Federated learning (FL) has garnered significant attention from academia and industry in recent years due to its advantages in data privacy, scalability, and communication efficiency. However, current FL algorithms face a critical limitation: their performance heavily depends on meticulously tuned hyperparameters, particularly the learning rate or stepsize. This manual tuning process is challenging in federated settings due to data heterogeneity and limited accessibility of local datasets. Consequently, the reliance on problem-specific parameters hinders the widespread adoption of FL and potentially compromises its performance in dynamic or diverse environments. To address this issue, we introduce PAdaMFed, a novel algorithm for nonconvex FL that carefully combines adaptive stepsize and momentum techniques. PAdaMFed offers two key advantages: 1) it operates autonomously without relying on problem-specific parameters; and 2) it manages data heterogeneity and partial participation without requiring heterogeneity bounds. Despite these benefits, PAdaMFed provides several strong theoretical guarantees: 1) It achieves state-of-the-art convergence rates with a sample complexity of $\mathcal{O}(\epsilon^{-4})$ and communication complexity of $\mathcal{O}(\epsilon^{-3})$ to obtain an accuracy of $||\nabla f\left(\boldsymbol{\theta}\right)|| \leq \epsilon$, even using constant learning rates; 2) these complexities can be improved to the best-known $\mathcal{O}(\epsilon^{-3})$ for sampling and $\mathcal{O}(\epsilon^{-2})$ for communication when incorporating variance reduction; 3) it exhibits linear speedup with respect to the number of local update steps and participating clients at each global round. These attributes make PAdaMFed highly scalable and adaptable for various real-world FL applications. Extensive empirical evidence on both image classification and sentiment analysis tasks validates the efficacy of our approaches.
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Miscellaneous Aspects of Machine Learning · Causality
Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability for large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of non-linear latent hierarchical causal models, relaxing previous assumptions in the literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for non-linear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. Furthermore, we demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks such as transfer learning.
Deep Learning · Graph Neural Networks
Graph condensation has emerged as a promising avenue to enable scalable training of GNNs by compressing the training dataset while preserving essential graph characteristics. Our study uncovers significant shortcomings in current graph condensation techniques. First, the majority of the algorithms paradoxically require training on the full dataset to perform condensation. Second, due to their gradient-emulating approach, these methods require fresh condensation for any change in hyperparameters or GNN architecture, limiting their flexibility and reusability. To address these challenges, we present Bonsai, a novel graph condensation method empowered by the observation that *computation trees* form the fundamental processing units of message-passing GNNs. Bonsai condenses datasets by encoding a careful selection of *exemplar* trees that maximize the representation of all computation trees in the training set. This unique approach imparts Bonsai as the first linear-time, model-agnostic graph condensation algorithm for node classification that outperforms existing baselines across $7$ real-world datasets on accuracy, while being $22$ times faster on average. Bonsai is grounded in rigorous mathematical guarantees on the adopted approximation strategies, making it robust to GNN architectures, datasets, and parameters.
Deep Learning · Algorithms
Metriplectic systems are learned from data in a way that scales quadratically in both the size of the state and the rank of the metriplectic operators. In addition to being provably energy-conserving and entropy-stable, the proposed neural metriplectic systems (NMS) approach includes approximation results that demonstrate its ability to accurately learn metriplectic dynamics from data, along with an error estimate that indicates its potential for generalization to unseen timescales when the approximation error is low. Examples are provided to illustrate performance both with full state information available and when entropic variables are unknown, confirming that the NMS approach exhibits superior accuracy and scalability without compromising on model expressivity.
