TeraHAC: Hierarchical Agglomerative Clustering of Trillion-Edge Graphs

We introduce TeraHAC, a $(1+\epsilon)$-approximate hierarchical agglomerative clustering (HAC) algorithm which scales to trillion-edge graphs. Our algorithm is based on a new approach to computing $(1+\epsilon)$-approximate HAC, which is a novel combination of the nearest-neighbor chain algorithm and the notion of $(1+\epsilon)$-approximate HAC. Our approach allows us to partition the graph among multiple machines and make significant progress in computing the clustering within each partition before any communication with other partitions is needed. We evaluate TeraHAC on a number of real-world and synthetic graphs of up to 8 trillion edges. We show that TeraHAC requires over 100x fewer rounds compared to previously known approaches for computing HAC. It is up to 8.3x faster than SCC, the state-of-the-art distributed algorithm for hierarchical clustering, while achieving 1.16x higher quality. In fact, TeraHAC essentially retains the quality of the celebrated HAC algorithm while significantly improving the running time.

Reconstructing Training Data from Model Gradient, Provably

Understanding when and how much a model gradient leaks information about the training sample is an important question in privacy. In this paper, we present a surprising result: even without training or memorizing the data, we can fully reconstruct the training samples from a single gradient query at a randomly chosen parameter value. We prove the identifiability of the training data under mild conditions: with shallow or deep neural networks and a wide range of activation functions. We also present a statistically and computationally efficient algorithm based on tensor decomposition to reconstruct the training data. As a provable attack that reveals sensitive training data, our findings suggest potential severe threats to privacy, especially in federated learning.

Label Noise SGD Provably Prefers Flat Global Minimizers

In overparametrized models, the noise in stochastic gradient descent (SGD) implicitly regularizes the optimization trajectory and determines which local minimum SGD converges to. Motivated by empirical studies that demonstrate that training with noisy labels improves generalization, we study the implicit regularization effect of SGD with label noise. We show that SGD with label noise converges to a stationary point of a regularized loss $L(\theta) +\lambda R(\theta)$, where $L(\theta)$ is the training loss, $\lambda$ is an effective regularization parameter depending on the step size, strength of the label noise, and the batch size, and $R(\theta)$ is an explicit regularizer that penalizes sharp minimizers. Our analysis uncovers an additional regularization effect of large learning rates beyond the linear scaling rule that penalizes large eigenvalues of the Hessian more than small ones. We also prove extensions to classification with general loss functions, SGD with momentum, and SGD with general noise covariance, significantly strengthening the prior work of Blanc et al. to global convergence and large learning rates and of HaoChen et al. to general models.

Iterative Refinement in the Continuous Space for Non-Autoregressive Neural Machine Translation

We propose an efficient inference procedure for non-autoregressive machine translation that iteratively refines translation purely in the continuous space. Given a continuous latent variable model for machine translation (Shu et al., 2020), we train an inference network to approximate the gradient of the marginal log probability of the target sentence, using only the latent variable as input. This allows us to use gradient-based optimization to find the target sentence at inference time that approximately maximizes its marginal probability. As each refinement step only involves computation in the latent space of low dimensionality (we use 8 in our experiments), we avoid computational overhead incurred by existing non-autoregressive inference procedures that often refine in token space. We compare our approach to a recently proposed EM-like inference procedure (Shu et al., 2020) that optimizes in a hybrid space, consisting of both discrete and continuous variables. We evaluate our approach on WMT'14 En-De, WMT'16 Ro-En and IWSLT'16 De-En, and observe two advantages over the EM-like inference: (1) it is computationally efficient, i.e. each refinement step is twice as fast, and (2) it is more effective, resulting in higher marginal probabilities and BLEU scores with the same number of refinement steps. On WMT'14 En-De, for instance, our approach is able to decode 6.2 times faster than the autoregressive model with minimal degradation to translation quality (0.9 BLEU).

On the Discrepancy between Density Estimation and Sequence Generation

Many sequence-to-sequence generation tasks, including machine translation and text-to-speech, can be posed as estimating the density of the output y given the input x: p(y|x). Given this interpretation, it is natural to evaluate sequence-to-sequence models using conditional log-likelihood on a test set. However, the goal of sequence-to-sequence generation (or structured prediction) is to find the best output y^ given an input x, and each task has its own downstream metric R that scores a model output by comparing against a set of references y*: R(y^, y* | x). While we hope that a model that excels in density estimation also performs well on the downstream metric, the exact correlation has not been studied for sequence generation tasks. In this paper, by comparing several density estimators on five machine translation tasks, we find that the correlation between rankings of models based on log-likelihood and BLEU varies significantly depending on the range of the model families being compared. First, log-likelihood is highly correlated with BLEU when we consider models within the same family (e.g. autoregressive models, or latent variable models with the same parameterization of the prior). However, we observe no correlation between rankings of models across different families: (1) among non-autoregressive latent variable models, a flexible prior distribution is better at density estimation but gives worse generation quality than a simple prior, and (2) autoregressive models offer the best translation performance overall, while latent variable models with a normalizing flow prior give the highest held-out log-likelihood across all datasets. Therefore, we recommend using a simple prior for the latent variable non-autoregressive model when fast generation speed is desired.

Deploying the NASA Valkyrie Humanoid for IED Response: An Initial Approach and Evaluation Summary

As part of a feasibility study, this paper shows the NASA Valkyrie humanoid robot performing an end-to-end improvised explosive device (IED) response task. To demonstrate and evaluate robot capabilities, sub-tasks highlight different locomotion, manipulation, and perception requirements: traversing uneven terrain, passing through a narrow passageway, opening a car door, retrieving a suspected IED, and securing the IED in a total containment vessel (TCV). For each sub-task, a description of the technical approach and the hidden challenges that were overcome during development are presented. The discussion of results, which explicitly includes existing limitations, is aimed at motivating continued research and development to enable practical deployment of humanoid robots for IED response. For instance, the data shows that operator pauses contribute to 50\% of the total completion time, which implies that further work is needed on user interfaces for increasing task completion efficiency.

Countering Language Drift via Visual Grounding

Emergent multi-agent communication protocols are very different from natural language and not easily interpretable by humans. We find that agents that were initially pretrained to produce natural language can also experience detrimental language drift: when a non-linguistic reward is used in a goal-based task, e.g. some scalar success metric, the communication protocol may easily and radically diverge from natural language. We recast translation as a multi-agent communication game and examine auxiliary training constraints for their effectiveness in mitigating language drift. We show that a combination of syntactic (language model likelihood) and semantic (visual grounding) constraints gives the best communication performance, allowing pre-trained agents to retain English syntax while learning to accurately convey the intended meaning.

Latent-Variable Non-Autoregressive Neural Machine Translation with Deterministic Inference using a Delta Posterior

Although neural machine translation models reached high translation quality, the autoregressive nature makes inference difficult to parallelize and leads to high translation latency. Inspired by recent refinement-based approaches, we propose a latent-variable non-autoregressive model with continuous latent variables and deterministic inference procedure. In contrast to existing approaches, we use a deterministic iterative inference algorithm to find a target sequence that maximizes the lowerbound to the log-probability. During inference, the length of translation automatically adapts itself. Our experiments show that the lowerbound can be greatly increased by running the inference algorithm for only one step, resulting in significantly improved translation quality. Our proposed model closes the gap between non-autoregressive and autoregressive approaches on ASPEC Ja-En dataset with 7.8x faster decoding. On WMT'14 En-De dataset, our model narrows the performance gap with autoregressive baseline down to 2.0 BLEU points with 12.5x speedup.