How can we rely on an end-to-end autonomous vehicle's complex decision-making system during deployment? One common solution is to have a ``fallback layer'' that checks the planned trajectory for rule violations and replaces it with a pre-defined safe action if necessary. Another approach involves adjusting the planner's decisions to minimize a pre-defined ``cost function'' using additional system predictions such as road layouts and detected obstacles. However, these pre-programmed rules or cost functions cannot learn and improve with new training data, often resulting in overly conservative behaviors. In this work, we propose Centaur (Cluster Entropy for Test-time trAining using Uncertainty) which updates a planner's behavior via test-time training, without relying on hand-engineered rules or cost functions. Instead, we measure and minimize the uncertainty in the planner's decisions. For this, we develop a novel uncertainty measure, called Cluster Entropy, which is simple, interpretable, and compatible with state-of-the-art planning algorithms. Using data collected at prior test-time time-steps, we perform an update to the model's parameters using a gradient that minimizes the Cluster Entropy. With only this sole gradient update prior to inference, Centaur exhibits significant improvements, ranking first on the navtest leaderboard with notable gains in safety-critical metrics such as time to collision. To provide detailed insights on a per-scenario basis, we also introduce navsafe, a challenging new benchmark, which highlights previously undiscovered failure modes of driving models.

We prove a convergence theorem for stochastic gradient descents on manifolds with adaptive learning rate and apply it to the weighted low-rank approximation problem.

We analyze the landscape and training dynamics of diagonal linear networks in a linear regression task, with the network parameters being perturbed by small isotropic normal noise. The addition of such noise may be interpreted as a stochastic form of sharpness-aware minimization (SAM) and we prove several results that relate its action on the underlying landscape and training dynamics to the sharpness of the loss. In particular, the noise changes the expected gradient to force balancing of the weight matrices at a fast rate along the descent trajectory. In the diagonal linear model, we show that this equates to minimizing the average sharpness, as well as the trace of the Hessian matrix, among all possible factorizations of the same matrix. Further, the noise forces the gradient descent iterates towards a shrinkage-thresholding of the underlying true parameter, with the noise level explicitly regulating both the shrinkage factor and the threshold.

The Nearest Neighbor model is the $\textit{de facto}$ thermodynamic model of RNA secondary structure formation and is a cornerstone of RNA structure prediction and sequence design. The current functional form (Turner 2004) contains $\approx13,000$ underlying thermodynamic parameters, and fitting these to both experimental and structural data is computationally challenging. Here, we leverage recent advances in $\textit{differentiable folding}$, a method for directly computing gradients of the RNA folding algorithms, to devise an efficient, scalable, and flexible means of parameter optimization that uses known RNA structures and thermodynamic experiments. Our method yields a significantly improved parameter set that outperforms existing baselines on all metrics, including an increase in the average predicted probability of ground-truth sequence-structure pairs for a single RNA family by over 23 orders of magnitude. Our framework provides a path towards drastically improved RNA models, enabling the flexible incorporation of new experimental data, definition of novel loss terms, large training sets, and even treatment as a module in larger deep learning pipelines. We make available a new database, RNAometer, with experimentally-determined stabilities for small RNA model systems.

The learning rate in stochastic gradient methods is a critical hyperparameter that is notoriously costly to tune via standard grid search, especially for training modern large-scale models with billions of parameters. We identify a theoretical advantage of learning rate annealing schemes that decay the learning rate to zero at a polynomial rate, such as the widely-used cosine schedule, by demonstrating their increased robustness to initial parameter misspecification due to a coarse grid search. We present an analysis in a stochastic convex optimization setup demonstrating that the convergence rate of stochastic gradient descent with annealed schedules depends sublinearly on the multiplicative misspecification factor $\rho$ (i.e., the grid resolution), achieving a rate of $O(\rho^{1/(2p+1)}/\sqrt{T})$ where $p$ is the degree of polynomial decay and $T$ is the number of steps, in contrast to the $O(\rho/\sqrt{T})$ rate that arises with fixed stepsizes and exhibits a linear dependence on $\rho$. Experiments confirm the increased robustness compared to tuning with a fixed stepsize, that has significant implications for the computational overhead of hyperparameter search in practical training scenarios.