Applications · Neuroscience, Cognitive Science
Current electrophysiological approaches can track the activity of many neurons, yet it is usually unknown which cell-types or brain areas are being recorded without further molecular or histological analysis. Developing accurate and scalable algorithms for identifying the cell-type and brain region of recorded neurons is thus crucial for improving our understanding of neural computation. In this work, we develop a multimodal contrastive learning approach for neural data that can be fine-tuned for different downstream tasks, including inference of cell-type and brain location. We utilize multimodal contrastive learning to jointly embed the activity autocorrelations and extracellular waveforms of individual neurons. We demonstrate that our embedding approach, Neuronal Embeddings via MultimOdal Contrastive Learning (NEMO), paired with supervised fine-tuning, achieves state-of-the-art cell-type classification for two opto-tagged datasets and brain region classification for the public International Brain Laboratory Brain-wide Map dataset. Our method represents a promising step towards accurate cell-type and brain region classification from electrophysiological recordings.
Probabilistic Methods · Monte Carlo and Sampling Methods
Many real-world datasets, such as healthcare, climate, and economics, are often collected as irregular time series, which poses challenges for accurate modeling. In this paper, we propose the Amortized Control of continuous State Space Model (ACSSM) for continuous dynamical modeling of time series for irregular and discrete observations. We first present a multi-marginal Doob's $h$-transform to construct a continuous dynamical system conditioned on these irregular observations. Following this, we introduce a variational inference algorithm with a tight evidence lower bound (ELBO), leveraging stochastic optimal control (SOC) theory to approximate the intractable Doob's $h$-transform and simulate the conditioned dynamics. To improve efficiency and scalability during both training and inference, ACSSM leverages auxiliary variable to flexibly parameterize the latent dynamics and amortized control. Additionally, it incorporates a simulation-free latent dynamics framework and a transformer-based data assimilation scheme, facilitating parallel inference of the latent states and ELBO computation. Through empirical evaluations across a variety of real-world datasets, ACSSM demonstrates superior performance in tasks such as classification, regression, interpolation, and extrapolation, while maintaining computational efficiency.
Probabilistic Methods · Monte Carlo and Sampling Methods
Many real-world datasets, such as healthcare, climate, and economics, are often collected as irregular time series, which poses challenges for accurate modeling. In this paper, we propose the Amortized Control of continuous State Space Model (ACSSM) for continuous dynamical modeling of time series for irregular and discrete observations. We first present a multi-marginal Doob's $h$-transform to construct a continuous dynamical system conditioned on these irregular observations. Following this, we introduce a variational inference algorithm with a tight evidence lower bound (ELBO), leveraging stochastic optimal control (SOC) theory to approximate the intractable Doob's $h$-transform and simulate the conditioned dynamics. To improve efficiency and scalability during both training and inference, ACSSM leverages auxiliary variable to flexibly parameterize the latent dynamics and amortized control. Additionally, it incorporates a simulation-free latent dynamics framework and a transformer-based data assimilation scheme, facilitating parallel inference of the latent states and ELBO computation. Through empirical evaluations across a variety of real-world datasets, ACSSM demonstrates superior performance in tasks such as classification, regression, interpolation, and extrapolation, while maintaining computational efficiency.
Optimization · Large Scale, Parallel and Distributed
Abstract Top-k selection algorithms are fundamental in a wide range of applications, including high-performance computing, information retrieval, big data processing, and neural network model training. In this paper, we present RTop-K, a highly efficient parallel row-wise top-k selection algorithm specifically designed for GPUs. RTop-K leverages a binary search-based approach to optimize row-wise top-k selection, providing a scalable and accelerated solution.We conduct a detailed analysis of early stopping in our algorithm, showing that it effectively maintains the testing accuracy of neural network models while substantially improving performance. Our GPU implementation of RTop-K demonstrates superior performance over state-of-the-art row-wise top-k GPU implementations, achieving an average speed-up of up to 11.49× with early stopping and 7.29× without early stopping. Moreover, RTop-K accelerates the overall training workflow of MaxK-GNNs, delivering speed-ups ranging from 11.97% to 33.29% across different models and datasets.
