Daily Papers

Collective cell responses to exogenous cues depend on cell-cell interactions. In principle, these can result in enhanced sensitivity to weak and noisy stimuli. However, this has not yet been shown experimentally, and, little is known about how multicellular signal processing modulates single cell sensitivity to extracellular signaling inputs, including those guiding complex changes in the tissue form and function. Here we explored if cell-cell communication can enhance the ability of cell ensembles to sense and respond to weak gradients of chemotactic cues. Using a combination of experiments with mammary epithelial cells and mathematical modeling, we find that multicellular sensing enables detection of and response to shallow Epidermal Growth Factor (EGF) gradients that are undetectable by single cells. However, the advantage of this type of gradient sensing is limited by the noisiness of the signaling relay, necessary to integrate spatially distributed ligand concentration information. We calculate the fundamental sensory limits imposed by this communication noise and combine them with the experimental data to estimate the effective size of multicellular sensory groups involved in gradient sensing. Functional experiments strongly implicated intercellular communication through gap junctions and calcium release from intracellular stores as mediators of collective gradient sensing. The resulting integrative analysis provides a framework for understanding the advantages and limitations of sensory information processing by relays of chemically coupled cells.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

This paper introduces a novel method for eigenvalue computation using a distributed cooperative neural network framework. Unlike traditional techniques that face scalability challenges in large systems, our decentralized algorithm enables multiple autonomous agents to collaboratively estimate the smallest eigenvalue of large matrices. Each agent employs a localized neural network, refining its estimates through communication with neighboring agents. Our empirical results confirm the algorithm's convergence towards the true eigenvalue, with estimates clustered closely around the true value. Even in the presence of communication delays or network disruptions, the method demonstrates strong robustness and scalability. Theoretical analysis further validates the accuracy and stability of the proposed approach, while empirical tests highlight its efficiency and precision, surpassing traditional centralized algorithms in large-scale eigenvalue computations.

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

We develop a multi-rate distributed unscented Kalman filter for nonlinear networks without a fusion center. Local continuous-discrete UKFs run on a common base grid, update at their own sampling instants, and exchange estimates within one-hop neighborhoods. Under a windowed collective-detectability condition, diffusion of information matrices gives uniformly bounded quotient covariances although no individual node need be observable. When the collectively invisible subspace is trivial and the statistical-linearization discrepancies satisfy an explicit coherence bound, the information weighted fused mean yields exponentially bounded mean-square errors without a contraction-mixing condition. This contrasts with the arithmetic diffusiojn mean, which requires one. A distributed H_{infty} variant uses a fixed attenuation penalty. A finite-prefix feasibility check and the one-hop detectability Gramian yield a uniform regularized-information margin - an explicit local-contraction-mixing condition then yields mean-square error boundedness. The developed methods are tested on a stochastic nonlinear benchmark and a three-inertia network in which every node misses at least one mode. Information diffusion is more accurate than five-round covariance-averaging consensus at one fifth of its communication. It remains stable under 3:2 multi-rate sampling, where the covariance-averaging consensus and the diffusion mean both diverge, and it keeps the quotient covariances bounded.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

We bound the time it takes for a group of birds to reach steady state in a standard flocking model. We prove that (i) within single exponential time fragmentation ceases and each bird settles on a fixed flying direction; (ii) the flocking network converges only after a number of steps that is an iterated exponential of height logarithmic in the number of birds. We also prove the highly surprising result that this bound is optimal. The model directs the birds to adjust their velocities repeatedly by averaging them with their neighbors within a fixed radius. The model is deterministic, but we show that it can tolerate a reasonable amount of stochastic or even adversarial noise. Our methods are highly general and we speculate that the results extend to a wider class of models based on undirected flocking networks, whether defined metrically or topologically. This work introduces new techniques of broader interest, including the "flight net," the "iterated spectral shift," and a certain "residue-clearing" argument in circuit complexity.

Computational sensing strategies often suffer from calibration errors in the physical implementation of their ideal sensing models. Such uncertainties are typically addressed by using multiple, accurately chosen training signals to recover the missing information on the sensing model, an approach that can be resource-consuming and cumbersome. Conversely, blind calibration does not employ any training signal, but corresponds to a bilinear inverse problem whose algorithmic solution is an open issue. We here address blind calibration as a non-convex problem for linear random sensing models, in which we aim to recover an unknown signal from its projections on sub-Gaussian random vectors, each subject to an unknown positive multiplicative factor (or gain). To solve this optimisation problem we resort to projected gradient descent starting from a suitable, carefully chosen initialisation point. An analysis of this algorithm allows us to show that it converges to the exact solution provided a sample complexity requirement is met, i.e., relating convergence to the amount of information collected during the sensing process. Interestingly, we show that this requirement grows linearly (up to log factors) in the number of unknowns of the problem. This sample complexity is found both in absence of prior information, as well as when subspace priors are available for both the signal and gains, allowing a further reduction of the number of observations required for our recovery guarantees to hold. Moreover, in the presence of noise we show how our descent algorithm yields a solution whose accuracy degrades gracefully with the amount of noise affecting the measurements. Finally, we present some numerical experiments in an imaging context, where our algorithm allows for a simple solution to blind calibration of the gains in a sensor array.

Collaborative perception (CP) is emerging as a promising solution to the inherent limitations of stand-alone intelligence. However, current wireless communication systems are unable to support feature-level and raw-level collaborative algorithms due to their enormous bandwidth demands. In this paper, we propose DiffCP, a novel CP paradigm that utilizes a specialized diffusion model to efficiently compress the sensing information of collaborators. By incorporating both geometric and semantic conditions into the generative model, DiffCP enables feature-level collaboration with an ultra-low communication cost, advancing the practical implementation of CP systems. This paradigm can be seamlessly integrated into existing CP algorithms to enhance a wide range of downstream tasks. Through extensive experimentation, we investigate the trade-offs between communication, computation, and performance. Numerical results demonstrate that DiffCP can significantly reduce communication costs by 14.5-fold while maintaining the same performance as the state-of-the-art algorithm.

We consider problems where agents in a network seek a common quantity, measured independently and periodically by each agent through a local time-varying process. Numerous solvers addressing such problems have been developed in the past, featuring various adaptations of the local processing and the consensus step. However, existing solvers still lack support for advanced techniques, such as superiorization and over-the-air function computation (OTA-C). To address this limitation, we introduce a comprehensive framework for the analysis of distributed algorithms by characterizing them using the quasi-Fejér type algorithms and an extensive communication model. Under weak assumptions, we prove almost sure convergence of the algorithm to a common estimate for all agents. Moreover, we develop a specific class of algorithms within this framework to tackle distributed optimization problems with time-varying objectives, and, assuming that a time-invariant solution exists, prove its convergence to a solution. We also present a novel OTA-C protocol for consensus step in large decentralized networks, reducing communication overhead and enhancing network autonomy as compared to the existing protocols. The effectiveness of the algorithm, featuring superiorization and OTA-C, is demonstrated in a real-world application of distributed supervised learning over time-varying wireless networks, highlighting its low-latency and energy-efficiency compared to standard approaches.

Groups coordinate more effectively when individuals are able to learn from others' successes. But acquiring such knowledge is not always easy, especially in real-world environments where success is hidden from public view. We suggest that social inference capacities may help bridge this gap, allowing individuals to update their beliefs about others' underlying knowledge and success from observable trajectories of behavior. We compared our social inference model against simpler heuristics in three studies of human behavior in a collective sensing task. In Experiment 1, we found that average performance improves as a function of group size at a rate greater than predicted by non-inferential models. Experiment 2 introduced artificial agents to evaluate how individuals selectively rely on social information. Experiment 3 generalized these findings to a more complex reward landscape. Taken together, our findings provide insight into the relationship between individual social cognition and the flexibility of collective behavior.

Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures-Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. LBW is inspired by linearized optimal transport and preserves key geometric features while enabling computational tractability. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm's robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.

We show that coherent, long-form musical composition can emerge from a decentralized swarm of identical, frozen foundation models that coordinate via stigmergic, peer-to-peer signals, without any weight updates. We compare a centralized multi-agent system with a global critic to a fully decentralized swarm in which bar-wise agents sense and deposit harmonic, rhythmic, and structural cues, adapt short-term memory, and reach consensus. Across symbolic, audio, and graph-theoretic analyses, the swarm yields superior quality while delivering greater diversity and structural variety and leads across creativity metrics. The dynamics contract toward a stable configuration of complementary roles, and self-similarity networks reveal a small-world architecture with efficient long-range connectivity and specialized bridging motifs, clarifying how local novelties consolidate into global musical form. By shifting specialization from parameter updates to interaction rules, shared memory, and dynamic consensus, MusicSwarm provides a compute- and data-efficient route to long-horizon creative structure that is immediately transferable beyond music to collaborative writing, design, and scientific discovery.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

We introduce Gradient Agreement Filtering (GAF) to improve on gradient averaging in distributed deep learning optimization. Traditional distributed data-parallel stochastic gradient descent involves averaging gradients of microbatches to calculate a macrobatch gradient that is then used to update model parameters. We find that gradients across microbatches are often orthogonal or negatively correlated, especially in late stages of training, which leads to memorization of the training set, reducing generalization. In this paper, we introduce a simple, computationally effective way to reduce gradient variance by computing the cosine distance between micro-gradients during training and filtering out conflicting updates prior to averaging. We improve validation accuracy with significantly smaller microbatch sizes. We also show this reduces memorizing noisy labels. We demonstrate the effectiveness of this technique on standard image classification benchmarks including CIFAR-100 and CIFAR-100N-Fine. We show this technique consistently outperforms validation accuracy, in some cases by up to 18.2\% compared to traditional training approaches while reducing the computation required nearly an order of magnitude because we can now rely on smaller microbatch sizes without destabilizing training.

Multi-robot collaboration allows robots to efficiently take on a wide range of tasks, from moving a couch through a doorway to assembling structures on a construction site. However, achieving such coordination in mobile multi-robot settings remains challenging: centralized methods conditioned on the combined observations of a team scale poorly with team size, and decentralized methods that train one policy per robot often require explicit alignment procedures or information sharing at inference time to overcome partial observability. Our key insight is that the visuomotor priors of pretrained vision-language-action (VLA) models should enable reactive, decentralized collaboration from each robot's local observations alone, without these inference-time assumptions. We propose CHORUS, a framework that adapts a single VLA backbone to control diverse, multi-robot teams. At inference time, each robot runs an independent copy of CHORUS, conditioned only on its own observations and a robot-identifying prompt. In real-world experiments including mobile tape measurement, library book handovers, and laundry basket lifting, CHORUS achieves a 64% point improvement over decentralized, from-scratch models, improves reactivity to teammate behavior by 40% points, and outperforms centralized baselines. Together, these results show that a shared VLA backbone is capable of achieving decentralized multi-robot collaboration, without per-robot policies or inter-robot communication at inference.

