Our most powerful artificial agents cannot be told exactly what to do, especially in complex planning environments. They almost exclusively rely on neural networks to perform their tasks, but neural networks cannot easily be told to obey certain rules or adhere to existing background knowledge. While such uncontrolled behaviour might be nothing more than a simple annoyance next time you ask an LLM to generate a schedule for reaching a deadline in two days and it starts to hallucinate that days have 48 hours instead of 24, it can be much more impactful when that same LLM is controlling an agent responsible for navigating a warehouse filled with TNT and it decides to go just a little too close to the storage compartments. Luckily, controlling neural networks has gained a lot of attention over the last years through the development of . Neurosymbolic AI, or NeSy for short, aims to combine the learning abilities of neural networks with the guarantees that symbolic methods based on automated mathematical reasoning offer.

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Deep neural networks, and in particular recurrent networks, are promising candidates to control autonomous agents that interact in real-time with the physical world. However, this requires a seamless integration of temporal features into the network's architecture. For the training of and inference with recurrent neural networks, they are usually rolled out over time, and different rollouts exist.

In this work, we introduce interactive structure learning, a framework that unifies many different interactive learning tasks. We present a generalization of the query-by-committee active learning algorithm for this setting, and we study its consistency and rate of convergence, both theoretically and empirically, with and without noise.

In order to help clarify our contributions and or-2 ganize them for readers, we provide the following table to summarize the differences between regrets.3 REVIEWER 4 Thank you for your comments. Concept drift occurs when the optimal model attimetmay no longer bethe optimal model10 at timet+1. Consider an online learning problem with concept drift withT = 3 time periods and loss functions:11 f1(x) = (x 1)2,f2(x) = (x 2)2,f3(x) = (x 3)2. Figure 1: SGD online with momentum Theoretical motivation via Calibration: A more formal motivation of our regret23 can be related to the concept of calibration [1]. The comment on line 110 can be24 rewritten as: If the updates{x1,,xT} are well-calibrated, then perturbingxt by25 anyucannot substantially reduce the cumulative loss.Hence, itcan besaid that the26 sequence {x1,,xT} is asymptotically calibrated with respect to{f1,,fT} if:27 Weindeedranexperiments usingSGDwithmomentum forvariousdecayparameters andconcluded thatSGDwith36 momentum is not even as stable as SGD-online (standard SGD without momentum) as shown in Figure 1.

We perform a wide variety of experiments and demonstrate that OST outperforms the existing algorithms in the low-shot scenario. On most datasets the method also presents a comparable accuracy with a single training example to the accuracy obtained by the other methods for the entire set of domainA images.

Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range bounded in $[0,1]$, the generalization error of $\gamma$-uniformly stable learning algorithm on $n$ samples is known to be at most $O((\gamma +1/n) \sqrt{n \log(1/\delta)})$ with probability at least $1-\delta$. Unfortunately, this bound does not lead to meaningful generalization bounds in many common settings where $\gamma \geq 1/\sqrt{n}$. At the same time the bound is known to be tight only when $\gamma = O(1/n)$. Here we prove substantially stronger generalization bounds for uniformly stable algorithms without any additional assumptions. First, we show that the generalization error in this setting is at most $O(\sqrt{(\gamma + 1/n) \log(1/\delta)})$ with probability at least $1-\delta$. In addition, we prove a tight bound of $O(\gamma^2 + 1/n)$ on the second moment of the generalization error. The best previous bound on the second moment of the generalization error is $O(\gamma + 1/n)$. Our proofs are based on new analysis techniques and our results imply substantially stronger generalization guarantees for several well-studied algorithms.

For decades, handmade narco subs have been some of the cocaine trade's most elusive and productive workhorses, ferrying multi-ton loads of illicit drugs from Colombian estuaries toward markets in North America and, increasingly, the rest of the world. Now off-the-shelf technology--Starlink terminals, plug-and-play nautical autopilots, high-resolution video cameras--may be advancing that cat-and-mouse game into a new phase. Uncrewed subs could move more cocaine over longer distances, and they wouldn't put human smugglers at risk of capture. And law enforcement around the world is just beginning to grapple with what this means for the future. This story is from the next print issue of magazine, which is all about crime. Google DeepMind is calling for the moral behavior of large language models--such as what they do when called on to act as companions, therapists, medical advisors, and so on--to be scrutinized with the same kind of rigor as their ability to code or do math.