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Khashayar Gatmiry, Nikunj Saunshi, Sashank J. Reddi, Stefanie Jegelka, Sanjiv Kumar

Transformers to do reasoning and few-shot learning, without any fine-tuning, is widely conjectured to stem from their ability to implicitly simulate a multi-step algorithms -- such as gradient descent -- with their weights in a single forward pass. Recently, there has been progress in understanding this complex phenomenon from an expressivity point of view, by demonstrating that Transformers can express such multi-step algorithms. However, our knowledge about the more fundamental aspect of its learnability, beyond single layer models, is very limited. In particular, *can training Transformers enable convergence to algorithmic solutions*? In this work we resolve this for in context linear regression with linear looped Transformers -- a multi-layer model with weight sharing that is conjectured to have an inductive bias to learn fix-point iterative algorithms. More specifically, for this setting we show that the global minimizer of the population training loss implements multi-step preconditioned gradient descent, with a preconditioner that adapts to the data distribution. Furthermore, we show a fast convergence for gradient flow on the regression loss, despite the non-convexity of the landscape, by proving a novel gradient dominance condition. To our knowledge, this is the first theoretical analysis for multi-layer Transformer in this setting. We further validate our theoretical findings through synthetic experiments.

Deep Learning · Sequential Models, Time series

Raunaq Bhirangi, Chenyu Wang, Venkatesh Pattabiraman, Carmel Majidi, Abhinav Gupta, Tess Hellebrekers, Lerrel Pinto

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

Deep Learning · Large Language Models

Ulyana Piterbarg, Lerrel Pinto, Rob Fergus

Neural Language Models (LMs) offer an exciting solution for general-purpose embodied control. However, a key technical issue arises when using an LM-based controller: environment observations must be converted to text, which coupled with history, results in long and verbose textual prompts. As a result, prior work in LM agents is limited to restricted domains with small observation size as well as minimal needs for interaction history or instruction finetuning. In this paper, we introduce diff history, a simple and highly effective solution to these issues. By applying the Unix diff command on consecutive text observations in the interaction histories used to prompt LM policies, we can both abstract away redundant information and focus the content of textual inputs on the salient changes in the environment. On NetHack, an unsolved video game that requires long-horizon reasoning for decision-making, LMs tuned with diff history match state-of-the-art performance for neural agents while needing 1800X fewer training examples compared to prior work. Even on the simpler BabyAI-Text environment with concise text observations, we find that although diff history increases the length of prompts, the representation it provides offers a 25% improvement in the efficiency of low-sample instruction finetuning. Further, we show that diff history scales favorably across different finetuning dataset sizes. We open-source our code and data to https://diffhistory.github.io.

Theory · Probabilistic Methods

Emile van Krieken, Pasquale Minervini, Edoardo Ponti, Antonio Vergari

State-of-the-art neurosymbolic learning systems use probabilistic reasoning to guide neural networks towards predictions that conform to logical constraints. Many such systems assume that the probabilities of the considered symbols are conditionally independent given the input to simplify learning and reasoning. We study and criticise this assumption, highlighting how it can hinder optimisation and prevent uncertainty quantification. We prove that loss functions bias conditionally independent neural networks to become overconfident in their predictions. As a result, they are unable to represent uncertainty over multiple valid options. Furthermore, we prove that the minima of such loss functions are usually highly disconnected and non-convex, and thus difficult to optimise. Our theoretical analysis gives the foundation for replacing the conditional independence assumption and designing more expressive neurosymbolic probabilistic models.

Theory · Reinforcement Learning and Planning

Asaf Cassel, Haipeng Luo, Aviv Rosenberg, Dmitry Sotnikov

In many real-world applications, it is hard to provide a reward signal in each step of a Reinforcement Learning (RL) process and more natural to give feedback when an episode ends. To this end, we study the recently proposed model of RL with Aggregate Bandit Feedback (RL-ABF), where the agent only observes the sum of rewards at the end of an episode instead of each reward individually. Prior work studied RL-ABF only in tabular settings, where the number of states is assumed to be small. In this paper, we extend ABF to linear function approximation and develop two efficient algorithms with near-optimal regret guarantees: a value-based optimistic algorithm built on a new randomization technique with a Q-functions ensemble, and a policy optimization algorithm that uses a novel hedging scheme over the ensemble.