In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the full picture. Such systems have inspired development of artificial intelligence algorithms in areas such as swarm optimization and cellular automata. Motivated by the emergence of collective behavior from complex cellular systems, we build systems that feed each sensory input from the environment into distinct, but identical neural networks, each with no fixed relationship with one another. We show that these sensory networks can be trained to integrate information received locally, and through communication via an attention mechanism, can collectively produce a globally coherent policy. Moreover, the system can still perform its task even if the ordering of its inputs is randomly permuted several times during an episode. These permutation invariant systems also display useful robustness and generalization properties that are broadly applicable. Interactive demo and videos of our results: https://attentionneuron.github.io/

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles theta_1, dots, theta_nin[0, 2pi) from m noisy measurements of their offsets theta_i-theta_j ;mod ; 2pi. Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed k-synchronization) is to estimate k groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels.

Can every robot in a swarm predict the same future collective state from only local observations and bandwidth-limited messages? We formulate this as decentralized shared-state prediction and introduce Collective-State JEPA (CS-JEPA), a recurrent joint-embedding predictive architecture whose output at every robot represents one common future token field. At deployment, each robot uses a 16-frame local history and one 64-float recurrent message per directed edge; there is no global pooling, target encoder, episode clock, or recorded future action. After pretraining without downstream collective labels, frozen representations are evaluated with ridge probes fitted on 6, 12, or 24 globally labeled episodes. Against raw-future reconstruction with the same receiver anchor and deployment capacity but 9,607 additional training-only parameters, a prospectively registered five-seed follow-up improves prediction-error and inter-robot-agreement label-budget AUC on in-distribution, ring, mutual-kNN, and unseen-size families up to 108 robots. Every effect favors CS-JEPA in 5/5 outer seeds. In a separate sealed eight-seed follow-up, matched action-conditioned predictors receive each candidate four-step plan before producing receiver-local predictive representations. CS-JEPA reduces branch-value MSE by 45.5% and improves within-context candidate-score Pearson correlation by 0.1291, with both effects favorable in 8/8 seeds, including at unseen N=32. These results support common-future JEPA targets as a label-efficient primitive for decentralized swarm prediction under topology and size shift, with additional evidence of planning-relevant value estimation.

Multi-agent systems (MASs) can autonomously learn to solve previously unknown tasks by means of each agent's individual intelligence as well as by collaborating and exploiting collective intelligence. This article considers a group of autonomous agents learning to track the same given reference trajectory in a possibly small number of trials. We propose a novel collective learning control method that combines iterative learning control (ILC) with a collective update strategy. We derive conditions for desirable convergence properties of such systems. We show that the proposed method allows the collective to combine the advantages of the agents' individual learning strategies and thereby overcomes trade-offs and limitations of single-agent ILC. This benefit is achieved by designing a heterogeneous collective, i.e., a different learning law is assigned to each agent. All theoretical results are confirmed in simulations and experiments with two-wheeled-inverted-pendulum robots (TWIPRs) that jointly learn to perform the desired maneuver.

In time-varying D-optimal subset selection, the number of replaced coordinates does not measure physical displacement: when the optimal selection for a set of mobile sensors changes, a single sensor may have to cross the entire graph. We therefore measure movement by a bottleneck matching distance on a fixed mobility graph, and define the distance margin at radius P as the smallest old-objective loss among configurations farther than P from the current maximizer. Our main result shows that if the projector drift is small and the distance margin at a chosen radius exceeds an explicit threshold, then every maximizer of the new objective lies within that radius, without tie-breaking rules or uniform conditioning assumptions over subsets. Moreover, we show that separation information of this kind is genuinely needed: a weighted-path construction shows that, at a fixed baseline eigengap, an arbitrarily small perturbation can move an optimal sensor from one end of the graph to the other, so no bound depending only on perturbation size and eigengap can vanish with the perturbation. We also give a finite certificate, conditions under which local and Voronoi restrictions retain a global optimum, and oversampled and regularized extensions, and we identify the learned dictionary criteria to which the results apply.

Autonomous edge computing in robotics, smart cities, and autonomous vehicles relies on the seamless integration of sensing, processing, and actuation for real-time decision-making in dynamic environments. At its core is the sensing-to-action loop, which iteratively aligns sensor inputs with computational models to drive adaptive control strategies. These loops can adapt to hyper-local conditions, enhancing resource efficiency and responsiveness, but also face challenges such as resource constraints, synchronization delays in multi-modal data fusion, and the risk of cascading errors in feedback loops. This article explores how proactive, context-aware sensing-to-action and action-to-sensing adaptations can enhance efficiency by dynamically adjusting sensing and computation based on task demands, such as sensing a very limited part of the environment and predicting the rest. By guiding sensing through control actions, action-to-sensing pathways can improve task relevance and resource use, but they also require robust monitoring to prevent cascading errors and maintain reliability. Multi-agent sensing-action loops further extend these capabilities through coordinated sensing and actions across distributed agents, optimizing resource use via collaboration. Additionally, neuromorphic computing, inspired by biological systems, provides an efficient framework for spike-based, event-driven processing that conserves energy, reduces latency, and supports hierarchical control--making it ideal for multi-agent optimization. This article highlights the importance of end-to-end co-design strategies that align algorithmic models with hardware and environmental dynamics and improve cross-layer interdependencies to improve throughput, precision, and adaptability for energy-efficient edge autonomy in complex environments.

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile, collective behavior requires resolution of the aforementioned challenges, and remains of importance to many state-of-the-art applications such as active matter physics, self-organizing systems, opinion dynamics, and biological or robotic swarms. Here, MARL via mean field control (MFC) offers a potential solution to scalability, but fails to consider decentralized and partially observable systems. In this paper, we enable decentralized behavior of agents under partial information by proposing novel models for decentralized partially observable MFC (Dec-POMFC), a broad class of problems with permutation-invariant agents allowing for reduction to tractable single-agent Markov decision processes (MDP) with single-agent RL solution. We provide rigorous theoretical results, including a dynamic programming principle, together with optimality guarantees for Dec-POMFC solutions applied to finite swarms of interest. Algorithmically, we propose Dec-POMFC-based policy gradient methods for MARL via centralized training and decentralized execution, together with policy gradient approximation guarantees. In addition, we improve upon state-of-the-art histogram-based MFC by kernel methods, which is of separate interest also for fully observable MFC. We evaluate numerically on representative collective behavior tasks such as adapted Kuramoto and Vicsek swarming models, being on par with state-of-the-art MARL. Overall, our framework takes a step towards RL-based engineering of artificial collective behavior via MFC.

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient computation, such as locking and memorization requirements. The cost is the requirement to guess the step direction, which is hard in high dimensions. While current solutions rely on weighted averages over isotropic guess vector distributions, we propose to strongly bias our gradient guesses in directions that are much more promising, such as feedback obtained from small, local auxiliary networks. For a standard computer vision neural network, we conduct a rigorous study systematically covering a variety of combinations of gradient targets and gradient guesses, including those previously presented in the literature. We find that using gradients obtained from a local loss as a candidate direction drastically improves on random noise in Forward Gradient methods.

This paper studies privacy-preserving distributed optimization using gradient tracking with one communication-free local update between consecutive communication rounds. Since local computation alone does not protect gradient information, we perturb both the primal state and the gradient-tracking direction at communication iterations while keeping local updates noise-free. We establish an aggregate variable for tracking, characterize the limiting consensus point in the presence of added random noise, and prove convergence in mean under certain parameter conditions. We also establish infinite-horizon pure differential privacy for the complete communication transcript under an affine objective adjacency relation and geometrically decaying Laplace perturbations. Simulation results illustrate the advantages of the proposed method in terms of the convergence and optimization accuracy given a privacy budget.

Collaborative state estimation using different heterogeneous sensors is a fundamental prerequisite for robotic swarms operating in GPS-denied environments, posing a significant research challenge. In this paper, we introduce a centralized system to facilitate collaborative LiDAR-ranging-inertial state estimation, enabling robotic swarms to operate without the need for anchor deployment. The system efficiently distributes computationally intensive tasks to a central server, thereby reducing the computational burden on individual robots for local odometry calculations. The server back-end establishes a global reference by leveraging shared data and refining joint pose graph optimization through place recognition, global optimization techniques, and removal of outlier data to ensure precise and robust collaborative state estimation. Extensive evaluations of our system, utilizing both publicly available datasets and our custom datasets, demonstrate significant enhancements in the accuracy of collaborative SLAM estimates. Moreover, our system exhibits remarkable proficiency in large-scale missions, seamlessly enabling ten robots to collaborate effectively in performing SLAM tasks. In order to contribute to the research community, we will make our code open-source and accessible at https://github.com/PengYu-team/Co-LRIO.

While significant advances have been made for single-agent perception, many applications require multiple sensing agents and cross-agent communication due to benefits such as coverage and robustness. It is therefore critical to develop frameworks which support multi-agent collaborative perception in a distributed and bandwidth-efficient manner. In this paper, we address the collaborative perception problem, where one agent is required to perform a perception task and can communicate and share information with other agents on the same task. Specifically, we propose a communication framework by learning both to construct communication groups and decide when to communicate. We demonstrate the generalizability of our framework on two different perception tasks and show that it significantly reduces communication bandwidth while maintaining superior performance.

We study the problem of identifying an anomalous subset of streams under correlated noise, motivated by monitoring and security in cyber-physical systems. This problem can be viewed as a form of combinatorial pure exploration, where each stream plays the role of an arm and measurements must be allocated sequentially under uncertainty. Existing combinatorial bandit and hypothesis testing methods typically assume independent observations and fail to exploit correlation for efficient measurement design. We propose ECC-AHT, an adaptive algorithm that selects continuous, constrained measurements to maximize Chernoff information between competing hypotheses, enabling active noise cancellation through differential sensing. ECC-AHT achieves optimal sample complexity guarantees and significantly outperforms state-of-the-art baselines in both synthetic and real-world correlated environments. The code is available on https://github.com/VincentdeCristo/ECC-AHT

Stochastic gradient MCMC methods, such as stochastic gradient Langevin dynamics (SGLD), employ fast but noisy gradient estimates to enable large-scale posterior sampling. Although we can easily extend SGLD to distributed settings, it suffers from two issues when applied to federated non-IID data. First, the variance of these estimates increases significantly. Second, delaying communication causes the Markov chains to diverge from the true posterior even for very simple models. To alleviate both these problems, we propose conducive gradients, a simple mechanism that combines local likelihood approximations to correct gradient updates. Notably, conducive gradients are easy to compute, and since we only calculate the approximations once, they incur negligible overhead. We apply conducive gradients to distributed stochastic gradient Langevin dynamics (DSGLD) and call the resulting method federated stochastic gradient Langevin dynamics (FSGLD). We demonstrate that our approach can handle delayed communication rounds, converging to the target posterior in cases where DSGLD fails. We also show that FSGLD outperforms DSGLD for non-IID federated data with experiments on metric learning and neural networks.

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.

