pwc-archive/papers-with-abstracts huggingface dataset:
Riemannian coordinate descent algorithms on matrix manifolds
Authors: Andi Han, Pratik Jawanpuria, Bamdev Mishra
Date: 2024-06-04 00:00:00
Tasks: Riemannian optimization

Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent direction on the manifold. This results in updating all the variables at every iteration. In this work, we provide a general framework for developing computationally efficient coordinate descent (CD) algorithms on matrix manifolds that allows updating only a few variables at every iteration while adhering to the manifold constraint. In particular, we propose CD algorithms for various manifolds such as Stiefel, Grassmann, (generalized) hyperbolic, symplectic, and symmetric positive (semi)definite. While the cost per iteration of the proposed CD algorithms is low, we further develop a more efficient variant via a first-order approximation of the objective function. We analyze their convergence and complexity, and empirically illustrate their efficacy in several applications.
SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining
Authors: Andi Han, Jiaxiang Li, Wei Huang, Mingyi Hong, Akiko Takeda, Pratik Jawanpuria, Bamdev Mishra
Date: 2024-06-04 00:00:00
Tasks: Quantization, Sparse Learning

Large language models (LLMs) have shown impressive capabilities across various tasks. However, training LLMs from scratch requires significant computational power and extensive memory capacity. Recent studies have explored low-rank structures on weights for efficient fine-tuning in terms of parameters and memory, either through low-rank adaptation or factorization. While effective for fine-tuning, low-rank structures are generally less suitable for pretraining because they restrict parameters to a low-dimensional subspace. In this work, we propose to parameterize the weights as a sum of low-rank and sparse matrices for pretraining, which we call SLTrain. The low-rank component is learned via matrix factorization, while for the sparse component, we employ a simple strategy of uniformly selecting the sparsity support at random and learning only the non-zero entries with the fixed support. While being simple, the random fixed-support sparse learning strategy significantly enhances pretraining when combined with low-rank learning. Our results show that SLTrain adds minimal extra parameters and memory costs compared to pretraining with low-rank parameterization, yet achieves substantially better performance, which is comparable to full-rank training. Remarkably, when combined with quantization and per-layer updates, SLTrain can reduce memory requirements by up to 73% when pretraining the LLaMA 7B model.
Rectifying Reinforcement Learning for Reward Matching
Authors: Haoran He, Emmanuel Bengio, Qingpeng Cai, Ling Pan
Date: 2024-06-04 00:00:00
Tasks: Decision Making, reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL), Sequential Decision Making

The Generative Flow Network (GFlowNet) is a probabilistic framework in which an agent learns a stochastic policy and flow functions to sample objects with probability proportional to an unnormalized reward function. GFlowNets share a strong resemblance to reinforcement learning (RL), that typically aims to maximize reward, due to their sequential decision-making processes. Recent works have studied connections between GFlowNets and maximum entropy (MaxEnt) RL, which modifies the standard objective of RL agents by learning an entropy-regularized objective. However, a critical theoretical gap persists: despite the apparent similarities in their sequential decision-making nature, a direct link between GFlowNets and standard RL has yet to be discovered, while bridging this gap could further unlock the potential of both fields. In this paper, we establish a new connection between GFlowNets and policy evaluation for a uniform policy. Surprisingly, we find that the resulting value function for the uniform policy has a close relationship to the flows in GFlowNets. Leveraging these insights, we further propose a novel rectified policy evaluation (RPE) algorithm, which achieves the same reward-matching effect as GFlowNets, offering a new perspective. We compare RPE, MaxEnt RL, and GFlowNets in a number of benchmarks, and show that RPE achieves competitive results compared to previous approaches. This work sheds light on the previously unexplored connection between (non-MaxEnt) RL and GFlowNets, potentially opening new avenues for future research in both fields.
On the Recoverability of Causal Relations from Temporally Aggregated I.I.D. Data
Authors: Shunxing Fan, Mingming Gong, Kun Zhang
Date: 2024-06-04 00:00:00
Tasks: Causal Discovery