Social Aspects · Fairness, Equity, Justice and Safety
Evaluating chatbot fairness is crucial given their rapid proliferation, yet typical chatbot tasks (e.g., resume writing, entertainment) diverge from the institutional decision-making tasks (e.g., resume screening) which have traditionally been central to discussion of algorithmic fairness. The open-ended nature and diverse use-cases of chatbots necessitate novel methods for bias assessment. This paper addresses these challenges by introducing a scalable counterfactual approach to evaluate "first-person fairness," meaning fairness toward chatbot users based on demographic characteristics. Our method employs a Language Model as a Research Assistant (LMRA) to yield quantitative measures of harmful stereotypes and qualitative analyses of demographic differences in chatbot responses. We apply this approach to assess biases in six of our language models across millions of interactions, covering sixty-six tasks in nine domains and spanning two genders and four races. Independent human annotations corroborate the LMRA-generated bias evaluations. This study represents the first large-scale fairness evaluation based on real-world chat data. We highlight that post-training reinforcement learning techniques significantly mitigate these biases. This evaluation provides a practical methodology for ongoing bias monitoring and mitigation.
Social Aspects · Accountability, Transparency and Interpretability
Many proposed applications of neural networks in machine learning, cognitive/brain science, and society hinge on the feasibility of inner interpretability via circuit discovery. This calls for empirical and theoretical explorations of viable algorithmic options. Despite advances in the design and testing of heuristics, there are concerns about their scalability and faithfulness at a time when we lack understanding of the complexity properties of the problems they are deployed to solve. To address this, we study circuit discovery with classical and parameterized computational complexity theory: (1) we describe a conceptual scaffolding to reason about circuit finding queries in terms of affordances for description, explanation, prediction and control; (2) we formalize a comprehensive set of queries for mechanistic explanation, and propose a formal framework for their analysis; (3) we use it to settle the complexity of many query variants and relaxations of practical interest on multi-layer perceptrons. Our findings reveal a challenging complexity landscape. Many queries are intractable, remain fixed-parameter intractable relative to model/circuit features, and inapproximable under additive, multiplicative, and probabilistic approximation schemes. To navigate this landscape, we prove there exist transformations to tackle some of these hard problems with better-understood heuristics, and prove the tractability or fixed-parameter tractability of more modest queries which retain useful affordances. This framework allows us to understand the scope and limits of interpretability queries, explore viable options, and compare their resource demands on existing and future architectures.
Reinforcement Learning · Deep RL
Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).
Theory · Learning Theory
Hierarchical clustering is a fundamental unsupervised machine learning task with the aim of organizing data into a hierarchy of clusters. Many applications of hierarchical clustering involve sensitive user information, therefore motivating recent studies on differentially private hierarchical clustering under the rigorous framework of Dasgupta's objective. However, it has been shown that any privacy-preserving algorithm under edge-level differential privacy necessarily suffers a large error. To capture practical applications of this problem, we focus on the weight privacy model, where each edge of the input graph is at least unit weight. We present a novel algorithm in the weight privacy model that shows significantly better approximation than known impossibility results in the edge-level DP setting. In particular, our algorithm achieves $O(\log^{1.5}n/\varepsilon)$ multiplicative error for $\varepsilon$-DP and runs in polynomial time, where $n$ is the size of the input graph, and the cost is never worse than the optimal additive error in existing work. We complement our algorithm by showing if the unit-weight constraint does not apply, the lower bound for weight-level DP hierarchical clustering is essentially the same as the edge-level DP, i.e. $\Omega(n^2/\varepsilon)$ additive error. As a result, we also obtain a new lower bound of $\tilde{\Omega}(1/\varepsilon)$ additive error for balanced sparsest cuts in the weight-level DP model, which may be of independent interest. Finally, we evaluate our algorithm on synthetic and real-world datasets. Our experimental results show that our algorithm performs well in terms of extra cost and has good scalability to large graphs.
Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning
The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However, since many interesting datasets are unlabelled, unsupervised ground metric learning approaches have been introduced. One promising option employs Wasserstein singular vectors (WSVs), which emerge when computing optimal transport distances between features and samples simultaneously. WSVs are effective, but can be prohibitively computationally expensive in some applications: $\mathcal{O}(n^2m^2(n \log(n) + m \log(m))$ for $n$ samples and $m$ features. In this work, we propose to augment the WSV method by embedding samples and features on trees, on which we compute the tree-Wasserstein distance (TWD). We demonstrate theoretically and empirically that the algorithm converges to a better approximation of the standard WSV approach than the best known alternatives, and does so with $\mathcal{O}(n^3+m^3+mn)$ complexity. In addition, we prove that the initial tree structure can be chosen flexibly, since tree geometry does not constrain the richness of the approximation up to the number of edge weights. This proof suggests a fast and recursive algorithm for computing the tree parameter basis set, which we find crucial to realising the efficiency gains at scale. Finally, we employ the tree-WSV algorithm to several single-cell RNA sequencing genomics datasets, demonstrating its scalability and utility for unsupervised cell-type clustering problems. These results poise unsupervised ground metric learning with TWD as a low-rank approximation of WSV with the potential for widespread application.
Miscellaneous Aspects of Machine Learning · Scalable Algorithms
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between probability measures. To reduce the computational complexity of OT solvers, methods like entropic regularization and sliced optimal transport have been proposed. The sliced OT framework improves efficiency by comparing one-dimensional projections (slices) of high-dimensional distributions. However, despite their computational efficiency, sliced-Wasserstein approaches lack a transportation plan between the input measures, limiting their use in scenarios requiring explicit coupling. In this paper, we address two key questions: Can a transportation plan be constructed between two probability measures using the sliced transport framework? If so, can this plan be used to define a metric between the measures? We propose a ‘lifting’ operation to extend one-dimensional optimal transport plans back to the original space of the measures. By computing the expectation of these lifted plans, we derive a new transportation plan, termed expected sliced transport (EST) plans. We further prove that using the EST plan to weight the sum of the individual Euclidean costs $\|x - y\|^p$ for moving from $x$ to $y$ results in a valid metric between the input discrete probability measures. Finally, we demonstrate the connection between our approach and the recently proposed min-SWGG, along with illustrative numerical examples that support our theoretical findings.
Theory · Optimization
Multi-task learning enables the acquisition of task-generic knowledge by training multiple tasks within a unified architecture. However, training all tasks together in a single architecture can lead to performance degradation, known as negative transfer, which is a main concern in multi-task learning. Previous works have addressed this issue by optimizing the multi-task network through gradient manipulation or weighted loss adjustments. However, their optimization strategy focuses on addressing task imbalance in shared parameters, neglecting the learning of task-specific parameters. As a result, they show limitations in mitigating negative transfer, since the learning of shared space and task-specific information influences each other during optimization. To address this, we propose a different approach to enhance multi-task performance by selectively grouping tasks and updating them for each batch during optimization. We introduce an algorithm that adaptively determines how to effectively group tasks and update them during the learning process. To track inter-task relations and optimize multi-task networks simultaneously, we propose proximal inter-task affinity, which can be measured during the optimization process. We provide a theoretical analysis on how dividing tasks into multiple groups and updating them sequentially significantly affects multi-task performance by enhancing the learning of task-specific parameters. Our methods substantially outperform previous multi-task optimization approaches and are scalable to different architectures and various numbers of tasks.
Deep Learning · Generative Models and Autoencoders
Aggregating data from multiple sources can be formalized as an *Optimal Transport* (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios, the presence of outliers and noise in the data measures can significantly hinder the performance of traditional statistical methods for estimating OT barycenters. To address this issue, we propose a novel scalable approach for estimating the *robust* continuous barycenter, leveraging the dual formulation of the *(semi-)unbalanced* OT problem. To the best of our knowledge, this paper is the first attempt to develop an algorithm for robust barycenters under the continuous distribution setup. Our method is framed as a $\min$-$\max$ optimization problem and is adaptable to *general* cost functions. We rigorously establish the theoretical underpinnings of the proposed method and demonstrate its robustness to outliers and class imbalance through a number of illustrative experiments. Our source code is publicly available at https://github.com/milenagazdieva/U-NOTBarycenters.