We study a family of distributed stochastic optimization algorithms where gradients are sampled by a token traversing a network of agents in random-walk fashion. Typically, these random-walks are chosen to be Markov chains that asymptotically sample from a desired target distribution, and play a critical role in the convergence of the optimization iterates. In this paper, we take a novel approach by replacing the standard linear Markovian token by one which follows a nonlinear Markov chain - namely the Self-Repellent Radom Walk (SRRW). Defined for any given 'base' Markov chain, the SRRW, parameterized by a positive scalar {\alpha}, is less likely to transition to states that were highly visited in the past, thus the name. In the context of MCMC sampling on a graph, a recent breakthrough in Doshi et al. (2023) shows that the SRRW achieves O(1/{\alpha}) decrease in the asymptotic variance for sampling. We propose the use of a 'generalized' version of the SRRW to drive token algorithms for distributed stochastic optimization in the form of stochastic approximation, termed SA-SRRW. We prove that the optimization iterate errors of the resulting SA-SRRW converge to zero almost surely and prove a central limit theorem, deriving the explicit form of the resulting asymptotic covariance matrix corresponding to iterate errors. This asymptotic covariance is always smaller than that of an algorithm driven by the base Markov chain and decreases at rate O(1/{\alpha}^2) - the performance benefit of using SRRW thereby amplified in the stochastic optimization context. Empirical results support our theoretical findings.

In this paper, we propose a novel approach where agents can form swarms to produce high-quality responses effectively. This is accomplished by utilizing agents capable of data inference and ranking, which can be effectively implemented using LLMs as response classifiers. We assess existing approaches for trustless agent inference, define our methodology, estimate practical parameters, and model various types of malicious agent attacks. Our method leverages the collective intelligence of swarms, ensuring robust and efficient decentralized AI inference with better accuracy, security, and reliability. We show that our approach is an order of magnitude faster than other trustless inference strategies reaching less than 125 ms validation latency.

Large Language Models (LLMs) show potential for complex reasoning, yet their capacity for emergent coordination in Multi-Agent Systems (MAS) when operating under strict constraints-such as limited local perception and communication, characteristic of natural swarms-remains largely unexplored, particularly concerning the nuances of swarm intelligence. Existing benchmarks often do not fully capture the unique challenges of decentralized coordination that arise when agents operate with incomplete spatio-temporal information. To bridge this gap, we introduce SwarmBench, a novel benchmark designed to systematically evaluate the swarm intelligence capabilities of LLMs acting as decentralized agents. SwarmBench features five foundational MAS coordination tasks within a configurable 2D grid environment, forcing agents to rely primarily on local sensory input (k x k view) and local communication. We propose metrics for coordination effectiveness and analyze emergent group dynamics. Evaluating several leading LLMs in a zero-shot setting, we find significant performance variations across tasks, highlighting the difficulties posed by local information constraints. While some coordination emerges, results indicate limitations in robust planning and strategy formation under uncertainty in these decentralized scenarios. Assessing LLMs under swarm-like conditions is crucial for realizing their potential in future decentralized systems. We release SwarmBench as an open, extensible toolkit-built upon a customizable and scalable physical system with defined mechanical properties. It provides environments, prompts, evaluation scripts, and the comprehensive experimental datasets generated, aiming to foster reproducible research into LLM-based MAS coordination and the theoretical underpinnings of Embodied MAS. Our code repository is available at https://github.com/x66ccff/swarmbench.

Autonomous aerial tracking with drones offers vast potential for surveillance, cinematography, and industrial inspection applications. While single-drone tracking systems have been extensively studied, swarm-based target tracking remains underexplored, despite its unique advantages of distributed perception, fault-tolerant redundancy, and multidirectional target coverage. To bridge this gap, we propose a novel decentralized LiDAR-based swarm tracking framework that enables visibility-aware, cooperative target tracking in complex environments, while fully harnessing the unique capabilities of swarm systems. To address visibility, we introduce a novel Spherical Signed Distance Field (SSDF)-based metric for 3-D environmental occlusion representation, coupled with an efficient algorithm that enables real-time onboard SSDF updating. A general Field-of-View (FOV) alignment cost supporting heterogeneous LiDAR configurations is proposed for consistent target observation. Swarm coordination is enhanced through cooperative costs that enforce inter-robot safe clearance, prevent mutual occlusions, and notably facilitate 3-D multidirectional target encirclement via a novel electrostatic-potential-inspired distribution metric. These innovations are integrated into a hierarchical planner, combining a kinodynamic front-end searcher with a spatiotemporal SE(3) back-end optimizer to generate collision-free, visibility-optimized trajectories.Deployed on heterogeneous LiDAR swarms, our fully decentralized implementation features collaborative perception, distributed planning, and dynamic swarm reconfigurability. Validated through rigorous real-world experiments in cluttered outdoor environments, the proposed system demonstrates robust cooperative tracking of agile targets (drones, humans) while achieving superior visibility maintenance.

Collaborative Simultaneous Localization And Mapping (C-SLAM) is a vital component for successful multi-robot operations in environments without an external positioning system, such as indoors, underground or underwater. In this paper, we introduce Swarm-SLAM, an open-source C-SLAM system that is designed to be scalable, flexible, decentralized, and sparse, which are all key properties in swarm robotics. Our system supports inertial, lidar, stereo, and RGB-D sensing, and it includes a novel inter-robot loop closure prioritization technique that reduces communication and accelerates convergence. We evaluated our ROS-2 implementation on five different datasets, and in a real-world experiment with three robots communicating through an ad-hoc network. Our code is publicly available: https://github.com/MISTLab/Swarm-SLAM

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free framework that removes this bottleneck completely. We decouple basis discovery from the solving process. We meta-train a dual-branch neural network on diverse Gaussian Random Fields. This offline process creates a universal dictionary of neural basis functions. At test time, we freeze the network. We solve the PDE by assembling a collocation matrix. We find the solution through a single linear least squares step. For non-linear PDEs, we apply the Newton-Raphson method to achieve fast quadratic convergence. Our experiments across six 2D and 3D PDEs show massive improvements. MetaColloc reaches state-of-the-art accuracy on smooth and non-linear problems. It also reduces test-time computation by several orders of magnitude. Finally, we provide a detailed frequency sweep analysis. This analysis reveals a critical mismatch between function approximation and operator stability at extremely high frequencies. This profound finding opens a clear path toward future operator-aware meta-learning.

We propose a novel framework to study asynchronous federated learning optimization with delays in gradient updates. Our theoretical framework extends the standard FedAvg aggregation scheme by introducing stochastic aggregation weights to represent the variability of the clients update time, due for example to heterogeneous hardware capabilities. Our formalism applies to the general federated setting where clients have heterogeneous datasets and perform at least one step of stochastic gradient descent (SGD). We demonstrate convergence for such a scheme and provide sufficient conditions for the related minimum to be the optimum of the federated problem. We show that our general framework applies to existing optimization schemes including centralized learning, FedAvg, asynchronous FedAvg, and FedBuff. The theory here provided allows drawing meaningful guidelines for designing a federated learning experiment in heterogeneous conditions. In particular, we develop in this work FedFix, a novel extension of FedAvg enabling efficient asynchronous federated training while preserving the convergence stability of synchronous aggregation. We empirically demonstrate our theory on a series of experiments showing that asynchronous FedAvg leads to fast convergence at the expense of stability, and we finally demonstrate the improvements of FedFix over synchronous and asynchronous FedAvg.

Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient descent with a finite number of particles and establishes its theoretical guarantees to optimize functions that are displacement convex in measures. Concretely, for Lipschitz displacement convex functions defined on probability over R^d, we prove that O(1/epsilon^2) particles and O(d/epsilon^4) computations are sufficient to find the epsilon-optimal solutions. We further provide improved complexity bounds for optimizing smooth displacement convex functions. We demonstrate the application of our results for function approximation with specific neural architectures with two-dimensional inputs.

Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

Training stability remains a critical bottleneck for Group Relative Policy Optimization (GRPO), often manifesting as a trade-off between reasoning plasticity and general capability retention. We identify a root cause as the geometric conflict between plasticity and stability gradients, which leads to destructive interference. Crucially, we argue that deterministic projection methods are suboptimal for GRPO as they overlook the intrinsic stochasticity of group-based gradient estimates. To address this, we propose Probabilistic Conflict Resolution (PCR), a Bayesian framework that models gradients as random variables. PCR dynamically arbitrates conflicts via an uncertainty-aware ``soft projection'' mechanism, optimizing the signal-to-noise ratio. Extensive experiments demonstrate that PCR significantly smooths the training trajectory and achieves superior performance in various reasoning tasks.

Iterative optimization is central to modern artificial intelligence (AI) and provides a crucial framework for understanding adaptive systems. This review provides a unified perspective on this subject, bridging classic theory with neural network training and biological learning. Although gradient-based methods, powered by the efficient but biologically implausible backpropagation (BP), dominate machine learning, their computational demands can hinder scalability in high-dimensional settings. In contrast, derivative-free or zeroth-order (ZO) optimization feature computationally lighter approaches that rely only on function evaluations and randomness. While generally less sample efficient, recent breakthroughs demonstrate that modern ZO methods can effectively approximate gradients and achieve performance competitive with BP in neural network models. This ZO paradigm is also particularly relevant for biology. Its core principles of random exploration (probing) and feedback-guided adaptation (reinforcing) parallel key mechanisms of biological learning, offering a mathematically principled perspective on how the brain learns. In this review, we begin by categorizing optimization approaches based on the order of derivative information they utilize, ranging from first-, second-, and higher-order gradient-based to ZO methods. We then explore how these methods are adapted to the unique challenges of neural network training and the resulting learning dynamics. Finally, we build upon these insights to view biological learning through an optimization lens, arguing that a ZO paradigm leverages the brain's intrinsic noise as a computational resource. This framework not only illuminates our understanding of natural intelligence but also holds vast implications for neuromorphic hardware, helping us design fast and energy-efficient AI systems that exploit intrinsic hardware noise.

This paper proposes a novel problem: vision-based perception to learn and predict the collective dynamics of multi-agent systems, specifically focusing on interaction strength and convergence time. Multi-agent systems are defined as collections of more than ten interacting agents that exhibit complex group behaviors. Unlike prior studies that assume knowledge of agent positions, we focus on deep learning models to directly predict collective dynamics from visual data, captured as frames or events. Due to the lack of relevant datasets, we create a simulated dataset using a state-of-the-art flocking simulator, coupled with a vision-to-event conversion framework. We empirically demonstrate the effectiveness of event-based representation over traditional frame-based methods in predicting these collective behaviors. Based on our analysis, we present event-based vision for Multi-Agent dynamic Prediction (evMAP), a deep learning architecture designed for real-time, accurate understanding of interaction strength and collective behavior emergence in multi-agent systems.