Reinforcement Learning · Deep RL

Ren-Jian Wang, Ke Xue, Cong Guan, Chao Qian

Quality-Diversity (QD) algorithms have emerged as a powerful optimization paradigm with the aim of generating a set of high-quality and diverse solutions. To achieve such a challenging goal, QD algorithms require maintaining a large archive and a large population in each iteration, which brings two main issues, sample and resource efficiency. Most advanced QD algorithms focus on improving the sample efficiency, while the resource efficiency is overlooked to some extent. Particularly, the resource overhead during the training process has not been touched yet, hindering the wider application of QD algorithms. In this paper, we highlight this important research question, i.e., how to efficiently train QD algorithms with limited resources, and propose a novel and effective method called RefQD to address it. RefQD decomposes a neural network into representation and decision parts, and shares the representation part with all decision parts in the archive to reduce the resource overhead. It also employs a series of strategies to address the mismatch issue between the old decision parts and the newly updated representation part. Experiments on different types of tasks from small to large resource consumption demonstrate the excellent performance of RefQD: it not only uses significantly fewer resources (e.g., 16% GPU memories on QDax and 3.7% on Atari) but also achieves comparable or better performance compared to sample-efficient QD algorithms. Our code is available at [https://github.com/lamda-bbo/RefQD](https://github.com/lamda-bbo/RefQD).

Deep Learning · Theory

Meng Ding, Kaiyi Ji, Di Wang, Jinhui Xu

Continual learning, focused on sequentially learning multiple tasks, has gained significant attention recently. Despite the tremendous progress made in the past, the theoretical understanding, especially factors contributing to $\textit{catastrophic forgetting}$, remains relatively unexplored. In this paper, we provide a general theoretical analysis of forgetting in the linear regression model via Stochastic Gradient Descent (SGD) applicable to both under-parameterized and overparameterized regimes. Our theoretical framework reveals some interesting insights into the intricate relationship between task sequence and algorithmic parameters, an aspect not fully captured in previous studies due to their restrictive assumptions. Specifically, we demonstrate that, given a sufficiently large data size, the arrangement of tasks in a sequence—where tasks with larger eigenvalues in their population data covariance matrices are trained later—tends to result in increased forgetting. Additionally, our findings highlight that an appropriate choice of step size will help mitigate forgetting in both under-parameterized and overparameterized settings. To validate our theoretical analysis, we conducted simulation experiments on both linear regression models and Deep Neural Networks (DNNs). Results from these simulations substantiate our theoretical findings.

Reinforcement Learning · Multi-agent

Kai Cui, Christian Fabian, Anam Tahir, Heinz Koeppl

Multi-agent reinforcement learning (MARL) remains difficult to scale to many agents. Recent MARL using Mean Field Control (MFC) provides a tractable and rigorous approach to otherwise difficult cooperative MARL. However, the strict MFC assumption of many independent, weakly-interacting agents is too inflexible in practice. We generalize MFC to instead simultaneously model many similar and few complex agents – as Major-Minor Mean Field Control (M3FC). Theoretically, we give approximation results for finite agent control, and verify the sufficiency of stationary policies for optimality together with a dynamic programming principle. Algorithmically, we propose Major-Minor Mean Field MARL (M3FMARL) for finite agent systems instead of the limiting system. The algorithm is shown to approximate the policy gradient of the underlying M3FC MDP. Finally, we demonstrate its capabilities experimentally in various scenarios. We observe a strong performance in comparison to state-of-the-art policy gradient MARL methods.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Yvonne Zhou, Mingyu Liang, Ivan Brugere, Danial Dervovic, Antigoni Polychroniadou, Min Wu, Dana Dachman-Soled

