paper, we analyze whether structured SSMs can work equally well for filtering of unknown systems. In particular, we train the SSM on trajectory samples from a set of systems. At run-time, the SSM is given the outputs of an unknown system from the same set and is expected to predict the next output online. Theoretically, under appropriate assumptions, we derive generalization bounds as to why SSMs succeed in such tasks. Empirically, we demonstrate the performance via several numerical examples. We also discuss the advantages and disadvantages of SSMs versus transformers for this task.

Pranjal Awasthi, Alex Tang, Aravindan Vijayaraghavan

We present polynomial time and sample efficient algorithms for learning an unknown depth-2 feedforward neural network with general ReLU activations, under mild non-degeneracy assumptions. In particular, we consider learning an unknown network of the form $f(x) = {a}^{\mathsf{T}}σ({W}^\mathsf{T}x+b)$, where $x$ is drawn from the Gaussian distribution, and $σ(t) := \max(t,0)$ is the ReLU activation. Prior works for learning networks with ReLU activations assume that the bias $b$ is zero. In order to deal with the presence of the bias terms, our proposed algorithm consists of robustly decomposing multiple higher order tensors arising from the Hermite expansion of the function $f(x)$. Using these ideas we also establish identifiability of the network parameters under minimal assumptions.

Piali Das, Valerio Perrone, Nikita Ivkin et al.

AutoML systems provide a black-box solution to machine learning problems by selecting the right way of processing features, choosing an algorithm and tuning the hyperparameters of the entire pipeline. Although these systems perform well on many datasets, there is still a non-negligible number of datasets for which the one-shot solution produced by each particular system would provide sub-par performance. In this paper, we present Amazon SageMaker Autopilot: a fully managed system providing an automated ML solution that can be modified when needed. Given a tabular dataset and the target column name, Autopilot identifies the problem type, analyzes the data and produces a diverse set of complete ML pipelines including feature preprocessing and ML algorithms, which are tuned to generate a leaderboard of candidate models. In the scenario where the performance is not satisfactory, a data scientist is able to view and edit the proposed ML pipelines in order to infuse their expertise and business knowledge without having to revert to a fully manual solution. This paper describes the different components of Autopilot, emphasizing the infrastructure choices that allow scalability, high quality models, editable ML pipelines, consumption of artifacts of offline meta-learning, and a convenient integration with the entire SageMaker suite allowing these trained models to be used in a production setting.