NeurIPS 2023 Papers

Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion, which slows down convergence and incurs more communication rounds to achieve desired solutions. Given the trade-off between lower per-round communication costs and additional rounds of communication, it is unclear whether communication compression reduces the total communication cost. This paper explores the conditions under which unbiased compression, a widely used form of compression, can reduce the total communication cost, as well as the extent to which it can do so. To this end, we present the first theoretical formulation for characterizing the total communication cost in distributed optimization with unbiased compressors. We demonstrate that unbiased compression alone does not necessarily save the total communication cost, but this outcome can be achieved if the compressors used by all workers are further assumed independent. We establish lower bounds on the communication rounds required by algorithms using independent unbiased compressors to minimize smooth convex functions and show that these lower bounds are tight by refining the analysis for ADIANA. Our results reveal that using independent unbiased compression can reduce the total communication cost by a factor of up to $\Theta(\sqrt{\min\\{n,\kappa\\}})$ when all local smoothness constants are constrained by a common upper bound, where $n$ is the number of workers and $\kappa$ is the condition number of the functions being minimized. These theoretical findings are supported by experimental results.

A recent development in Bayesian optimization is the use of local optimization strategies, which can deliver strong empirical performance on high-dimensional problems compared to traditional global strategies. The "folk wisdom" in the literature is that the focus on local optimization sidesteps the curse of dimensionality; however, little is known concretely about the expected behavior or convergence of Bayesian local optimization routines. We first study the behavior of the local approach, and find that the statistics of individual local solutions of Gaussian process sample paths are surprisingly good compared to what we would expect to recover from global methods. We then present the first rigorous analysis of such a Bayesian local optimization algorithm recently proposed by Müller et al. (2021), and derive convergence rates in both the noisy and noiseless settings.

Classical analysis of convex and non-convex optimization methods often requires the Lipschitz continuity of the gradient, which limits the analysis to functions bounded by quadratics. Recent work relaxed this requirement to a non-uniform smoothness condition with the Hessian norm bounded by an affine function of the gradient norm, and proved convergence in the non-convex setting via gradient clipping, assuming bounded noise. In this paper, we further generalize this non-uniform smoothness condition and develop a simple, yet powerful analysis technique that bounds the gradients along the trajectory, thereby leading to stronger results for both convex and non-convex optimization problems. In particular, we obtain the classical convergence rates for (stochastic) gradient descent and Nesterov's accelerated gradient method in the convex and/or non-convex setting under this general smoothness condition. The new analysis approach does not require gradient clipping and allows heavy-tailed noise with bounded variance in the stochastic setting.

Through considerable effort and intuition, several recent works have reverse-engineered nontrivial behaviors of transformer models. This paper systematizes the mechanistic interpretability process they followed. First, researchers choose a metric and dataset that elicit the desired model behavior. Then, they apply activation patching to find which abstract neural network units are involved in the behavior. By varying the dataset, metric, and units under investigation, researchers can understand the functionality of each component. We automate one of the process' steps: finding the connections between the abstract neural network units that form a circuit. We propose several algorithms and reproduce previous interpretability results to validate them. For example, the ACDC algorithm rediscovered 5/5 of the component types in a circuit in GPT-2 Small that computes the Greater-Than operation. ACDC selected 68 of the 32,000 edges in GPT-2 Small, all of which were manually found by previous work. Our code is available at https://github.com/ArthurConmy/Automatic-Circuit-Discovery

We establish precise structural and risk equivalences between subsampling and ridge regularization for ensemble ridge estimators. Specifically, we prove that linear and quadratic functionals of subsample ridge estimators, when fitted with different ridge regularization levels $\lambda$ and subsample aspect ratios $\psi$, are asymptotically equivalent along specific paths in the $(\lambda,\psi)$-plane (where $\psi$ is the ratio of the feature dimension to the subsample size). Our results only require bounded moment assumptions on feature and response distributions and allow for arbitrary joint distributions. Furthermore, we provide a data-dependent method to determine the equivalent paths of $(\lambda,\psi)$. An indirect implication of our equivalences is that optimally tuned ridge regression exhibits a monotonic prediction risk in the data aspect ratio. This resolves a recent open problem raised by Nakkiran et al. for general data distributions under proportional asymptotics, assuming a mild regularity condition that maintains regression hardness through linearized signal-to-noise ratios.