The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially- private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

Lucas Spangher, Allen Wang, Andrew Maris, Myles Stapelberg, Viraj Mehta, Alex Saperstein, Stephen Lane-Walsh, Akshata Moharir, Alessandro Pau, Cristina Rea

Magnetic confinement fusion may one day provide reliable, carbon-free energy, but the field currently faces technical hurdles. In this position paper, we highlight six key research challenges in the field of fusion energy that we believe should be research priorities for the Machine Learning (ML) community because they are especially ripe for ML applications: (1) disruption prediction, (2) simulation and dynamics modeling (3) resolving partially observed data, (4) improving controls, (5) guiding experiments with optimal design, and (6) enhancing materials discovery. For each problem, we give background, review past ML work, suggest features of future models, and list challenges and idiosyncrasies facing ML development. We also discuss ongoing efforts to update the fusion data ecosystem and identify opportunities further down the line that will be enabled as fusion and its data infrastructure advance. It is our position that fusion energy offers especially exciting opportunities for ML practitioners to impact decarbonization and the future of energy.

Optimization · Optimization and Learning under Uncertainty

Hao Wang, Kaifeng Yang, Michael Affenzeller

Hypervolume improvement (HVI) is commonly employed in multi-objective Bayesian optimization algorithms to define acquisition functions due to its Pareto-compliant property. Rather than focusing on specific statistical moments of HVI, this work aims to provide the exact expression of HVI's probability distribution for bi-objective problems. Considering a bi-variate Gaussian random variable resulting from Gaussian process (GP) modeling, we derive the probability distribution of its hypervolume improvement via a cell partition-based method. Our exact expression is superior in numerical accuracy and computation efficiency compared to the Monte Carlo approximation of HVI's distribution. Utilizing this distribution, we propose a novel acquisition function - $\varepsilon$-probability of hypervolume improvement ($\varepsilon$-PoHVI). Experimentally, we show that on many widely-applied bi-objective test problems, $\varepsilon$-PoHVI significantly outperforms other related acquisition functions, e.g., $\varepsilon$-PoI, and expected hypervolume improvement, when the GP model exhibits a large the prediction uncertainty.

Applications · Chemistry and Drug Discovery

Henrik Schopmans, Pascal Friederich

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been used to learn the Boltzmann distribution directly, without samples. However, this approach is susceptible to mode collapse and thus often does not explore the full configurational space. In this work, we address this challenge by separating the problem into two levels, the fine-grained and coarse-grained degrees of freedom. A normalizing flow conditioned on the coarse-grained space yields a probabilistic connection between the two levels. To explore the configurational space, we employ coarse-grained simulations with active learning which allows us to update the flow and make all-atom potential energy evaluations only when necessary. Using alanine dipeptide as an example, we show that our methods obtain a speedup to molecular dynamics simulations of approximately $15.9$ to $216.2$ compared to the speedup of $4.5$ of the current state-of-the-art machine learning approach.

Miscellaneous Aspects of Machine Learning · Causality

Danru Xu, Dingling Yao, Sébastien Lachapelle, Perouz Taslakian, Julius von Kügelgen, Francesco Locatello, Sara Magliacane

Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially observed setting, in which each measurement only provides information about a subset of the underlying causal state. Prior work has studied this setting with multiple domains or views, each depending on a fixed subset of latents. Here, we focus on learning from unpaired observations from a dataset with an instance-dependent partial observability pattern. Our main contribution is to establish two identifiability results for this setting: one for linear mixing functions without parametric assumptions on the underlying causal model, and one for piecewise linear mixing functions with Gaussian latent causal variables. Based on these insights, we propose two methods for estimating the underlying causal variables by enforcing sparsity in the inferred representation. Experiments on different simulated datasets and established benchmarks highlight the effectiveness of our approach in recovering the ground-truth latents.