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

We identify a new phenomenon in neural network optimization which arises from the interaction of depth and a particular heavy-tailed structure in natural data. Our result offers intuitive explanations for several previously reported observations about network training dynamics. In particular, it implies a conceptually new cause for progressive sharpening and the edge of stability; we also highlight connections to other concepts in optimization and generalization including grokking, simplicity bias, and Sharpness-Aware Minimization. Experimentally, we demonstrate the significant influence of paired groups of outliers in the training data with strong opposing signals: consistent, large magnitude features which dominate the network output throughout training and provide gradients which point in opposite directions. Due to these outliers, early optimization enters a narrow valley which carefully balances the opposing groups; subsequent sharpening causes their loss to rise rapidly, oscillating between high on one group and then the other, until the overall loss spikes. We describe how to identify these groups, explore what sets them apart, and carefully study their effect on the network's optimization and behavior. We complement these experiments with a mechanistic explanation on a toy example of opposing signals and a theoretical analysis of a two-layer linear network on a simple model. Our finding enables new qualitative predictions of training behavior which we confirm experimentally. It also provides a new lens through which to study and improve modern training practices for stochastic optimization, which we highlight via a case study of Adam versus SGD.

Multi-robot systems such as swarms of aerial robots are naturally suited to offer additional flexibility, resilience, and robustness in several tasks compared to a single robot by enabling cooperation among the agents. To enhance the autonomous robot decision-making process and situational awareness, multi-robot systems have to coordinate their perception capabilities to collect, share, and fuse environment information among the agents in an efficient and meaningful way such to accurately obtain context-appropriate information or gain resilience to sensor noise or failures. In this paper, we propose a general-purpose Graph Neural Network (GNN) with the main goal to increase, in multi-robot perception tasks, single robots' inference perception accuracy as well as resilience to sensor failures and disturbances. We show that the proposed framework can address multi-view visual perception problems such as monocular depth estimation and semantic segmentation. Several experiments both using photo-realistic and real data gathered from multiple aerial robots' viewpoints show the effectiveness of the proposed approach in challenging inference conditions including images corrupted by heavy noise and camera occlusions or failures.

Group Relative Policy Optimisation (GRPO) enhances large language models by estimating advantages across a group of sampled trajectories. However, mapping these trajectory-level advantages to policy updates requires aggregating token-level probabilities within each sequence. Relying on a fixed aggregation mechanism for this step fundamentally limits the algorithm's adaptability. Empirically, we observe a critical trade-off: certain fixed aggregations frequently suffer from training collapse, while others fail to yield satisfactory performance. To resolve this, we propose HölderPO, a generalised policy optimisation framework unifying token-level probability aggregation via the Hölder mean. By explicitly modulating the parameter p, our framework provides continuous control over the trade-off between gradient concentration and variance bounds. Theoretically, we prove that a larger p concentrates the gradient to amplify sparse learning signals, whereas a smaller p strictly bounds gradient variance. Because no static configuration can universally resolve this concentration-stability trade-off, we instantiate the framework with a dynamic annealing algorithm that progressively schedules p across the training lifecycle. Extensive evaluations demonstrate superior stability and convergence over existing baselines. Specifically, our approach achieves a state-of-the-art average accuracy of 54.9% across multiple mathematical benchmarks, yielding a substantial 7.2% relative gain over standard GRPO and secures an exceptional 93.8% success rate on ALFWorld.

When are multi-agent LLM systems merely a collection of individual agents versus an integrated collective with higher-order structure? We introduce an information-theoretic framework to test -- in a purely data-driven way -- whether multi-agent systems show signs of higher-order structure. This information decomposition lets us measure whether dynamical emergence is present in multi-agent LLM systems, localize it, and distinguish spurious temporal coupling from performance-relevant cross-agent synergy. We implement a practical criterion and an emergence capacity criterion operationalized as partial information decomposition of time-delayed mutual information (TDMI). We apply our framework to experiments using a simple guessing game without direct agent communication and minimal group-level feedback with three randomized interventions. Groups in the control condition exhibit strong temporal synergy but little coordinated alignment across agents. Assigning a persona to each agent introduces stable identity-linked differentiation. Combining personas with an instruction to ``think about what other agents might do'' shows identity-linked differentiation and goal-directed complementarity across agents. Taken together, our framework establishes that multi-agent LLM systems can be steered with prompt design from mere aggregates to higher-order collectives. Our results are robust across emergence measures and entropy estimators, and not explained by coordination-free baselines or temporal dynamics alone. Without attributing human-like cognition to the agents, the patterns of interaction we observe mirror well-established principles of collective intelligence in human groups: effective performance requires both alignment on shared objectives and complementary contributions across members.

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where M^* in R^{n times n} is a positive semi-definite unknown matrix of rank r ll n, and one uses a symmetric parameterization XX^top to learn M^*. Here X in R^{n times k} with k > r is the factor matrix. We give a novel Omega (1/T^2) lower bound of randomly initialized GD for the over-parameterized case (k >r) where T is the number of iterations. This is in stark contrast to the exact-parameterization scenario (k=r) where the convergence rate is exp (-Omega (T)). Next, we study asymmetric setting where M^* in R^{n_1 times n_2} is the unknown matrix of rank r ll min{n_1,n_2}, and one uses an asymmetric parameterization FG^top to learn M^* where F in R^{n_1 times k} and G in R^{n_2 times k}. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case (k=r) with an exp (-Omega(T)) rate. Furthermore, we give the first global exact convergence result for the over-parameterization case (k>r) with an exp(-Omega(alpha^2 T)) rate where alpha is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from Omega (1/T^2) to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of alpha, recovering the rate in the exact-parameterization case.

Generative models have changed how machine learning represents complex data distributions, especially in language and vision, yet many real-world systems are observed instead as continuous, high-dimensional, and noisy sensor time series. Existing generative modeling of sensor data, however, remains fragmented across modalities, datasets, and task formulations, limiting a systematic understanding of when, how, and why generative models succeed or fail in real-world settings. To address this gap, we introduce SensorGen, a large-scale study of sensor-signal generation spanning 14 settings across 4 domains, 7 datasets, and 12 signal modalities. Leveraging SensorGen, we systematically evaluate generative models from five major families and uncover three key findings: (1) flow-matching models provide strong overall performance across most settings; (2) signal properties matter, with demographic covariates improving longitudinal generation and time-frequency modeling improving high-frequency signal generation; and (3) generated signals have practical utility beyond visual realism, with scaling improving generation quality and synthetic data improving downstream performance. Together, SensorGen establishes a broader understanding of design choices, evaluation protocols, and failure modes in real-world sensor data generation.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

We present a non-asymptotic theory of generalization in deep learning where the empirical neural tangent kernel partitions the output space. In directions corresponding to signal, error dissipates rapidly; in the vast orthogonal dimensions corresponding to noise, the kernel's near-zero eigenvalues trap residual error in a test-invisible reservoir. Within the signal channel, minibatch SGD ensures that coherent population signal accumulates via fast linear drift, while idiosyncratic memorization is suppressed into a slow, diffusive random walk. We prove generalization survives even when the kernel evolves O(1) in operator norm, the full feature-learning regime. This theory naturally explains disparate phenomena in deep learning theory, such as benign overfitting, double descent, implicit bias, and grokking. Lastly, we derive an exact population-risk objective from a single training run with no validation data, for any architecture, loss, or optimizer, and prove that it measures precisely the noise in the signal channel. This objective reduces in practice to an SNR preconditioner on top of Adam, adding one state vector at no extra cost; it accelerates grokking by 5 times, suppresses memorization in PINNs and implicit neural representations, and improves DPO fine-tuning under noisy preferences while staying 3 times closer to the reference policy.

We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the best of our knowledge, this is the first recovery guarantee of gradient-based algorithms for convolutional filter on non-Gaussian input distributions. Our theory also justifies the two-stage learning rate strategy in deep neural networks. While our focus is theoretical, we also present experiments that illustrate our theoretical findings.

Multiple robots could perceive a scene (e.g., detect objects) collaboratively better than individuals, although easily suffer from adversarial attacks when using deep learning. This could be addressed by the adversarial defense, but its training requires the often-unknown attacking mechanism. Differently, we propose ROBOSAC, a novel sampling-based defense strategy generalizable to unseen attackers. Our key idea is that collaborative perception should lead to consensus rather than dissensus in results compared to individual perception. This leads to our hypothesize-and-verify framework: perception results with and without collaboration from a random subset of teammates are compared until reaching a consensus. In such a framework, more teammates in the sampled subset often entail better perception performance but require longer sampling time to reject potential attackers. Thus, we derive how many sampling trials are needed to ensure the desired size of an attacker-free subset, or equivalently, the maximum size of such a subset that we can successfully sample within a given number of trials. We validate our method on the task of collaborative 3D object detection in autonomous driving scenarios.

Vehicle-to-vehicle (V2V) communications have greatly enhanced the perception capabilities of connected and automated vehicles (CAVs) by enabling information sharing to "see through the occlusions", resulting in significant performance improvements. However, developing and training complex multi-agent perception models from scratch can be expensive and unnecessary when existing single-agent models show remarkable generalization capabilities. In this paper, we propose a new framework termed MACP, which equips a single-agent pre-trained model with cooperation capabilities. We approach this objective by identifying the key challenges of shifting from single-agent to cooperative settings, adapting the model by freezing most of its parameters and adding a few lightweight modules. We demonstrate in our experiments that the proposed framework can effectively utilize cooperative observations and outperform other state-of-the-art approaches in both simulated and real-world cooperative perception benchmarks while requiring substantially fewer tunable parameters with reduced communication costs. Our source code is available at https://github.com/PurdueDigitalTwin/MACP.

This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape. Local extrema with low generalization error have a large proportion of almost-zero eigenvalues in the Hessian with very few positive or negative eigenvalues. We leverage upon this observation to construct a local-entropy-based objective function that favors well-generalizable solutions lying in large flat regions of the energy landscape, while avoiding poorly-generalizable solutions located in the sharp valleys. Conceptually, our algorithm resembles two nested loops of SGD where we use Langevin dynamics in the inner loop to compute the gradient of the local entropy before each update of the weights. We show that the new objective has a smoother energy landscape and show improved generalization over SGD using uniform stability, under certain assumptions. Our experiments on convolutional and recurrent networks demonstrate that Entropy-SGD compares favorably to state-of-the-art techniques in terms of generalization error and training time.

Optimizing communication topology is fundamental to the efficiency and effectiveness of Large Language Model (LLM)-based Multi-Agent Systems (MAS). While recent approaches utilize reinforcement learning to dynamically construct task-specific graphs, they typically rely on single-sample policy gradients with absolute rewards (e.g., binary correctness). This paradigm suffers from severe gradient variance and the credit assignment problem: simple queries yield non-informative positive rewards for suboptimal structures, while difficult queries often result in failures that provide no learning signal. To address these challenges, we propose Graph-GRPO, a novel topology optimization framework that integrates Group Relative Policy Optimization. Instead of evaluating a single topology in isolation, Graph-GRPO samples a group of diverse communication graphs for each query and computes the advantage of specific edges based on their relative performance within the group. By normalizing rewards across the sampled group, our method effectively mitigates the noise derived from task difficulty variance and enables fine-grained credit assignment. Extensive experiments on reasoning and code generation benchmarks demonstrate that Graph-GRPO significantly outperforms state-of-the-art baselines, achieving superior training stability and identifying critical communication pathways previously obscured by reward noise.