We propose VIBE, a model-agnostic framework that trains classifiers resilient to backdoor attacks. The key concept behind our approach is to treat malicious inputs and corrupted labels from the training dataset as observed random variables, while the actual clean labels are latent. VIBE then recovers the corresponding latent clean label posterior through variational inference. The resulting training procedure follows the expectation-maximization (EM) algorithm. The E-step infers the clean pseudolabels by solving an entropy-regularized optimal transport problem, while the M-step updates the classifier parameters via gradient descent. Being modular, VIBE can seamlessly integrate with recent advancements in self-supervised representation learning, which enhance its ability to resist backdoor attacks. We experimentally validate the method effectiveness against contemporary backdoor attacks on standard datasets, a large-scale setup with 1$k$ classes, and a dataset poisoned with multiple attacks. VIBE consistently outperforms previous defenses across all tested scenarios.

Bayesian inference for hierarchical models can be very challenging. MCMC methods have difficulty scaling to large models with many observations and latent variables. While variational inference (VI) and reweighted wake-sleep (RWS) can be more scalable, they are gradient-based methods and so often require many iterations to converge. Our key insight was that modern massively parallel importance weighting methods (Bowyer et al., 2024) give fast and accurate posterior moment estimates, and we can use these moment estimates to rapidly learn an approximate posterior. Specifically, we propose using expectation maximization to fit the approximate posterior, which we call QEM. The expectation step involves computing the posterior moments using high-quality massively parallel estimates from Bowyer et al. (2024). The maximization step involves fitting the approximate posterior using these moments, which can be done straightforwardly for simple approximate posteriors such as Gaussian, Gamma, Beta, Dirichlet, Binomial, Multinomial, Categorical, etc. (or combinations thereof). We show that QEM is faster than state-of-the-art, massively parallel variants of RWS and VI, and is invariant to reparameterizations of the model that dramatically slow down gradient based methods.

Water quality data can supply a substantial decision support for water resources utilization and pollution prevention. However, there are numerous missing values in water quality data due to inescapable factors like sensor failure, thereby leading to biased result for hydrological analysis and failing to support environmental governance decision accurately. A Latent Factorization of Tensors (LFT) with Stochastic Gradient Descent (SGD) proves to be an efficient imputation method. However, a standard SGD-based LFT model commonly surfers from the slow convergence that impairs its efficiency. To tackle this issue, this paper proposes a Fast Latent Factorization of Tensors (FLFT) model. It constructs an adjusted instance error into SGD via leveraging a nonlinear PID controller to incorporates the past, current and future information of prediction error for improving convergence rate. Comparing with state-of-art models in real world datasets, the results of experiment indicate that the FLFT model achieves a better convergence rate and higher accuracy.

Domain Generalization (DG) research has gained considerable traction as of late, since the ability to generalize to unseen data distributions is a requirement that eludes even state-of-the-art training algorithms. In this paper we observe that the initial iterations of model training play a key role in domain generalization effectiveness, since the loss landscape may be significantly different across the training and test distributions, contrary to the case of i.i.d. data. Conflicts between gradients of the loss components of each domain lead the optimization procedure to undesirable local minima that do not capture the domain-invariant features of the target classes. We propose alleviating domain conflicts in model optimization, by iteratively annealing the parameters of a model in the early stages of training and searching for points where gradients align between domains. By discovering a set of parameter values where gradients are updated towards the same direction for each data distribution present in the training set, the proposed Gradient-Guided Annealing (GGA) algorithm encourages models to seek out minima that exhibit improved robustness against domain shifts. The efficacy of GGA is evaluated on five widely accepted and challenging image classification domain generalization benchmarks, where its use alone is able to establish highly competitive or even state-of-the-art performance. Moreover, when combined with previously proposed domain-generalization algorithms it is able to consistently improve their effectiveness by significant margins.

In distributed learning, sign-based compression algorithms such as signSGD with majority vote provide a lightweight alternative to SGD with an additional advantage: fault tolerance (almost) for free. However, for signSGD with majority vote, this fault tolerance has been shown to cover only the case of weaker adversaries, i.e., ones that are not omniscient or cannot collude to base their attack on common knowledge and strategy. In this work, we close this gap and provide new insights into how signSGD with majority vote can be resilient against omniscient and colluding adversaries, which craft an attack after communicating with other adversaries, thus having better information to perform the most damaging attack based on a common optimal strategy. Our core contribution is in providing a proof that begins by defining the omniscience framework and the strongest possible damage against signSGD with majority vote without imposing any restrictions on the attacker. Thanks to the filtering effect of the sign-based method, we upper-bound the space of attacks to the optimal strategy for maximizing damage by an attacker. Hence, we derive an explicit probabilistic bound in terms of incorrect aggregation without resorting to unknown constants, providing a convergence bound on signSGD with majority vote in the presence of Byzantine attackers, along with a precise convergence rate. Our findings are supported by experiments on the MNIST dataset in a distributed learning environment with adversaries of varying strength.