Applications · Time Series

Tobia Boschi, FRANCESCA BONIN, Rodrigo Ordonez-Hurtado, Alessandra Pascale, Jonathan Epperlein

This paper introduces a novel methodology for Feature Selection for Functional Classification, FSFC, that addresses the challenge of jointly performing feature selection and classification of functional data in scenarios with categorical responses and multivariate longitudinal features. FSFC tackles a newly defined optimization problem that integrates logistic loss and functional features to identify the most crucial variables for classification. To address the minimization procedure, we employ functional principal components and develop a new adaptive version of the Dual Augmented Lagrangian algorithm. The computational efficiency of FSFC enables handling high-dimensional scenarios where the number of features may considerably exceed the number of statistical units. Simulation experiments demonstrate that FSFC outperforms other machine learning and deep learning methods in computational time and classification accuracy. Furthermore, the FSFC feature selection capability can be leveraged to significantly reduce the problem's dimensionality and enhance the performances of other classification algorithms. The efficacy of FSFC is also demonstrated through a real data application, analyzing relationships between four chronic diseases and other health and demographic factors. FSFC source code is publicly available at https://github.com/IBM/funGCN.

Theory · Optimization

Weijia Shao

This work proposes an algorithm improving the dimensionality dependence for gradient-free optimisation over cross-polytopes, which has many applications such as adversarial attacks, explainable AI and sparse regression. For bandit convex optimisation with two-point feedback over cross-polytopes, the state-of-the-art algorithms have a dimensionality dependence of $\mathcal{O}(\sqrt{d\log d})$, while the known lower bound is of the form $\Omega(\sqrt{d(\log d)^{-1}})$. We propose a mirror descent algorithm equipped with a symmetric version of the negative $\frac{1}{2}$-Tsallis entropy. Combined with an $\ell_1$-ellipsoidal smoothing-based gradient estimator, the proposed algorithm guarantees a dimensionality dependence on $\mathcal{O}(\sqrt{d})$, which improves the state-of-the-art algorithms by a factor of $\sqrt{\log d}$. The idea can be further applied to optimising non-smooth and non-convex functions. We propose an algorithm with a convergence depending on $\mathcal{O}(d)$, which is the best-known dimensionality dependence.

Theory · Reinforcement Learning and Planning

Jiin Woo, Laixi Shi, Gauri Joshi, Yuejie Chi

Offline reinforcement learning (RL), which seeks to learn an optimal policy using offline data, has garnered significant interest due to its potential in critical applications where online data collection is infeasible or expensive. This work explores the benefit of federated learning for offline RL, aiming at collaboratively leveraging offline datasets at multiple agents. Focusing on finite-horizon episodic tabular Markov decision processes (MDPs), we design FedLCB-Q, a variant of the popular model-free Q-learning algorithm tailored for federated offline RL. FedLCB-Q updates local Q-functions at agents with novel learning rate schedules and aggregates them at a central server using importance averaging and a carefully designed pessimistic penalty term. Our sample complexity analysis reveals that, with appropriately chosen parameters and synchronization schedules, FedLCB-Q achieves linear speedup in terms of the number of agents without requiring high-quality datasets at individual agents, as long as the local datasets collectively cover the state-action space visited by the optimal policy, highlighting the power of collaboration in the federated setting. In fact, the sample complexity almost matches that of the single-agent counterpart, as if all the data are stored at a central location, up to polynomial factors of the horizon length. Furthermore, FedLCB-Q is communication-efficient, where the number of communication rounds is only linear with respect to the horizon length up to logarithmic factors.