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is closely related to the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named Li_2, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \textbf{L}azy learning, (II) \textbf{i}ndependent feature learning and (III) \textbf{i}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. Thanks to lazy learning and weight decay, the backpropagated gradient G_F from the top layer now carries information about the target label, with a specific structure that enables each hidden node to learn their representation independently. Interestingly, the independent dynamics follows exactly the gradient ascent of an energy function E, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how G_F changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

Collaborative generation, which coordinates multiple diffusion trajectories to extend the capabilities of pretrained priors, has emerged as a powerful paradigm for extending the applicability of diffusion models. Among existing approaches, diffusion synchronization provides a scenario-agnostic solution by introducing general guidance mechanisms. However, current synchronization approaches rely heavily on heuristics and still require task-specific tailoring, which limits their generalizability and performance. In this work, we mathematically derive a synchronization framework based on optimal control, providing a principled explanation of diffusion synchronization. During sampling, we optimize control variables to guide multiple trajectories toward coherent solutions while remaining close to the underlying diffusion prior. Our method operates entirely at test-time without additional training, thereby enabling broad applicability across diverse generation scenarios when combined with strong pretrained priors. We demonstrate consistent improvements over baselines on three representative collaborative generation tasks, covering a wide range of modalities and applications. Beyond performance gains, our work establishes a novel foundation for collaborative generation, opening a principled path toward extending pretrained generative models to new collaborative generation settings.

Co-saliency detection (Co-SOD) aims to segment the common salient foreground in a group of relevant images. In this paper, inspired by human behavior, we propose a gradient-induced co-saliency detection (GICD) method. We first abstract a consensus representation for the grouped images in the embedding space; then, by comparing the single image with consensus representation, we utilize the feedback gradient information to induce more attention to the discriminative co-salient features. In addition, due to the lack of Co-SOD training data, we design a jigsaw training strategy, with which Co-SOD networks can be trained on general saliency datasets without extra pixel-level annotations. To evaluate the performance of Co-SOD methods on discovering the co-salient object among multiple foregrounds, we construct a challenging CoCA dataset, where each image contains at least one extraneous foreground along with the co-salient object. Experiments demonstrate that our GICD achieves state-of-the-art performance. Our codes and dataset are available at https://mmcheng.net/gicd/.

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

We present a differentiable optimization framework for multi-agent coordination. An input is decomposed into overlapping local views, each processed by an agent that solves a convex subproblem parameterized by a neural encoder. Agents coordinate through the Alternating Direction Method of Multipliers (ADMM) with inter-agent constraints specified by a cellular sheaf. The sheaf specifies which aspects of neighboring solutions must agree, allowing for heterogeneous notions of global consensus. Backpropagating through the unrolled optimization jointly trains all components of the multi-agent system. We evaluate on maze pathfinding, image classification, and Sudoku, where agents with individually insufficient local views learn to coordinate to produce correct global outputs. On MNIST, the local-view decomposition yields improved robustness to distribution shifts relative to a standard CNN. On Sudoku, the optimization-derived structure yields markedly higher solve rates than parameter-matched MPNN baselines. Finally, the ADMM structure exposes distinct primal, consensus, and dual state variables, opening the coordination dynamics to direct analysis and intervention -- a property unavailable in standard message-passing architectures.

In this paper, we focus on one centralized and one decentralized problem of active hypothesis testing in the presence of an eavesdropper. For the centralized problem including a single legitimate agent, we present a new framework based on NeuroEvolution (NE), whereas, for the decentralized problem, we develop a novel NE-based method for solving collaborative multi-agent tasks, which interestingly maintains all computational benefits of single-agent NE. The superiority of the proposed EAHT approaches over conventional active hypothesis testing policies, as well as learning-based methods, is validated through numerical investigations in an example use case of anomaly detection over wireless sensor networks.

Masked Diffusion Models (MDMs) have emerged as a promising non-autoregressive paradigm for generative tasks, offering parallel decoding and bidirectional context utilization. However, current sampling methods rely on simple confidence-based heuristics that ignore the long-term impact of local decisions, leading to trajectory lock-in where early hallucinations cascade into global incoherence. While search-based methods mitigate this, they incur prohibitive computational costs (O(K) forward passes per step). In this work, we propose Backward-on-Entropy (BoE) Steering, a gradient-guided inference framework that approximates infinite-horizon lookahead via a single backward pass. We formally derive the Token Influence Score (TIS) from a first-order expansion of the trajectory cost functional, proving that the gradient of future entropy with respect to input embeddings serves as an optimal control signal for minimizing uncertainty. To ensure scalability, we introduce ActiveQueryAttention, a sparse adjoint primitive that exploits the structure of the masking objective to reduce backward pass complexity. BoE achieves a superior Pareto frontier for inference-time scaling compared to existing unmasking methods, demonstrating that gradient-guided steering offers a mathematically principled and efficient path to robust non-autoregressive generation. We will release the code.

Unmanned Aerial Vehicle (UAV) swarm systems necessitate efficient collaborative perception mechanisms for diverse operational scenarios. Current Bird's Eye View (BEV)-based approaches exhibit two main limitations: bounding-box representations fail to capture complete semantic and geometric information of the scene, and their performance significantly degrades when encountering undefined or occluded objects. To address these limitations, we propose a novel multi-UAV collaborative occupancy prediction framework. Our framework effectively preserves 3D spatial structures and semantics through integrating a Spatial-Aware Feature Encoder and Cross-Agent Feature Integration. To enhance efficiency, we further introduce Altitude-Aware Feature Reduction to compactly represent scene information, along with a Dual-Mask Perceptual Guidance mechanism to adaptively select features and reduce communication overhead. Due to the absence of suitable benchmark datasets, we extend three datasets for evaluation: two virtual datasets (Air-to-Pred-Occ and UAV3D-Occ) and one real-world dataset (GauUScene-Occ). Experiments results demonstrate that our method achieves state-of-the-art accuracy, significantly outperforming existing collaborative methods while reducing communication overhead to only a fraction of previous approaches.

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

We identify a new dimension for enhancing rollout diversity in Group Relative Policy Optimization (GRPO) for LLMs. While GRPO relies on diverse rollouts, prevailing strategies primarily increase diversity by injecting more token-level randomness, which may introduce step-wise noise and lead to incoherent trajectories. We uncover that smaller models within the same model family inherently exhibit higher policy-level diversity, indicated by their superior pass@k relative to larger counterparts as sample counts increase. Unlike token-level noise, this diversity is temporally correlated, preserves logical consistency, and provides structured exploration signals for gradient estimation. We thus propose S2L-PO (Small-to-Large Policy Optimization), a framework that leverages fixed small models as natural explorers to train larger models. To balance exploration and exploitation, we design a progressive annealing strategy that transitions from offline small-model rollouts to the large learner's own sampling. This shift elegantly avoids mid-training performance drops caused by the small model's capacity limits, achieving faster convergence and unlocking a higher performance ceiling. S2L-PO improves accuracy on diverse mathematical reasoning benchmarks (e.g., +8.8% on AIME 24 using a 1.7B explorer to guide the 8B model) while reducing rollout compute.

We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.

Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function), where it branches at saddles - easy-to-find bifurcation points. We generalize this idea to non-conservative, multi-agent gradient systems by proposing a method - denoted Generalized Ridge Rider (GRR) - for finding arbitrary bifurcation points. We give theoretical motivation for our method by leveraging machinery from the field of dynamical systems. We construct novel toy problems where we can visualize new phenomena while giving insight into high-dimensional problems of interest. Finally, we empirically evaluate our method by finding diverse solutions in the iterated prisoners' dilemma and relevant machine learning problems including generative adversarial networks.

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this paper, we provide a unified convergence analysis of communication-efficient local training methods for distributed variational inequality problems (VIPs). Our approach is based on a general key assumption on the stochastic estimates that allows us to propose and analyze several novel local training algorithms under a single framework for solving a class of structured non-monotone VIPs. We present the first local gradient descent-accent algorithms with provable improved communication complexity for solving distributed variational inequalities on heterogeneous data. The general algorithmic framework recovers state-of-the-art algorithms and their sharp convergence guarantees when the setting is specialized to minimization or minimax optimization problems. Finally, we demonstrate the strong performance of the proposed algorithms compared to state-of-the-art methods when solving federated minimax optimization problems.

As centralized AI hits compute ceilings and diminishing returns from ever-larger training runs, meeting demand requires an inference layer that scales horizontally in both capacity and capability. We present Fortytwo, a novel protocol that leverages swarm intelligence principles and distributed pairwise ranking consensus to achieve superior performance in AI inference. Our approach reimagines collaboration among AI nodes using swarm inference: a peer-ranked, reputation-weighted consensus across heterogeneous models that surfaces the highest-quality responses. Using pairwise ranking with a custom Bradley-Terry-style aggregation model, we demonstrate that swarm inference substantially outperforms majority voting, achieving 85.90% on GPQA Diamond versus 68.69% for majority voting with the same model set - an improvement of +17.21 percentage points (approximately +25.1% relative). The protocol incorporates on-chain reputation so node influence adapts to demonstrated accuracy over time, yielding a meritocratic consensus that filters low-quality or malicious participants. To resist Sybil attacks, Fortytwo employs proof-of-capability in its consensus: nodes must successfully complete calibration/test requests and stake reputation to enter ranking rounds, making multi-identity attacks economically unattractive while preserving openness. Across six challenging benchmarks, including GPQA Diamond, LiveCodeBench, and AIME, our evaluation indicates higher accuracy and strong resilience to adversarial and noisy free-form prompting (e.g., prompt-injection degradation of only 0.12% versus 6.20% for a monolithic single-model baseline), while retaining practical deployability. Together, these results establish a foundation for decentralized AI systems - democratizing access to high-quality inference through collective intelligence without sacrificing reliability or security.

The blooming of social media and face recognition (FR) systems has increased people's concern about privacy and security. A new type of adversarial privacy cloak (class-universal) can be applied to all the images of regular users, to prevent malicious FR systems from acquiring their identity information. In this work, we discover the optimization dilemma in the existing methods -- the local optima problem in large-batch optimization and the gradient information elimination problem in small-batch optimization. To solve these problems, we propose Gradient Accumulation (GA) to aggregate multiple small-batch gradients into a one-step iterative gradient to enhance the gradient stability and reduce the usage of quantization operations. Experiments show that our proposed method achieves high performance on the Privacy-Commons dataset against black-box face recognition models.