Probabilistic Methods · Everything Else
In this work, we tackle the problems of efficiency and scalability for predictive coding networks (PCNs) in machine learning. To do so, we propose a library that focuses on performance and simplicity, and use it to implement a large set of standard benchmarks for the community to use for their experiments. As most works in the field propose their own tasks and architectures, do not compare one against each other, and focus on small-scale tasks, a simple and fast open-source library, and a comprehensive set of benchmarks, would address all of these concerns. Then, we perform extensive tests on such benchmarks using both existing algorithms for PCNs, as well as adaptations of other methods popular in the bio-plausible deep learning community. All of this has allowed us to (i) test architectures much larger than commonly used in the literature, on more complex datasets; (ii) reach new state-of-the-art results in all of the tasks and dataset provided; (iii) clearly highlight what the current limitations of PCNs are, allowing us to state important future research directions. With the hope of galvanizing community efforts towards one of the main open problems in the field, scalability, we will release the code, tests, and benchmarks.
Applications · Neuroscience, Cognitive Science
Neural activity in the brain is known to encode low-dimensional, time-evolving, behaviour-related variables. A long-standing goal of neural data analysis has been to identify these variables and their mapping to neural activity. A productive and canonical approach has been to simply visualise neural "tuning curves" as a function of behaviour. However, significant discrepancies between behaviour and the true latent variables -- such as an agent thinking of position Y whilst located at position X -- distort and blur the tuning curves, decreasing their interpretability. To address this, latent variable models propose to learn the latent variable from data; these are typically expensive, hard to tune, or scale poorly, complicating their adoption. Here we propose SIMPL (Scalable Iterative Maximization of Population-coded Latents), an EM-style algorithm which iteratively optimises latent variables and tuning curves. SIMPL is fast, scalable and exploits behaviour as an initial condition to further improve convergence and identifiability. It can accurately recover latent variables in spatial and non-spatial tasks. When applied to a large hippocampal dataset SIMPL converges on smaller, more numerous, and more uniformly sized place fields than those based on behaviour, suggesting the brain may encode space with greater resolution than previously thought.
Optimization · Sampling and Optimization
Learning-based methods have gained attention as general-purpose solvers due to their ability to automatically learn problem-specific heuristics, reducing the need for manually crafted heuristics. However, these methods often face scalability challenges. To address these issues, the improved Sampling algorithm for Combinatorial Optimization (iSCO), using discrete Langevin dynamics, has been proposed, demonstrating better performance than several learning-based solvers. This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA). QQA smoothly transitions the objective function, starting from a simple convex function, minimized at half-integral values, to the original objective function, where the relaxed variables are minimized only in the discrete space. Furthermore, we incorporate parallel run communication leveraging GPUs to enhance exploration capabilities and accelerate convergence. Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers across various benchmark problems. Notably, our method exhibits superior speed-quality trade-offs for large-scale instances compared to iSCO, learning-based solvers, commercial solvers, and specialized algorithms.
Optimization · Learning for Optimization
Neural Combinatorial Optimization (NCO) methods have exhibited promising performance in solving Vehicle Routing Problems (VRPs). However, most NCO methods rely on the conventional self-attention mechanism that induces excessive computational complexity, thereby struggling to contend with large-scale VRPs and hindering their practical applicability. In this paper, we propose a lightweight cross-attention mechanism with linear complexity, by which a Transformer network is developed to learn efficient and favorable solutions for large-scale VRPs. We also propose a Self-Improved Training (SIT) algorithm that enables direct model training on large-scale VRP instances, bypassing extensive computational overhead for attaining labels. By iterating solution reconstruction, the Transformer network itself can generate improved partial solutions as pseudo-labels to guide the model training. Experimental results on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes indicate that our method consistently achieves superior performance for synthetic and real-world benchmarks, significantly boosting the scalability of NCO methods.