Table 1: Payoff matrix of the one-step multi-state non-monotonic cooperative matrix game and reconstructed resultsfromcorresponding baselines.

It allows for both latent confounders and selection variables, although inthis paper we assume the absence of selection variables.

Notethattheaccuracyof δl 1 isnotmeasureddirectlyforReLU because it does not have an explicit inversion. This precludes stability forα = 0 and dl > dl 1 (expanding layer), as the matrix productWlBl will be singular. Forexample,inthenonlinearregression experiment shown in the main text, we initialize the SLDI feedback asB = B1B2, whereB1 and B2 are the feedback matrices for sequential DI. Once again, when the controller has no leak, this will produce the same steady state assequential dynamicinversion. We study a simple case here as an illustration, and leave a more thorough analysis for futurework.

Based onLemma 5.1anditsproof, weknownthatthePMP oftheauxiliary control system, (S.2), is exactly the differential PMP equations (13). Thus below, we only look at the differential PMP equationsin(S.2). In the system identification experiment, we collect a total number of five trajectories from systems (in Table 2) with dynamics known, wherein different trajectoriesξo = {xo0:T,u0:T 1}havedifferent initial conditionsx0 andhorizonsT (T ranges from10to20),with randominputsu0:T 1 drawnfromuniformdistribution. In fact, throughout the entire learning process, PDP always guarantees that the policyconstraint isperfectly respected (as the forward pass strictly follows the policy). Please seeAppendix Fig. S4for validation.

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to neural dynamical systems that encompass modern large-scale diffusion and flow matching models. Despite the scalability of training, the generation of high-quality samples and their corresponding likelihood under the model requires expensive numerical simulation -- inhibiting adoption in numerous scientific applications such as equilibrium sampling of molecular systems. In this paper, we revisit classical normalizing flows as one-step generative models with exact likelihoods and propose a novel, scalable training objective that does not require computing the expensive change of variable formula used in conventional maximum likelihood training. We propose Forward-Only Regression Training (FORT), a simple $\ell_2$-regression objective that maps prior samples under our flow to specifically chosen targets. We demonstrate that FORT supports a wide class of targets, such as optimal transport targets and targets from pre-trained continuous-time normalizing flows (CNF). We further demonstrate that by using CNF targets, our one-step flows allow for larger-scale training that exceeds the performance and stability of maximum likelihood training, while unlocking a broader class of architectures that were previously challenging to train. Empirically, we elucidate that our trained flows can perform equilibrium conformation sampling in Cartesian coordinates of alanine dipeptide, alanine tripeptide, and alanine tetrapeptide.

Consider a team of three guards (in green) trying to defend a fort from a team of three attackers (in red) in Figure 1. In this "Fort Attack" (FA) domain, each agent can move in one of four cardinal directions with a particular velocity, rotate clockwise or anticlockwise, shoot at an opponent within a given range, or do nothing. Each agent may have partial or full knowledge of the state of the world (e.g., location, status of each agent) at each step, but it has no prior experience of working with the other agents. Also, each agent may have limited (or no) ability to communicate with others. An episode ends when all members of a team are eliminated, an attacker reaches the fort, or the guards protect the fort for a sufficient time period.

We present an architecture for ad hoc teamwork, which refers to collaboration in a team of agents without prior coordination. State of the art methods for this problem often include a data-driven component that uses a long history of prior observations to model the behaviour of other agents (or agent types) and to determine the ad hoc agent's behaviour. In many practical domains, it is challenging to find large training datasets, and necessary to understand and incrementally extend the existing models to account for changes in team composition or domain attributes. Our architecture combines the principles of knowledge-based and data-driven reasoning and learning. Specifically, we enable an ad hoc agent to perform non-monotonic logical reasoning with prior commonsense domain knowledge and incrementally-updated simple predictive models of other agents' behaviour. We use the benchmark simulated multi-agent collaboration domain Fort Attack to demonstrate that our architecture supports adaptation to unforeseen changes, incremental learning and revision of models of other agents' behaviour from limited samples, transparency in the ad hoc agent's decision making, and better performance than a data-driven baseline.

Facebook recently added a new report to its transparency center. The "widely viewed content" report was ostensibly meant to shed light on what's been a long-running debate: What is the most popular content on Facebook? The 20-page report raised more questions than answers. For example, it showed that the most viewed URL was a seemingly obscure website associated with former Green Bay Packers players. It boasted nearly 90 million views even though its official Facebook page has just a few thousand followers.

In addition to new outfits and backpacks, face masks are now an essential addition to kids' back-to-school gear. According to new guidelines released by the Centers for Disease Control and Prevention, all students and staff should wear masks inside schools, regardless of vaccination status. But kids used to virtual learning may not have much experience interacting or communicating with their peers or teachers while masked. And parents and child development experts alike are wondering how that will affect children as they return to school. For instance, to assess whether kids can accurately interpret a masked person's emotions, researchers from the University of Wisconsin-Madison's Child Emotion Lab showed children ages seven to 13 pictures of people displaying different emotions.

Connect, download a free E-Book, watch a keynote, or browse my blog. In the early days of life on Earth, biological organisms were exceedingly simple. They were microscopic unicellular creatures with little to no ability to coordinate – a little like me still to be frank, especially after I've been travelling. Yet billions of years of evolution through competition and natural selection led to the complex life forms we have today – as well as complex human intelligence. Researchers at OpenAI, the San Francisco based for-profit AI research lab, are now testing a hypothesis – if you could mimic that kind of competition in a virtual world, would it also give rise to much more sophisticated artificial intelligence?