Dave Epstein, Ben Poole, Ben Mildenhall, Alexei Efros, Aleksander Holynski

We introduce a method to generate 3D scenes that are disentangled into their component objects. This disentanglement is unsupervised, relying only on the knowledge of a large pretrained text-to-image model. Our key insight is that objects can be discovered by finding parts of a 3D scene that, when rearranged spatially, still produce valid configurations of the same scene. Concretely, our method jointly optimizes multiple NeRFs---each representing its own object---along with a *set of layouts* that composite these objects into scenes. We then encourage these composited scenes to be in-distribution according to the image generator. We show that despite its simplicity, our approach successfully generates 3D scenes decomposed into individual objects, enabling new capabilities in text-to-3D content creation.

Social Aspects · Accountability, Transparency and Interpretability

Arjun Karuvally, Terrence Sejnowski, Hava Siegelmann

Traveling waves are a fundamental phenomenon in the brain, playing a crucial role in short-term information storage. In this study, we leverage the concept of traveling wave dynamics within a neural lattice to formulate a theoretical model of neural working memory in Recurrent Neural Networks (RNNs), study its properties, and its real world implications in AI. The proposed model diverges from traditional approaches, which assume information storage in static, register-like locations updated by interference. Instead, the model stores data as waves that is updated by the wave's boundary conditions. We rigorously examine the model's capabilities in representing and learning state histories, which are vital for learning history-dependent dynamical systems. The findings reveal that the model reliably stores external information and enhances the learning process by addressing the diminishing gradient problem of RNNs. To understand the model's real-world applicability, we explore two cases: linear boundary condition and non-linear, self-attention-driven boundary condition. The experiments reveal that the linear scenario is effectively *learned* by RNNs through backpropagation when modeling history-dependent dynamical systems. Conversely, the non-linear scenario parallels an attention-only transformer. Collectively, our findings suggest the broader relevance of traveling waves in AI and its potential in advancing neural network architectures.

Deep Learning · Graph Neural Networks

Slimane Thabet, Mehdi Djellabi, Igor Sokolov, Sachin Kasture, Louis-Paul Henry, Loic Henriet

In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.

Lu Yin, You Wu, Zhenyu Zhang, Cheng-Yu Hsieh, Yaqing Wang, Yiling Jia, Gen Li, Ajay Jaiswal, Mykola Pechenizkiy, Yi Liang 等

Large Language Models (LLMs), renowned for their remarkable performance across diverse domains, present a challenge due to their colossal model size when it comes to practical deployment. In response to this challenge, efforts have been directed toward the application of traditional network pruning techniques to LLMs, uncovering a massive number of parameters can be pruned in one-shot without hurting performance. Building upon insights gained from pre-LLM models, particularly BERT-level language models, prevailing LLM pruning strategies have consistently adhered to the practice of uniformly pruning all layers at equivalent sparsity levels, resulting in robust performance. However, this observation stands in contrast to the prevailing trends observed in the field of vision models, where non-uniform layerwise sparsity typically yields substantially improved results. To elucidate the underlying reasons for this disparity, we conduct a comprehensive analysis of the distribution of token features within LLMs. In doing so, we discover a strong correlation with the emergence of outliers, defined as features exhibiting significantly greater magnitudes compared to their counterparts in feature dimensions. Inspired by this finding, we introduce a novel LLM pruning methodology that incorporates a tailored set of **non-uniform layerwise sparsity ratios** specifically designed for LLM pruning, termed as **O**utlier **W**eighed **L**ayerwise sparsity (**OWL**). The sparsity ratio of OWL is directly proportional to the outlier ratio observed within each layer, facilitating a more effective alignment between layerwise weight sparsity and outlier ratios. Our empirical evaluation, conducted across the LLaMA-V1/V2, Vicuna, OPT, and Mistral, spanning various benchmarks, demonstrates the distinct advantages offered by OWL over previous methods. For instance, OWL exhibits a remarkable performance gain, surpassing the state-of-the-art Wanda and SparseGPT by **61.22** and **6.80** perplexity at a high sparsity level of 70%, respectively, while delivering **2.6$\times$** end-to-end inference speed-up in the DeepSparse inference engine. Code is available at https://github.com/luuyin/OWL.git.