We consider the effect of temporal aggregation on instantaneous (non-temporal) causal discovery in general setting. This is motivated by the observation that the true causal time lag is often considerably shorter than the observational interval. This discrepancy leads to high aggregation, causing time-delay causality to vanish and instantaneous dependence to manifest. Although we expect such instantaneous dependence has consistency with the true causal relation in certain sense to make the discovery results meaningful, it remains unclear what type of consistency we need and when will such consistency be satisfied. We proposed functional consistency and conditional independence consistency in formal way correspond functional causal model-based methods and conditional independence-based methods respectively and provide the conditions under which these consistencies will hold. We show theoretically and experimentally that causal discovery results may be seriously distorted by aggregation especially in complete nonlinear case and we also find causal relationship still recoverable from aggregated data if we have partial linearity or appropriate prior. Our findings suggest community should take a cautious and meticulous approach when interpreting causal discovery results from such data and show why and when aggregation will distort the performance of causal discovery methods.
Fast and Scalable Multi-Kernel Encoder Classifier
Authors: Cencheng Shen
Date: 2024-06-04 00:00:00
Tasks: Graph Embedding

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding, and seamlessly integrates multiple kernels to enhance the learning process. Our theoretical analysis offers a population-level characterization of this approach using random variables. Empirically, our method demonstrates superior running time compared to standard approaches such as support vector machines and two-layer neural network, while achieving comparable classification accuracy across various simulated and real datasets.
DNCs Require More Planning Steps
Authors: Yara Shamshoum, Nitzan Hodos, Yuval Sieradzki, Assaf Schuster
Date: 2024-06-04 00:00:00

Many recent works use machine learning models to solve various complex algorithmic problems. However, these models attempt to reach a solution without considering the problem's required computational complexity, which can be detrimental to their ability to solve it correctly. In this work we investigate the effect of computational time and memory on generalization of implicit algorithmic solvers. To do so, we focus on the Differentiable Neural Computer (DNC), a general problem solver that also lets us reason directly about its usage of time and memory. In this work, we argue that the number of planning steps the model is allowed to take, which we call "planning budget", is a constraint that can cause the model to generalize poorly and hurt its ability to fully utilize its external memory. We evaluate our method on Graph Shortest Path, Convex Hull, Graph MinCut and Associative Recall, and show how the planning budget can drastically change the behavior of the learned algorithm, in terms of learned time complexity, training time, stability and generalization to inputs larger than those seen during training.
AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields
Authors: Louis Serrano, Thomas X Wang, Etienne Le Naour, Jean-Noël Vittaut, Patrick Gallinari
Date: 2024-06-04 00:00:00
Tasks: Decoder

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.
Branches: Efficiently Seeking Optimal Sparse Decision Trees with AO*
Authors: Ayman Chaouki, Jesse Read, Albert Bifet
Date: 2024-06-04 00:00:00
Tasks: Computational Efficiency, Interpretable Machine Learning

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch & Bound. However, most of these approaches rely on a Depth-First-Search strategy, which is inefficient when searching for DTs at high depths and requires the definition of a maximum depth hyperparameter. Best-First-Search was also employed by other methods to circumvent these issues. The downside of this strategy is its higher memory consumption, as such, it has to be designed in a fully efficient manner that takes full advantage of the problem's structure. We formulate the problem within an AND/OR graph search framework and we solve it with a novel AO*-type algorithm called Branches. We prove both optimality and complexity guarantees for Branches and we show that it is more efficient than the state of the art theoretically and on a variety of experiments. Furthermore, Branches supports non-binary features unlike the other methods, we show that this property can further induce larger gains in computational efficiency.
Learning the Hodgkin-Huxley Model with Operator Learning Techniques
Authors: Edoardo Centofanti, Massimiliano Ghiotto, Luca F. Pavarino
Date: 2024-06-04 00:00:00
Tasks: Operator learning

We construct and compare three operator learning architectures, DeepONet, Fourier Neural Operator, and Wavelet Neural Operator, in order to learn the operator mapping a time-dependent applied current to the transmembrane potential of the Hodgkin- Huxley ionic model. The underlying non-linearity of the Hodgkin-Huxley dynamical system, the stiffness of its solutions, and the threshold dynamics depending on the intensity of the applied current, are some of the challenges to address when exploiting artificial neural networks to learn this class of complex operators. By properly designing these operator learning techniques, we demonstrate their ability to effectively address these challenges, achieving a relative L2 error as low as 1.4% in learning the solutions of the Hodgkin-Huxley ionic model.
Stein Random Feature Regression
Authors: Houston Warren, Rafael Oliveira, Fabio Ramos
Date: 2024-06-01 00:00:00
Tasks: Gaussian Processes, regression

