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版本更新 · v2arXiv:2605.10613

Exact Fixed-Point Constraints in Neural-ODEs: Injecting Prior Knowledge into the Network Parameters

Feliciano Giuseppe Pacifico, Duccio Fanelli, Lorenzo Buffoni, Lorenzo Chicchi, Diego Febbe, Raffaele Marino

原文摘要

Neural ordinary differential equations (Neural-ODEs) learn a velocity field from data. Often, however, additional information on the target field is available, such as the location of some of its equilibria or, more generally, its values at given points. We introduce a method to inject this information directly into the parameters of a Neural-ODE, so that a finite set of prescribed fixed points holds exactly throughout training, with no penalty terms and no post-hoc projection. The output matrix is parametrized through the Moore-Penrose pseudoinverse, implemented by a thin QR factorization of the hidden features at the prescribed points. This splits the output matrix into a component determined by the constraints and a free one, which shapes the field away from the prescribed points without altering its values there. As a result, the constrained Neural-ODE remains a universal approximator of the continuous vector fields compatible with the constraints. We test the method on a two-dimensional Lotka-Volterra competition model with four equilibria. In vector field regression, the constrained model keeps the fixed-point residual at single-precision round-off, and its test error is up to about five times lower than that of an unconstrained network of the same architecture. A soft penalty on the equilibria lowers the residual only at the cost of accuracy, and still leaves it at least an order of magnitude above that of the constrained model. Trained to convergence on datasets of increasing size, the unconstrained and penalized networks saturate already on small datasets, while the constrained model keeps improving over a wider range. Close to the equilibria and over long time horizons, the constrained model is the most accurate at every dataset size considered. This also holds when the models are trained on observed trajectories, by backpropagation through the ODE solver.

cond-mat.dis-nn · cs.LG · physics.bio-ph

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2610.25113

A learner-free swarm approximates the explore-exploit equilibrium allocation: A self-organized attractor in place of reinforcement-learning machinery

Galen J. Wilkerson

原文摘要

Reinforcement learning (RL) solves the explore-exploit problem by training a learner on reward; its multi-agent, resource-sharing form has an equilibrium allocation as its optimum -- the ideal-free distribution (IFD), the Nash equilibrium of a congestion game. We show a minimal swarm approximates it with no learner at all. We present a decentralized, learner-free method for this problem: agents explore by heavy-tailed (Levy) flights, recruit neighbours to a discovery through a degree-normalized threshold cascade, and disperse as a patch crowds. The method drives the collective to the shape of the equilibrium allocation (pooled spatial matching slope 1.14, R^2=0.61) with no training, no stored parameters, and no reward in its dynamics; it reaches this as a self-organized attractor and holds it, re-finding it when the resources move -- though it reaches the shape, not the exact equilibrium, and stays measurably exploitable (Nash-gap 1.46). Coupling recruitment to movement causes the allocation: removing it collapses the matching (slope 0.006). Against Proximal Policy Optimization (PPO) learners (feedforward, centralized-critic, graph message-passing, and recurrent) trained in the same sensing-limited environment, the method at zero training is the only arm left unbiased w.r.t. the IFD gradient (slope ~1, CI containing 1, vs learners 0.69-0.97, all under-concentrating) and ties the best learner's harvest where resource is clustered, while the learner collects more where resource is scarce (0.33 vs 0.22) and holds a tighter per-capita intake. Learning buys precision and transfer across reward structures, not a better allocation shape. A companion paper develops the mechanism.

cs.LG · cs.AI · cs.SI · math-ph · nlin.AO · physics.bio-ph

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arXiv ↗PDF ↗
版本更新 · v2arXiv:1303.7276

The effect of limb kinematics on the speed of a legged robot on granular media

Chen Li, Paul B. Umbanhowar, Haldun Komsuoglu, Daniel I. Goldman

原文摘要

Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb-ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters minimize body acceleration and limb interference, and utilize solidification features of granular media.

physics.bio-ph · cond-mat.soft · cs.RO · physics.flu-dyn · q-bio.QM

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.08314

从少量轨迹中学习集体运动的可解释多体相互作用规律

Interpretable many-body interaction laws for collective motion from few trajectories

Timon S. Gutleb

AI 速读 基于摘要

作者提出dACE（方向性原子团簇展开），将原子团簇展开迁移到自驱动个体上，用少量轨迹把加速度分解为1体、2体、3体及更高阶的可解释相互作用项。

cs.LG · physics.bio-ph · q-bio.QM

arXiv ↗PDF ↗
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Models of collective motion usually reduce social interactions to pairwise forces, despite empirical evidence for many-body effects. We introduce the directional atomic cluster expansion (dACE), which adapts the atomic cluster expansion (ACE) of interatomic potentials to self-propelled agents. dACE provides a systematically improvable, exactly equivariant expansion of an agent's acceleration that splits uniquely into 1-, 2-, 3-body and higher contributions, along with a self term for the agent's own past motion that is fitted so that it does not absorb the interactions. On simulated collectives in two and three dimensions with known rules, dACE recovers the interaction law body order by body order from little data, while the neural model SocialNet, the current closest competitor, needs more data, has much larger errors on many-body or chiral rules and is restricted to 2D. On real data sets of tracked zebrafish and golden shiners, the laws learned by dACE agree better between disjoint halves of the data than SocialNet's. The learned laws are interpretable, and in the shiners the 3-body term opposes the pairwise response as neighbourhoods get dense. Finally, we show that next-step prediction accuracy mostly measures self-propulsion and noise rather than the interactions, and suggest more robust combinations of error measures for interaction learning.