We study the problem of regret minimization in Multi-Agent Multi-Armed Bandits (MAMABs) where the rewards are defined through a factor graph. We derive an instance-specific regret lower bound and characterize the minimal expected number of times each global action should be explored. Unfortunately, this bound and the corresponding optimal exploration process are obtained by solving a combinatorial optimization problem with a set of variables and constraints exponentially growing with the number of agents. We approximate the regret lower bound problem via Mean Field techniques to reduce the number of variables and constraints. By tuning the latter, we explore the trade-off between achievable regret and complexity. We devise Efficient Sampling for MAMAB (ESM), an algorithm whose regret asymptotically matches the corresponding approximated lower bound. We assess the regret and computational complexity of ESM numerically, using both synthetic and real-world experiments in radio communications networks.

Finetuning language models with reinforcement learning (RL), e.g. from human feedback (HF), is a prominent method for alignment. But optimizing against a reward model can improve on reward while degrading performance in other areas, a phenomenon known as reward hacking, alignment tax, or language drift. First, we argue that commonly-used test metrics are insufficient and instead measure how different algorithms tradeoff between reward and drift. The standard method modified the reward with a Kullback-Lieber (KL) penalty between the online and initial model. We propose Elastic Reset, a new algorithm that achieves higher reward with less drift without explicitly modifying the training objective. We periodically reset the online model to an exponentially moving average (EMA) of itself, then reset the EMA model to the initial model. Through the use of an EMA, our model recovers quickly after resets and achieves higher reward with less drift in the same number of steps. We demonstrate that fine-tuning language models with Elastic Reset leads to state-of-the-art performance on a small scale pivot-translation benchmark, outperforms all baselines in a medium-scale RLHF-like IMDB mock sentiment task and leads to a more performant and more aligned technical QA chatbot with LLaMA-7B. Code available https://github.com/mnoukhov/elastic-reset

The visual object category reports of artificial neural networks (ANNs) are notoriously sensitive to tiny, adversarial image perturbations. Because human category reports (aka human percepts) are thought to be insensitive to those same small-norm perturbations -- and locally stable in general -- this argues that ANNs are incomplete scientific models of human visual perception. Consistent with this, we show that when small-norm image perturbations are generated by standard ANN models, human object category percepts are indeed highly stable. However, in this very same "human-presumed-stable" regime, we find that robustified ANNs reliably discover low-norm image perturbations that strongly disrupt human percepts. These previously undetectable human perceptual disruptions are massive in amplitude, approaching the same level of sensitivity seen in robustified ANNs. Further, we show that robustified ANNs support precise perceptual state interventions: they guide the construction of low-norm image perturbations that strongly alter human category percepts toward specific prescribed percepts. In sum, these contemporary models of biological visual processing are now accurate enough to guide strong and precise interventions on human perception.

The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural networks yield similar neural predictions, but it remains unclear how to differentiate among models that perform equally well at predicting neural responses. To gain insight into this, we use a recent theoretical framework that relates the generalization error from regression to the spectral properties of the model and the target. We apply this theory to the case of regression between model activations and neural responses and decompose the neural prediction error in terms of the model eigenspectra, alignment of model eigenvectors and neural responses, and the training set size. Using this decomposition, we introduce geometrical measures to interpret the neural prediction error. We test a large number of deep neural networks that predict visual cortical activity and show that there are multiple types of geometries that result in low neural prediction error as measured via regression. The work demonstrates that carefully decomposing representational metrics can provide interpretability of how models are capturing neural activity and points the way towards improved models of neural activity.

This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The algorithms we propose exhibit sublinear regret rates in the worst cases and achieve logarithmic regrets when the data is "easy," with per-round time almost linear in the number of investment alternatives. The regret bounds are derived using novel smoothness characterizations of the logarithmic loss, a local norm-based analysis of following the regularized leader (FTRL) with self-concordant regularizers, which are not necessarily barriers, and an implicit variant of optimistic FTRL with the log-barrier.

Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact and approximate combinatorial algorithms for computing the optimal transport distance are hard to parallelize. This has motivated the development of numerical solvers (e.g. Sinkhorn method) that can exploit GPU parallelism and produce approximate solutions. We introduce the first parallel combinatorial algorithm to find an additive $\varepsilon$-approximation of the OT distance. The parallel complexity of our algorithm is $O(\log(n)/ \varepsilon^2)$ where $n$ is the total support size for the input distributions. In Massive Parallel Computation (MPC) frameworks such as Hadoop and MapReduce, our algorithm computes an $\varepsilon$-approximate transport plan in $O(\log (\log (n/\varepsilon))/\varepsilon^2)$ rounds with $O(n/\varepsilon)$ space per machine; all prior algorithms in the MPC framework take $\Omega(\log n)$ rounds. We also provide a GPU-friendly matrix-based interpretation of our algorithm where each step of the algorithm is row or column manipulation of the matrix. Experiments suggest that our combinatorial algorithm is faster than the state-of-the-art approximate solvers in the GPU, especially for higher values of $n$.

Control Barrier Functions (CBFs) are a popular approach for safe control of nonlinear systems. In CBF-based control, the desired safety properties of the system are mapped to nonnegativity of a CBF, and the control input is chosen to ensure that the CBF remains nonnegative for all time. Recently, machine learning methods that represent CBFs as neural networks (neural control barrier functions, or NCBFs) have shown great promise due to the universal representability of neural networks. However, verifying that a learned CBF guarantees safety remains a challenging research problem. This paper presents novel exact conditions and algorithms for verifying safety of feedforward NCBFs with ReLU activation functions. The key challenge in doing so is that, due to the piecewise linearity of the ReLU function, the NCBF will be nondifferentiable at certain points, thus invalidating traditional safety verification methods that assume a smooth barrier function. We resolve this issue by leveraging a generalization of Nagumo's theorem for proving invariance of sets with nonsmooth boundaries to derive necessary and sufficient conditions for safety. Based on this condition, we propose an algorithm for safety verification of NCBFs that first decomposes the NCBF into piecewise linear segments and then solves a nonlinear program to verify safety of each segment as well as the intersections of the linear segments. We mitigate the complexity by only considering the boundary of the safe region and by pruning the segments with Interval Bound Propagation (IBP) and linear relaxation. We evaluate our approach through numerical studies with comparison to state-of-the-art SMT-based methods. Our code is available at https://github.com/HongchaoZhang-HZ/exactverif-reluncbf-nips23.

We present a new combinatorial bandit model, the \textit{cascading contextual assortment bandit}. This model serves as a generalization of both existing cascading bandits and assortment bandits, broadening their applicability in practice. For this model, we propose our first UCB bandit algorithm, UCB-CCA. We prove that this algorithm achieves a $T$-step regret upper-bound of $\tilde{\mathcal{O}}(\frac{1}{\kappa}d\sqrt{T})$, sharper than existing bounds for cascading contextual bandits by eliminating dependence on cascade length $K$. To improve the dependence on problem-dependent constant $\kappa$, we introduce our second algorithm, UCB-CCA+, which leverages a new Bernstein-type concentration result. This algorithm achieves $\tilde{\mathcal{O}}(d\sqrt{T})$ without dependence on $\kappa$ in the leading term. We substantiate our theoretical claims with numerical experiments, demonstrating the practical efficacy of our proposed methods.

We consider the stochastic multi-armed bandit problem and fully characterize the interplays among three desired properties for policy design: worst-case optimality, instance-dependent consistency, and light-tailed risk. We show how the order of expected regret exactly affects the decaying rate of the regret tail probability for both the worst-case and instance-dependent scenario. A novel policy is proposed to achieve the optimal regret tail risk for any regret threshold. Concretely, for any given $\alpha\in[1/2, 1)$ and $\beta\in[0, 1)$, our policy achieves a worst-case expected regret of $\tilde O(T^\alpha)$ and instance-dependent expected regret of $\tilde O(T^\beta)$, while enjoys a probability of incurring an $\Omega(T^\delta)$ regret that decays exponentially with a polynomial $T$ term. Such decaying rate is proved to be best achievable. We also generalize our analysis to the stochastic multi-armed bandit problem with non-stationary baseline rewards, where in each time period $t$, the decision maker pulls one of $K$ arms and collects a reward which is the sum of three terms: the mean of the pulled arm, an independent noise, and a non-stationary baseline reward as a function of $t$. Our results reveal insights on the trade-off between expected regret and tail risk for both worst-case and instance-dependent scenario, indicating that more sub-optimality and inconsistency leaves space for more light-tailed risk of incurring a large regret.