In large-scale regression problems, random Fourier features (RFFs) have significantly enhanced the computational scalability and flexibility of Gaussian processes (GPs) by defining kernels through their spectral density, from which a finite set of Monte Carlo samples can be used to form an approximate low-rank GP. However, the efficacy of RFFs in kernel approximation and Bayesian kernel learning depends on the ability to tractably sample the kernel spectral measure and the quality of the generated samples. We introduce Stein random features (SRF), leveraging Stein variational gradient descent, which can be used to both generate high-quality RFF samples of known spectral densities as well as flexibly and efficiently approximate traditionally non-analytical spectral measure posteriors. SRFs require only the evaluation of log-probability gradients to perform both kernel approximation and Bayesian kernel learning that results in superior performance over traditional approaches. We empirically validate the effectiveness of SRFs by comparing them to baselines on kernel approximation and well-known GP regression problems.
SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDP
Authors: Subhojyoti Mukherjee, Josiah P. Hanna, Robert Nowak
Date: 2024-06-04 00:00:00

In this paper, we study safe data collection for the purpose of policy evaluation in tabular Markov decision processes (MDPs). In policy evaluation, we are given a \textit{target} policy and asked to estimate the expected cumulative reward it will obtain. Policy evaluation requires data and we are interested in the question of what \textit{behavior} policy should collect the data for the most accurate evaluation of the target policy. While prior work has considered behavior policy selection, in this paper, we additionally consider a safety constraint on the behavior policy. Namely, we assume there exists a known default policy that incurs a particular expected cost when run and we enforce that the cumulative cost of all behavior policies ran is better than a constant factor of the cost that would be incurred had we always run the default policy. We first show that there exists a class of intractable MDPs where no safe oracle algorithm with knowledge about problem parameters can efficiently collect data and satisfy the safety constraints. We then define the tractability condition for an MDP such that a safe oracle algorithm can efficiently collect data and using that we prove the first lower bound for this setting. We then introduce an algorithm SaVeR for this problem that approximates the safe oracle algorithm and bound the finite-sample mean squared error of the algorithm while ensuring it satisfies the safety constraint. Finally, we show in simulations that SaVeR produces low MSE policy evaluation while satisfying the safety constraint.
Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs
Authors: Luca Arnaboldi, Yatin Dandi, Florent Krzakala, Bruno Loureiro, Luca Pesce, Ludovic Stephan
Date: 2024-06-04 00:00:00

We study the impact of the batch size $n_b$ on the iteration time $T$ of training two-layer neural networks with one-pass stochastic gradient descent (SGD) on multi-index target functions of isotropic covariates. We characterize the optimal batch size minimizing the iteration time as a function of the hardness of the target, as characterized by the information exponents. We show that performing gradient updates with large batches $n_b \lesssim d^{\frac{\ell}{2}}$ minimizes the training time without changing the total sample complexity, where $\ell$ is the information exponent of the target to be learned \citep{arous2021online} and $d$ is the input dimension. However, larger batch sizes than $n_b \gg d^{\frac{\ell}{2}}$ are detrimental for improving the time complexity of SGD. We provably overcome this fundamental limitation via a different training protocol, \textit{Correlation loss SGD}, which suppresses the auto-correlation terms in the loss function. We show that one can track the training progress by a system of low-dimensional ordinary differential equations (ODEs). Finally, we validate our theoretical results with numerical experiments.
Almost linear time differentially private release of synthetic graphs
Authors: Jingcheng Liu, Jalaj Upadhyay, Zongrui Zou
Date: 2024-06-04 00:00:00

In this paper, we give an almost linear time and space algorithms to sample from an exponential mechanism with an $\ell_1$-score function defined over an exponentially large non-convex set. As a direct result, on input an $n$ vertex $m$ edges graph $G$, we present the \textit{first} $\widetilde{O}(m)$ time and $O(m)$ space algorithms for differentially privately outputting an $n$ vertex $O(m)$ edges synthetic graph that approximates all the cuts and the spectrum of $G$. These are the \emph{first} private algorithms for releasing synthetic graphs that nearly match this task's time and space complexity in the non-private setting while achieving the same (or better) utility as the previous works in the more practical sparse regime. Additionally, our algorithms can be extended to private graph analysis under continual observation.
Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law
Authors: Jingdong Zhang, Qunxi Zhu, Wei Lin
Date: 2024-06-04 00:00:00

Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural Koopman Operator (HNKO), integrating the knowledge of mathematical physics in learning the Koopman operator, and making it automatically sustain and even discover the conservation laws. We demonstrate the outperformance of the HNKO and its extension using a number of representative physical systems even with hundreds or thousands of freedoms. Our results suggest that feeding the prior knowledge of the underlying system and the mathematical theory appropriately to the learning framework can reinforce the capability of machine learning in solving physical problems.
Activation Bottleneck: Sigmoidal Neural Networks Cannot Forecast a Straight Line
Authors: Maximilian Toller, Hussain Hussain, Bernhard C Geiger
Date: 2024-06-04 00:00:00