新论文 · v1arXiv:2611.06122

Ab Initio Accuracy Beyond the Cutoff: Distributed Message-Passing Equivariant Attention at Tens-of-Millions-of-Atom Scale

Allex Kan, Ji Zhang, Hao Yin, Hao Li, Owen Fu, Xunxing Chen, Lin Huang, Zion Wang 等 13 位作者

原文摘要

Molecular dynamics predicts molecular motion from atomic forces and trajectory integration. Density functional theory (DFT) provides first-principles forces, but its $O(N^3)$ cost limits simulations to thousands of atoms; empirical force fields scale to millions but miss bond breaking and charge transfer. Equivariant message-passing Transformers learn the ab initio potential at linear cost. Stacked layers propagate information beyond a single cutoff, giving four layers a receptive field up to 23Å. At this frontier, scale is limited by communication: layers exchange boundary features across devices, force backpropagation repeats the exchange, and moving atoms change neighbor graphs and tensor shapes. We present Tessera, a distributed runtime that fixes workload shapes between rebuilds. It sorts atoms along a space-filling curve into equal-count shards, ensuring identical atom counts and tensor shapes per rank. Peer sets scale as $K^{0.5}$, not $K$. A conservative neighbor skin preserves topology across updates, enabling each rebuild interval to replay as one CUDA Graph. Fused kernels, three-level neighbor search, and overlapped All-to-All complete it. On 512 GPUs, Tessera sustains 30.7M atoms at 89.7% weak-scaling efficiency (77--90% across three per-GPU loads); per-step time rises 1.11--1.29x as machine and problem grow 16x. Graph reuse cuts full-step time $1.87\times$. Across an $8\times$ device increase, neighbor-search cost grows $1.7\times$, versus $3.0\times$ for Morton order. In a live $10.24$M-atom salt solution, NVE energy drift is $0.42\,μ$eV/atom/ps over $10$ ps, and structure matches a serial reference. A 10.06M-atom Norovirus capsid sustains 100 ps of NVT at $\approx 8$ ps/day on 256 A100 GPUs. Over 200,000 steps, it has no broken bonds or anomalously close pairs and uses three compiled variants, with no graph breaks or eager fallbacks.

cs.DC · cs.AI · physics.bio-ph

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2610.24865

A self-organizing mechanism for collective foraging: recruitment cascades couple Levy search to a clustered maximum-entropy resource field

Galen J. Wilkerson

原文摘要

Foraging recruitment is modeled as a contagion: an agent that finds a resource triggers a linear-threshold cascade on the group's communication network. Because activation is degree-normalized, crowding shuts the cascade off, so the swarm aggregates on a resource and then disperses to explore again. Acting on the cascade moves agents in space, and that motion rewires the network, so recruitment and exploration are one coupled process; removing this coupling alone abolishes the self-limitation. Recruitment spreads only within a connectivity window, bounded below by percolation onset and above by degree-blocking. The swarm self-organizes to the near-critical edge of this window -- self-organized quasi-criticality: recruitment sits near but below the critical point without settling onto a clean, size-invariant critical state, and the activity spectrum has a finite correlation time (Lorentzian-like, not 1/f), consistent with local rather than global criticality. Recruitment raises harvest up to 2.7x over solitary search on sparse, clustered resource fields and loses (down to 0.37x) on abundant or uniform ones; because resources generically aggregate, the favourable regime is the common one. The empirically motivated Levy search and the resource field it exploits are both least-committal: the search a maximum-caliber walk, and the field a maximum-entropy point process whose generic, aggregation-set sign is clustered (attractive). The search exponent that maximizes harvest tracks the field's fractal dimension (a heavier-tailed, more ballistic search for more strongly clustered fields). These are one coupled mechanism: heavy-tailed Levy exploration crosses the field's sparse voids while recruitment cascades exploit its clusters, so one maximum-entropy geometry binds exploration and recruitment into a single self-organizing cycle.

physics.soc-ph · cs.DC · cs.SI · math-ph · physics.bio-ph

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arXiv ↗PDF ↗
新论文 · v1arXiv:2611.02564

Central pivot point control of a body-attached spring-mass runner: periodic gaits, stabilization, template embedding and approximate analytic return maps

İzel Sever, O. Kaan Karagöz, M. Mert Ankaralı

原文摘要

The spring-loaded inverted pendulum (SLIP) describes the center-of-mass (COM) motion of runners but has no trunk. In trunk models, the hip torque couples posture and COM motion and destroys the central-force structure on which SLIP analysis relies. As a result, trunk models have been studied almost only numerically. We show that this structure can be restored. The central pivot point (CPP), a hip-torque law that directs the ground reaction force through the COM, decouples pitch exactly and reduces stance to a planar central-force problem. At upright posture, time-reversal symmetry produces one-parameter families of periodic gaits. A stance-phase pitch law and a stride-level regulator stabilize all computed gaits, also with bounded hip torque and friction. Under CPP, any radial force law in virtual-leg coordinates can be embedded independently of posture. For a linear radial template, the stance radius and the constant-momentum sweep have exact closed forms. With a new gravity correction, the resulting analytic return map, to our knowledge the first for a trunk model, predicts liftoff velocity and apex position with mean errors of 1.6% and 0.9%. The natural gaits of the embedded runner are symmetric and need no force step at touchdown. A near-reversibility argument explains their unit multiplier, and a scalar equation predicts them within 0.8%. A deadbeat stride controller based on the analytic map tracks changes of speed, height and posture. CPP thus makes trunk models accessible to the analytic tools developed for SLIP.

cs.RO · eess.SY · math.DS · physics.bio-ph

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arXiv ↗PDF ↗