Cooperative perception enables autonomous agents to share encoded representations over wireless communication to enhance each other's live situational awareness. However, the tension between the limited communication bandwidth and the rich sensor information hinders its practical deployment. Recent studies have explored selection strategies that share only a subset of features per frame while striving to keep the performance on par. Nevertheless, the bandwidth requirement still stresses current wireless technologies. To fundamentally ease the tension, we take a proactive approach, exploiting the temporal continuity to identify features that capture environment dynamics, while avoiding repetitive and redundant transmission of static information. By incorporating temporal awareness, agents are empowered to dynamically adapt the sharing quantity according to environment complexity. We instantiate this intuition into an adaptive selection framework, COOPERTRIM, which introduces a novel conformal temporal uncertainty metric to gauge feature relevance, and a data-driven mechanism to dynamically determine the sharing quantity. To evaluate COOPERTRIM, we take semantic segmentation and 3D detection as example tasks. Across multiple open-source cooperative segmentation and detection models, COOPERTRIM achieves up to 80.28% and 72.52% bandwidth reduction respectively while maintaining a comparable accuracy. Relative to other selection strategies, COOPERTRIM also improves IoU by as much as 45.54% with up to 72% less bandwidth. Combined with compression strategies, COOPERTRIM can further reduce bandwidth usage to as low as 1.46% without compromising IoU performance. Qualitative results show COOPERTRIM gracefully adapts to environmental dynamics, localization error, and communication latency, demonstrating flexibility and paving the way for real-world deployment.

Density peak clustering (DPC) connects each observation to its nearest neighbor of higher density and identifies cluster centers as high-density observations with unusually large nearest neighbor uphill shifts. The resulting uphill paths from observations to cluster centers, however, can be irregular and unstable in low-density regions, making the clustering assignments sensitive to local perturbations and obscuring the population geometry of the DPC graph. In this paper, we introduce gradient-guided density peak clustering (GGDPC), which performs a gradient ascent step before each nearest neighbor uphill search. We develop a stability theory that relates the GGDPC graph to the gradient ascent flow of the population density. In particular, we establish consistency of GGDPC under five complementary criteria: recovery of local modes, adjusted Rand index, dendrogram (cluster tree), path length, and waterfall measure. Together, these results provide new statistical, geometric, and topological interpretations of DPC-type clustering algorithms.

The continued release of new and better image generation models increases the demand for synthetic image detectors. In such a dynamic field, detectors need to be able to generalize widely and be robust to uncontrolled alterations. The present work is motivated by this setting, when looking at the role of time, image transformations and data sources, for detector generalization. In these experiments, none of the evaluated detectors is found universal, but results indicate an ensemble could be. Experiments on data collected in the wild show this task to be more challenging than the one defined by large-scale datasets, pointing to a gap between experimentation and actual practice. Finally, we observe a race equilibrium effect, where better generators lead to better detectors, and vice versa. We hypothesize this pushes the field towards a perpetually close race between generators and detectors.

Microbial swarming on mucosal surfaces reshapes microbial communities and influences mucosal healing and antibiotic tolerance. Yet even with time-lapse microscopy and deep learning, analyses of swarming colonies remain descriptive and cannot forecast how their fronts reorganize in time. This limitation is significant because the advancing edge determines access to nutrients, host tissue and competing microbes. We recast the expansion of Enterobacter sp. SM3 swarms as a problem of morphological forecasting, and assemble SwarmEvo, a time-lapse dataset represented as boundary-resolved segmentations. TexPol--Net, a texture- and geometry-aware segmentation model, sharpens diffuse edges and preserves fingered fronts, creating a stable substrate for dynamics. On this representation, we develop Morpher, an autoregressive forecasting network with a ``Morphon'' memory that links local curvature to long-range temporal dependencies. Morpher outperforms leading video-prediction models in maintaining front localization and anisotropic branching, and modest segmentation improvements yield noticeably more stable forecasts. Ablations across sequence models, inference strategies and observation ratios show that attention-based architectures with structural memory best preserve dense-finger propagation. By uniting geometry-aware segmentation with morphology-level forecasting, this framework turns swarming expansion into a predictive dynamical system, enabling quantitative interrogation and potential control of microbial collectives during mucosal repair and gut ecosystem engineering.

Local loss-landscape stabilization under sample growth is typically measured either pointwise or through isotropic averaging in the full parameter space. Despite practical value, both choices probe directions that contribute little to the dominant local deformation of strongly anisotropic neural landscapes. We recast stabilization as an observational problem and introduce a unified family of criteria parameterized by an aggregation order and a probing distribution; within this family we propose a curvature-aligned criterion Δ_2^{(D)} that probes the loss increment field in the top-D eigenspace of the empirical Hessian near a trained solution. Solely from a local quadratic model, we prove that Δ_2^{(D)} preserves the O(k^{-2}) mean-squared rate of the full-space criterion while replacing ambient-dimension curvature dependence with dependence on the subspace dimension D; a corollary gives a closed-form spectral expression and a proposition identifies the top-D eigenspace as extremal within the eigenspace-aligned family. We also derive scalable estimators based on Hessian-vector products, subspace Monte Carlo, and a closed-form Gaussian-moment proxy. On a decoder-only transformer, a curvature-aligned probe occupying a tiny fraction of parameter space already reproduces the full-space mean-squared signal to within numerical noise throughout the validated local regime, and the closed-form estimator is orders of magnitude faster than direct Monte Carlo after subspace construction.

High network communication cost for synchronizing gradients and parameters is the well-known bottleneck of distributed training. In this work, we propose TernGrad that uses ternary gradients to accelerate distributed deep learning in data parallelism. Our approach requires only three numerical levels {-1,0,1}, which can aggressively reduce the communication time. We mathematically prove the convergence of TernGrad under the assumption of a bound on gradients. Guided by the bound, we propose layer-wise ternarizing and gradient clipping to improve its convergence. Our experiments show that applying TernGrad on AlexNet does not incur any accuracy loss and can even improve accuracy. The accuracy loss of GoogLeNet induced by TernGrad is less than 2% on average. Finally, a performance model is proposed to study the scalability of TernGrad. Experiments show significant speed gains for various deep neural networks. Our source code is available.

Many deep learning applications benefit from using large models with billions of parameters. Training these models is notoriously expensive due to the need for specialized HPC clusters. In this work, we consider alternative setups for training large models: using cheap "preemptible" instances or pooling existing resources from multiple regions. We analyze the performance of existing model-parallel algorithms in these conditions and find configurations where training larger models becomes less communication-intensive. Based on these findings, we propose SWARM parallelism, a model-parallel training algorithm designed for poorly connected, heterogeneous and unreliable devices. SWARM creates temporary randomized pipelines between nodes that are rebalanced in case of failure. We empirically validate our findings and compare SWARM parallelism with existing large-scale training approaches. Finally, we combine our insights with compression strategies to train a large Transformer language model with 1B shared parameters (approximately 13B before sharing) on preemptible T4 GPUs with less than 200Mb/s network.

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

Generative models have emerged as a major paradigm for offline multi-agent reinforcement learning (MARL), but existing approaches require many iterative sampling steps. Recent few-step accelerations either distill a joint teacher into independent students or apply averaged velocities independently per agent, suggesting that few-step inference requires sacrificing inter-agent coordination. We show this trade-off is not necessary: single-pass multi-agent generation can preserve coordination when the velocity field is natively joint-coupled. We propose Coordinated few-step Flow (CoFlow), an architecture that combines Coordinated Velocity Attention (CVA) with Adaptive Coordination Gating. A finite-difference consistency surrogate further replaces memory-prohibitive Jacobian-vector product backpropagation through the averaged velocity field with two stop-gradient forward passes. Across 60 configurations spanning MPE, MA-MuJoCo, and SMAC, CoFlow matches or surpasses Gaussian / value-based, transformer, diffusion, and prior flow baselines on episodic return. Three independent coordination probes confirm that the gains flow through inter-agent coordination rather than per-agent capacity. A denoising-step sweep shows that single-pass inference suffices on every configuration. CoFlow reaches state-of-the-art coordination quality in 1-3 denoising steps under both centralized and decentralized execution. Project page: https://github.com/Guowei-Zou/coflow.

We study the dynamics of Stochastic Gradient Descent (SGD), which is known to steer deep neural networks toward invariant sets that correspond to simpler subnetworks. How this steering unfolds over time remains poorly understood. We answer this by modeling the stochastic gradient flow (SGF) as a percolation process, in which architectural symmetries force subnetworks to merge in discrete simultaneous blocks rather than one at a time. These structural transitions register as variance spikes in a macroscopic order parameter, echoing physical phase transitions. We further show this trapping mechanism and its associated scaling cascade extend to Adam and AdamW under an explicit heavy-tailed noise model.

Model compression is essential in the deployment of large Computer Vision models on embedded devices. However, static optimization techniques (e.g. pruning, quantization, etc.) neglect the fact that different inputs have different complexities, thus requiring different amount of computations. Dynamic Neural Networks allow to condition the number of computations to the specific input. The current literature on the topic is very extensive and fragmented. We present a comprehensive survey that synthesizes and unifies existing Dynamic Neural Networks research in the context of Computer Vision. Additionally, we provide a logical taxonomy based on which component of the network is adaptive: the output, the computation graph or the input. Furthermore, we argue that Dynamic Neural Networks are particularly beneficial in the context of Sensor Fusion for better adaptivity, noise reduction and information prioritization. We present preliminary works in this direction. We complement this survey with a curated repository listing all the surveyed papers, each with a brief summary of the solution and the code base when available: https://github.com/DTU-PAS/awesome-dynn-for-cv .

In this paper, we propose the problem of collaborative perception, where robots can combine their local observations with those of neighboring agents in a learnable way to improve accuracy on a perception task. Unlike existing work in robotics and multi-agent reinforcement learning, we formulate the problem as one where learned information must be shared across a set of agents in a bandwidth-sensitive manner to optimize for scene understanding tasks such as semantic segmentation. Inspired by networking communication protocols, we propose a multi-stage handshake communication mechanism where the neural network can learn to compress relevant information needed for each stage. Specifically, a target agent with degraded sensor data sends a compressed request, the other agents respond with matching scores, and the target agent determines who to connect with (i.e., receive information from). We additionally develop the AirSim-CP dataset and metrics based on the AirSim simulator where a group of aerial robots perceive diverse landscapes, such as roads, grasslands, buildings, etc. We show that for the semantic segmentation task, our handshake communication method significantly improves accuracy by approximately 20% over decentralized baselines, and is comparable to centralized ones using a quarter of the bandwidth.

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, and neural network theory, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new algorithm, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep neural network training, and provide preliminary numerical evidence for its superior performance.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a non-differentiable function with a differentiable density distribution with full support, smoothing it and enabling gradient estimation. Our theory starts at first principles to derive stochastic smoothing with reduced assumptions, without requiring a differentiable density nor full support, and we present a general framework for relaxation and gradient estimation of non-differentiable black-box functions f:R^ntoR^m. We develop variance reduction for gradient estimation from 3 orthogonal perspectives. Empirically, we benchmark 6 distributions and up to 24 variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.

