The variables of the low-level model (left) are divided into partitions (center) such that each low-level partition corresponds to a high level variable from the high-level model (right). The circles represent variables and the arrows represent causal dependencies. Blue circles are variables that are not being intervened on and red circles are variables that are being intervened on. Observe that a low-level causal dependence between partitions does not necessarily result in a high-level causal dependence between variables and that not every low-level intervention results in a high level intervention.

Define an agent's current state information as s = (x,y,θ,vx,vy), which includes the x,y positions in the coordinate space, and the yaw angle θ, and the velocities in the X and Y directions. The inverse kinematics can be used to calculate the actions for behavior cloning purpose. With the Bicycle action space, we propose a model to approximate the vehicle dynamics with the goal of minimizing the discrepancy between the predicted vehicle states and the recorded vehicle states. More specifically, define the vehicle's coordinates as x,y in the global coordinate system, and the predicted coordinates as ˆx,ˆy, the goal is to minimize (x ˆx)2 + (y ˆy)2. Define the current vehicle's state information as s, which includes the coordinates of the vehicle in the global coordinate system (x,y), the vehicle's yaw angle θ, the vehicle's speed in the x and y direction vx,vy.

We demonstrate our framework's utility by proving and methods that are guaranteed to be defended against deception, given bounded sistent conclusions about performance. Our framework enables us to prove EHPO put forth a logical framework to capture its semantics and how it can lead to inconrigorous. We call this process epistemic hyperparameter optimization (EHPO), and deception, the process of drawing conclusions from HPO should be made more provide a theoretical complement to this prior work, arguing that, to avoid such the opposite. In short, the way we choose hyperparameters can deceive us. We yield the conclusion that J outperforms K, whereas searching another can entail research.

Finite-context models (FCMs) are widely used for compressing symbolic sequences such as DNA, where predictive performance depends critically on the context length k and smoothing parameter α. In practice, these hyperparameters are typically selected through exhaustive search, which is computationally expensive and scales poorly with model complexity. This paper proposes a statistically grounded two-step sequential approach for efficient hyperparameter selection in FCMs. The key idea is to decompose the joint optimization problem into two independent stages. First, the context length k is estimated using categorical serial dependence measures, including Cramér's ν, Cohen's \k{appa} and partial mutual information (pami). Second, the smoothing parameter α is estimated via maximum likelihood conditional on the selected context length k. Simulation experiments were conducted on synthetic symbolic sequences generated by FCMs across multiple (k, α) configurations, considering a four-letter alphabet and different sample sizes. Results show that the dependence measures are substantially more sensitive to variations in k than in α, supporting the sequential estimation strategy. As expected, the accuracy of the hyperparameter estimation improves with increasing sample size. Furthermore, the proposed method achieves compression performance comparable to exhaustive grid search in terms of average bitrate (bits per symbol), while substantially reducing computational cost. Overall, the results on simulated data show that the proposed sequential approach is a practical and computationally efficient alternative to exhaustive hyperparameter tuning in FCMs.

Neural Information Processing Systems http://nips.cc/

Figure 2: These two graphs cannot be distinguished by 1-WL-test. The COMBINE step takes the result of AGGREGATE and the previous representation of current node asinput. Wereduce theFFN inner-layer dimension of4din [47] tod, which does not appreciably hurt the performance but significantly save the parameters. The embedding dropout ratio is set to 0.1 by default in many previous Transformer works[11,34]. The rest of hyper-parameters remain unchanged. Table 8 summarizes the hyper-parameters used for fine-tuning Graphormer on OGBGMolPCBA.