A neural network has an activation bottleneck if one of its hidden layers has a bounded image. We show that networks with an activation bottleneck cannot forecast unbounded sequences such as straight lines, random walks, or any sequence with a trend: The difference between prediction and ground truth becomes arbitrary large, regardless of the training procedure. Widely-used neural network architectures such as LSTM and GRU suffer from this limitation. In our analysis, we characterize activation bottlenecks and explain why they prevent sigmoidal networks from learning unbounded sequences. We experimentally validate our findings and discuss modifications to network architectures which mitigate the effects of activation bottlenecks.
NeoRL: Efficient Exploration for Nonepisodic RL
Authors: Bhavya Sukhija, Lenart Treven, Florian Dörfler, Stelian Coros, Andreas Krause
Date: 2024-06-03 00:00:00
Tasks: Efficient Exploration, Reinforcement Learning (RL)

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose Nonepisodic Optimistic RL (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, we provide a first-of-its-kind regret bound of $\setO(\beta_T \sqrt{T \Gamma_T})$ for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.
Optimality of Matrix Mechanism on $\ell_p^p$-metric
Authors: Jingcheng Liu, Jalaj Upadhyay, Zongrui Zou
Date: 2024-06-04 00:00:00

In this paper, we introduce the $\ell_p^p$-error metric (for $p \geq 2$) when answering linear queries under the constraint of differential privacy. We characterize such an error under $(\epsilon,\delta)$-differential privacy. Before this paper, tight characterization in the hardness of privately answering linear queries was known under $\ell_2^2$-error metric (Edmonds et al., STOC 2020) and $\ell_p^2$-error metric for unbiased mechanisms (Nikolov and Tang, ITCS 2024). As a direct consequence of our results, we give tight bounds on answering prefix sum and parity queries under differential privacy for all constant $p$ in terms of the $\ell_p^p$ error, generalizing the bounds in Henzinger et al. (SODA 2023) for $p=2$.
SimulTron: On-Device Simultaneous Speech to Speech Translation
Authors: Alex Agranovich, Eliya Nachmani, Oleg Rybakov, Yifan Ding, Ye Jia, Nadav Bar, Heiga Zen, Michelle Tadmor Ramanovich
Date: 2024-06-04 00:00:00
Tasks: Simultaneous Speech-to-Speech Translation, Speech-to-Speech Translation, Translation

Simultaneous speech-to-speech translation (S2ST) holds the promise of breaking down communication barriers and enabling fluid conversations across languages. However, achieving accurate, real-time translation through mobile devices remains a major challenge. We introduce SimulTron, a novel S2ST architecture designed to tackle this task. SimulTron is a lightweight direct S2ST model that uses the strengths of the Translatotron framework while incorporating key modifications for streaming operation, and an adjustable fixed delay. Our experiments show that SimulTron surpasses Translatotron 2 in offline evaluations. Furthermore, real-time evaluations reveal that SimulTron improves upon the performance achieved by Translatotron 1. Additionally, SimulTron achieves superior BLEU scores and latency compared to previous real-time S2ST method on the MuST-C dataset. Significantly, we have successfully deployed SimulTron on a Pixel 7 Pro device, show its potential for simultaneous S2ST on-device.
When to Sense and Control? A Time-adaptive Approach for Continuous-Time RL
Authors: Lenart Treven, Bhavya Sukhija, Yarden As, Florian Dörfler, Andreas Krause
Date: 2024-06-03 00:00:00
Tasks: Reinforcement Learning (RL)

Reinforcement learning (RL) excels in optimizing policies for discrete-time Markov decision processes (MDP). However, various systems are inherently continuous in time, making discrete-time MDPs an inexact modeling choice. In many applications, such as greenhouse control or medical treatments, each interaction (measurement or switching of action) involves manual intervention and thus is inherently costly. Therefore, we generally prefer a time-adaptive approach with fewer interactions with the system. In this work, we formalize an RL framework, Time-adaptive Control & Sensing (TaCoS), that tackles this challenge by optimizing over policies that besides control predict the duration of its application. Our formulation results in an extended MDP that any standard RL algorithm can solve. We demonstrate that state-of-the-art RL algorithms trained on TaCoS drastically reduce the interaction amount over their discrete-time counterpart while retaining the same or improved performance, and exhibiting robustness over discretization frequency. Finally, we propose OTaCoS, an efficient model-based algorithm for our setting. We show that OTaCoS enjoys sublinear regret for systems with sufficiently smooth dynamics and empirically results in further sample-efficiency gains.