The Weighted-Mean Subsequence Reduced (W-MSR) algorithm, the state-of-the-art method for Byzantine-resilient design of decentralized multi-robot systems, is based on discarding outliers received over Linear Consensus Protocol (LCP). Although W-MSR provides well-understood theoretical guarantees relating robust network connectivity to the convergence of the underlying consensus, the method comes with several limitations preventing its use at scale: (1) the number of Byzantine robots, F, to tolerate should be known a priori, (2) the requirement that each robot maintains 2F+1 neighbors is impractical for large F, (3) information propagation is hindered by the requirement that F+1 robots independently make local measurements of the consensus property in order for the swarm's decision to change, and (4) W-MSR is specific to LCP and does not generalize to applications not implemented over LCP. In this work, we propose a Decentralized Blocklist Protocol (DBP) based on inter-robot accusations. Accusations are made on the basis of locally-made observations of misbehavior, and once shared by cooperative robots across the network are used as input to a graph matching algorithm that computes a blocklist. DBP generalizes to applications not implemented via LCP, is adaptive to the number of Byzantine robots, and allows for fast information propagation through the multi-robot system while simultaneously reducing the required network connectivity relative to W-MSR. On LCP-type applications, DBP reduces the worst-case connectivity requirement of W-MSR from (2F+1)-connected to (F+1)-connected and the number of cooperative observers required to propagate new information from F+1 to just 1 observer. We demonstrate empirically that our approach to Byzantine resilience scales to hundreds of robots on cooperative target tracking, time synchronization, and localization case studies.

From optical sensors to microwave radars, leveraging the complementary strengths of remote sensing (RS) sensors is crucial for achieving dense spatio-temporal monitoring of our planet. In contrast, recent deep learning models, whether task-specific or foundational, are often specific to single sensors or to fixed combinations: adapting such models to different sensory inputs requires both architectural changes and re-training, limiting scalability and generalization across multiple RS sensors. On the contrary, a single model able to modulate its feature representations to accept diverse sensors as input would pave the way to agile and flexible multi-sensor RS data processing. To address this, we introduce SMARTIES, a generic and versatile foundation model lifting sensor-specific/dependent efforts and enabling scalability and generalization to diverse RS sensors: SMARTIES projects data from heterogeneous sensors into a shared spectrum-aware space, enabling the use of arbitrary combinations of bands both for training and inference. To obtain sensor-agnostic representations, we train a single, unified transformer model reconstructing masked multi-sensor data with cross-sensor token mixup. On both single- and multi-modal tasks across diverse sensors, SMARTIES outperforms previous models that rely on sensor-specific pretraining. Our code and pretrained models are available at https://gsumbul.github.io/SMARTIES.

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-beta-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios.

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.

This paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, we discuss how optimization problems arise in machine learning and what makes them challenging. A major theme of our study is that large-scale machine learning represents a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter. Based on this viewpoint, we present a comprehensive theory of a straightforward, yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion about the next generation of optimization methods for large-scale machine learning, including an investigation of two main streams of research on techniques that diminish noise in the stochastic directions and methods that make use of second-order derivative approximations.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Wearable motion sensing provides a continuous and scalable window into human behavior and health, making it a natural fit for foundation models, yet its pretraining and scaling principles remain poorly understood. Prior work studies isolated design choices, such as sensor placement or sampling frequency, often under fixed settings and narrow downstream tasks that fail to capture real-world sensing diversity. We introduce Inertia-1, a fully open exploration of wearable motion foundation models. Using massive corpora of accelerometer data from global sources spanning more than 18.2M hours, we build a controlled framework for studying the full lifecycle of wearable motion foundation models, covering data choices such as sensor modality, device placement, sampling rate, window length; model choices such as architectures and model size; and training choices such as pretraining objective and data scale. Extensive evaluations across 15 datasets spanning human activity recognition, freezing-of-gait detection, and disease prediction reveal intriguing findings for building motion foundation models that generalize across tasks and sensing conditions. Collectively, Inertia-1 not only presents state-of-the-art recipes for diverse downstream tasks, but also serves as a comprehensive, practical, and open cookbook for wearable motion representation learning.

Agent-native social platforms such as Moltbook are rapidly emerging, yet they inherit and amplify classical influence and abuse attacks, where coordinated agents strategically comment and upvote to manipulate visibility and propagate narratives across communities. However, rigorous measurement and learning-based monitoring remain constrained by the absence of longitudinal, graph-native datasets for agentic social networks that jointly capture heterogeneous interactions, temporal drift, and visibility signals needed to connect coordination behavior to downstream exposure. We introduce MoltGraph as a realistic longitudinal agentic social-network graph dataset for studying how agents behave, coordinate, and evolve in the wild, enabling reproducible measurement on emerging multi-agent social ecosystems. Using MoltGraph, we provide the first graph-centric characterization of Moltbook as a dynamic network: (i) heavy-tailed connectivity with power-law exponents in the range alpha in [1.86, 2.72], (ii) accelerating hub formation and attention centralization where the top 1% agents account for 29.00% of engagements, (iii) bursty, short-lived coordination episodes, 98.33% last under 24 hours, and (iv) measurable exposure effects across submolts. In matched analyses, posts receiving coordinated engagement exhibit 506.35% higher early interaction rates (within H=5 days) and 242.63% higher downstream exposure in feeds than non-coordinated controls.

We introduce a Wireless Signal based Efficient multi-Robot eXploration (WiSER-X) algorithm applicable to a decentralized team of robots exploring an unknown environment with communication bandwidth constraints. WiSER-X relies only on local inter-robot relative position estimates, that can be obtained by exchanging signal pings from onboard sensors such as WiFi, Ultra-Wide Band, amongst others, to inform the exploration decisions of individual robots to minimize redundant coverage overlaps. Furthermore, WiSER-X also enables asynchronous termination without requiring a shared map between the robots. It also adapts to heterogeneous robot behaviors and even complete failures in unknown environment while ensuring complete coverage. Simulations show that WiSER-X leads to 58% lower overlap than a zero-information-sharing baseline algorithm-1 and only 23% more overlap than a full-information-sharing algorithm baseline algorithm-2. Hardware experiments further validate the feasibility of WiSER-X using full onboard sensing.

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation in the presence of stragglers. In this paper, we consider the distributed computation of a sequence of gradients {g(1),g(2),ldots,g(J)}, where processing of each gradient g(t) starts in round-t and finishes by round-(t+T). Here Tgeq 0 denotes a delay parameter. For the GC scheme, coding is only across computing nodes and this results in a solution where T=0. On the other hand, having T>0 allows for designing schemes which exploit the temporal dimension as well. In this work, we propose two schemes that demonstrate improved performance compared to GC. Our first scheme combines GC with selective repetition of previously unfinished tasks and achieves improved straggler mitigation. In our second scheme, which constitutes our main contribution, we apply GC to a subset of the tasks and repetition for the remainder of the tasks. We then multiplex these two classes of tasks across workers and rounds in an adaptive manner, based on past straggler patterns. Using theoretical analysis, we demonstrate that our second scheme achieves significant reduction in the computational load. In our experiments, we study a practical setting of concurrently training multiple neural networks over an AWS Lambda cluster involving 256 worker nodes, where our framework naturally applies. We demonstrate that the latter scheme can yield a 16\% improvement in runtime over the baseline GC scheme, in the presence of naturally occurring, non-simulated stragglers.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

The convergence of generative large language models (LLMs), edge networks, and multi-agent systems represents a groundbreaking synergy that holds immense promise for future wireless generations, harnessing the power of collective intelligence and paving the way for self-governed networks where intelligent decision-making happens right at the edge. This article puts the stepping-stone for incorporating multi-agent generative artificial intelligence (AI) in wireless networks, and sets the scene for realizing on-device LLMs, where multi-agent LLMs are collaboratively planning and solving tasks to achieve a number of network goals. We further investigate the profound limitations of cloud-based LLMs, and explore multi-agent LLMs from a game theoretic perspective, where agents collaboratively solve tasks in competitive environments. Moreover, we establish the underpinnings for the architecture design of wireless multi-agent generative AI systems at the network level and the agent level, and we identify the wireless technologies that are envisioned to play a key role in enabling on-device LLM. To demonstrate the promising potentials of wireless multi-agent generative AI networks, we highlight the benefits that can be achieved when implementing wireless generative agents in intent-based networking, and we provide a case study to showcase how on-device LLMs can contribute to solving network intents in a collaborative fashion. We finally shed lights on potential challenges and sketch a research roadmap towards realizing the vision of wireless collective intelligence.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

Federated optimization, an emerging paradigm which finds wide real-world applications such as federated learning, enables multiple clients (e.g., edge devices) to collaboratively optimize a global function. The clients do not share their local datasets and typically only share their local gradients. However, the gradient information is not available in many applications of federated optimization, which hence gives rise to the paradigm of federated zeroth-order optimization (ZOO). Existing federated ZOO algorithms suffer from the limitations of query and communication inefficiency, which can be attributed to (a) their reliance on a substantial number of function queries for gradient estimation and (b) the significant disparity between their realized local updates and the intended global updates. To this end, we (a) introduce trajectory-informed gradient surrogates which is able to use the history of function queries during optimization for accurate and query-efficient gradient estimation, and (b) develop the technique of adaptive gradient correction using these gradient surrogates to mitigate the aforementioned disparity. Based on these, we propose the federated zeroth-order optimization using trajectory-informed surrogate gradients (FZooS) algorithm for query- and communication-efficient federated ZOO. Our FZooS achieves theoretical improvements over the existing approaches, which is supported by our real-world experiments such as federated black-box adversarial attack and federated non-differentiable metric optimization.

Neural networks trained with gradient descent often learn solutions of increasing complexity over time, a phenomenon known as simplicity bias. Despite being widely observed across architectures, existing theoretical treatments lack a unifying framework. We present a theoretical framework that explains a simplicity bias arising from saddle-to-saddle learning dynamics for a general class of neural networks, incorporating fully-connected, convolutional, and attention-based architectures. Here, simple means expressible with few hidden units, i.e., hidden neurons, convolutional kernels, or attention heads. Specifically, we show that linear networks learn solutions of increasing rank, ReLU networks learn solutions with an increasing number of kinks, convolutional networks learn solutions with an increasing number of convolutional kernels, and self-attention models learn solutions with an increasing number of attention heads. By analyzing fixed points, invariant manifolds, and dynamics of gradient descent learning, we show that saddle-to-saddle dynamics operates by iteratively evolving near an invariant manifold, approaching a saddle, and switching to another invariant manifold. Our analysis also disentangles data-induced and initialization-induced saddle-to-saddle dynamics. In particular, the former leads to low-rank weights while the latter to sparse weights. Equipped with the theory, we predict the effects of data distribution and weight initialization on the duration and number of plateaus in learning. Overall, our theory offers a framework for understanding when and why gradient descent progressively learns increasingly complex solutions.

This paper studies the measurement scheduling problem for a group of N mobile robots moving on a flat surface that are preforming cooperative localization (CL). We consider a scenario in which due to the limited on-board resources such as battery life and communication bandwidth only a given number of relative measurements per robot are allowed at observation and update stage. Optimal selection of which teammates a robot should take a relative measurement from such that the updated joint localization uncertainty of the team is minimized is an NP-hard problem. In this paper, we propose a suboptimal greedy approach that allows each robot to choose its landmark robots locally in polynomial time. Our method, unlike the known results in the literature, does not assume full-observability of CL algorithm. Moreover, it does not require inter-robot communication at scheduling stage. That is, there is no need for the robots to collaborate to carry out the landmark robot selections. We discuss the application of our method in the context of an state-of-the-art decentralized CL algorithm and demonstrate its effectiveness through numerical simulations. Even though our solution does not come with rigorous performance guarantees, its low computational cost along with no communication requirement makes it an appealing solution for operatins with resource constrained robots.

We introduce ORIGEN, the first zero-shot method for 3D orientation grounding in text-to-image generation across multiple objects and diverse categories. While previous work on spatial grounding in image generation has mainly focused on 2D positioning, it lacks control over 3D orientation. To address this, we propose a reward-guided sampling approach using a pretrained discriminative model for 3D orientation estimation and a one-step text-to-image generative flow model. While gradient-ascent-based optimization is a natural choice for reward-based guidance, it struggles to maintain image realism. Instead, we adopt a sampling-based approach using Langevin dynamics, which extends gradient ascent by simply injecting random noise--requiring just a single additional line of code. Additionally, we introduce adaptive time rescaling based on the reward function to accelerate convergence. Our experiments show that ORIGEN outperforms both training-based and test-time guidance methods across quantitative metrics and user studies.

Graphics processing unit (GPU) architectures are growing in size to meet the increasing compute and memory requirements. As GPU sizes increase, intra-socket wire transfer delay increases significantly. While previous research has optimized for compute and memory locality within a socket, the spatial impact on inter-GPU communication has not been well-studied. We introduce the term non-uniform network access (NUNA) to describe this emerging optimization dimension in multi-GPU systems. We specifically focus on latency-sensitive collective communication, common in machine learning inference. First, we highlight the need for NUNA-aware routing (NAR), choosing optimized, spatially-aware inter-GPU paths in large scale-up network topologies. Second, we introduce NUNA-aware placement (NAP), placing threadblocks and data near I/O to optimize the inter-GPU traffic. We demonstrate that the NAP optimizations alone offer up to 1.5x collective speedups over a locality-unaware baseline. Combining NAP with NAR yields up to 1.8x faster collectives over the locality-unaware baseline. This leads to 7% mean (28% max) time per output token speedup in machine learning inference.

Recently, flat minima are proven to be effective for improving generalization and sharpness-aware minimization (SAM) achieves state-of-the-art performance. Yet the current definition of flatness discussed in SAM and its follow-ups are limited to the zeroth-order flatness (i.e., the worst-case loss within a perturbation radius). We show that the zeroth-order flatness can be insufficient to discriminate minima with low generalization error from those with high generalization error both when there is a single minimum or multiple minima within the given perturbation radius. Thus we present first-order flatness, a stronger measure of flatness focusing on the maximal gradient norm within a perturbation radius which bounds both the maximal eigenvalue of Hessian at local minima and the regularization function of SAM. We also present a novel training procedure named Gradient norm Aware Minimization (GAM) to seek minima with uniformly small curvature across all directions. Experimental results show that GAM improves the generalization of models trained with current optimizers such as SGD and AdamW on various datasets and networks. Furthermore, we show that GAM can help SAM find flatter minima and achieve better generalization.

In this work, we explore an untapped signal in diffusion model inference. While all previous methods generate images independently at inference, we instead ask if samples can be generated collaboratively. We propose Group Diffusion, unlocking the attention mechanism to be shared across images, rather than limited to just the patches within an image. This enables images to be jointly denoised at inference time, learning both intra and inter-image correspondence. We observe a clear scaling effect - larger group sizes yield stronger cross-sample attention and better generation quality. Furthermore, we introduce a qualitative measure to capture this behavior and show that its strength closely correlates with FID. Built on standard diffusion transformers, our GroupDiff achieves up to 32.2% FID improvement on ImageNet-256x256. Our work reveals cross-sample inference as an effective, previously unexplored mechanism for generative modeling.

We introduce and train distributed neural architectures (DNA) in vision and language domains. DNAs are initialized with a proto-architecture that consists of (transformer, MLP, attention, etc.) modules and routers. Any token (or patch) can traverse any series of modules in any order. DNAs are a natural generalization of the sparse methods such as Mixture-of-Experts, Mixture-of-Depths, parameter sharing, etc. Computation and communication patterns of DNA modules are learnt end-to-end during training and depend on the content and context of each token (or patch). These patterns can be shaped by further requirements added to the optimization objective such as compute/memory efficiency or load balancing. We empirically show that (i) trained DNAs are competitive with the dense baselines in both domains and (ii) compute efficiency/parameter sharing can be learnt from data. Next, we analyze the emergent connectivity and computation patterns in the trained DNAs. We find that the paths that tokens take through the models are themselves distributed according to a power-law. We show that some paths (or, equivalently, groups of modules) show emergent specialization. Finally, we demonstrate that models learn to allocate compute and active parameters in an interpretable way.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives.

Deep neural networks are vulnerable to universal adversarial perturbation (UAP), an instance-agnostic perturbation capable of fooling the target model for most samples. Compared to instance-specific adversarial examples, UAP is more challenging as it needs to generalize across various samples and models. In this paper, we examine the serious dilemma of UAP generation methods from a generalization perspective -- the gradient vanishing problem using small-batch stochastic gradient optimization and the local optima problem using large-batch optimization. To address these problems, we propose a simple and effective method called Stochastic Gradient Aggregation (SGA), which alleviates the gradient vanishing and escapes from poor local optima at the same time. Specifically, SGA employs the small-batch training to perform multiple iterations of inner pre-search. Then, all the inner gradients are aggregated as a one-step gradient estimation to enhance the gradient stability and reduce quantization errors. Extensive experiments on the standard ImageNet dataset demonstrate that our method significantly enhances the generalization ability of UAP and outperforms other state-of-the-art methods. The code is available at https://github.com/liuxuannan/Stochastic-Gradient-Aggregation.

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent manifolds of arbitrary topology, we propose to learn a mixture model of variational autoencoders. Here, every encoder-decoder pair represents one chart of a manifold. We propose a loss function for maximum likelihood estimation of the model weights and choose an architecture that provides us the analytical expression of the charts and of their inverses. Once the manifold is learned, we use it for solving inverse problems by minimizing a data fidelity term restricted to the learned manifold. To solve the arising minimization problem we propose a Riemannian gradient descent algorithm on the learned manifold. We demonstrate the performance of our method for low-dimensional toy examples as well as for deblurring and electrical impedance tomography on certain image manifolds.

Large-scale AI model training divides work across thousands of GPUs, then synchronizes gradients across them at each step. This incurs a significant network burden that only centralized, monolithic clusters can support, driving up infrastructure costs and straining power systems. We propose Decentralized Diffusion Models, a scalable framework for distributing diffusion model training across independent clusters or datacenters by eliminating the dependence on a centralized, high-bandwidth networking fabric. Our method trains a set of expert diffusion models over partitions of the dataset, each in full isolation from one another. At inference time, the experts ensemble through a lightweight router. We show that the ensemble collectively optimizes the same objective as a single model trained over the whole dataset. This means we can divide the training burden among a number of "compute islands," lowering infrastructure costs and improving resilience to localized GPU failures. Decentralized diffusion models empower researchers to take advantage of smaller, more cost-effective and more readily available compute like on-demand GPU nodes rather than central integrated systems. We conduct extensive experiments on ImageNet and LAION Aesthetics, showing that decentralized diffusion models FLOP-for-FLOP outperform standard diffusion models. We finally scale our approach to 24 billion parameters, demonstrating that high-quality diffusion models can now be trained with just eight individual GPU nodes in less than a week.

Context-sensitive two-point layer 5 pyramidal cells (L5PCs) were discovered as long ago as 1999. However, the potential of this discovery to provide useful neural computation has yet to be demonstrated. Here we show for the first time how a transformative L5PCs-driven deep neural network (DNN), termed the multisensory cooperative computing (MCC) architecture, can effectively process large amounts of heterogeneous real-world audio-visual (AV) data, using far less energy compared to best available 'point' neuron-driven DNNs. A novel highly-distributed parallel implementation on a Xilinx UltraScale+ MPSoC device estimates energy savings up to 245759 times 50000 muJ (i.e., 62% less than the baseline model in a semi-supervised learning setup) where a single synapse consumes 8e^{-5}muJ. In a supervised learning setup, the energy-saving can potentially reach up to 1250x less (per feedforward transmission) than the baseline model. The significantly reduced neural activity in MCC leads to inherently fast learning and resilience against sudden neural damage. This remarkable performance in pilot experiments demonstrates the embodied neuromorphic intelligence of our proposed cooperative L5PC that receives input from diverse neighbouring neurons as context to amplify the transmission of most salient and relevant information for onward transmission, from overwhelmingly large multimodal information utilised at the early stages of on-chip training. Our proposed approach opens new cross-disciplinary avenues for future on-chip DNN training implementations and posits a radical shift in current neuromorphic computing paradigms.

Spiking neural networks have significant potential utility in robotics due to their high energy efficiency on specialized hardware, but proof-of-concept implementations have not yet typically achieved competitive performance or capability with conventional approaches. In this paper, we tackle one of the key practical challenges of scalability by introducing a novel modular ensemble network approach, where compact, localized spiking networks each learn and are solely responsible for recognizing places in a local region of the environment only. This modular approach creates a highly scalable system. However, it comes with a high-performance cost where a lack of global regularization at deployment time leads to hyperactive neurons that erroneously respond to places outside their learned region. Our second contribution introduces a regularization approach that detects and removes these problematic hyperactive neurons during the initial environmental learning phase. We evaluate this new scalable modular system on benchmark localization datasets Nordland and Oxford RobotCar, with comparisons to standard techniques NetVLAD, DenseVLAD, and SAD, and a previous spiking neural network system. Our system substantially outperforms the previous SNN system on its small dataset, but also maintains performance on 27 times larger benchmark datasets where the operation of the previous system is computationally infeasible, and performs competitively with the conventional localization systems.

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and improve them by replacing their conversion of neural features into group representations, with an optimization whose loss intuitively measures the distance between group orbits. This change makes our approach applicable to a broader range of matrix groups, such as the Lorentz group O(1, 3), than these two proposals. We experimentally show our method's competitiveness on the SO(2) image classification task, and also its increased generality on the task with O(1, 3). Our implementation will be made accessible at https://github.com/tiendatnguyen-vision/Orbit-symmetrize.