The observation of WikiHow is represented in exactly the same way with Zhang et al. [2023]. Table 1: Patterns of WebShop pages Pattern Description search The page to search for an item itemlisting The page listing the search results item The information page of a specific item others The item description page, item feature page, and review pageThe similarity lookup table is defined in Table 2. 1 Table 2: Lookup table of the page similarity of WebShop search itemlisting item others search 1 0 0 0 itemlisting 0 1 0 0 item 0 0 1 0.3 others 0 0 0.3 1 2.2 Lookup table of the instruction similarity function of WikiHow Table 3. Table 3: Patterns of WikiHow instructions Pattern Name Pattern Template search Search an article to learn . . . Owing to the limit of budgets, a subset of only 20 tasks is sampled from the full test set. The visualization is available in Figure 2. It can be seen that the performance of R However, there seems to be a saturation for the performance, which may be attributed to the limited number of the active exemplars and training tasks. The saturation of the average reward comes later than that of the success rate. Double Q-Learning [van Hasselt, 2010] is usually leveraged to ameliorate over-estimation for lookup-based Q-Learning.

The determination of sample size in qualitative research has traditionally relied on the subjective and often ambiguous principle of data saturation, which can lead to inconsistencies and threaten methodological rigor. This study introduces a new, systematic model based on machine learning (ML) to make this process more objective. Utilizing a dataset derived from five fundamental qualitative research approaches - namely, Case Study, Grounded Theory, Phenomenology, Narrative Research, and Ethnographic Research - we developed an ensemble learning model. Ten critical parameters, including research scope, information power, and researcher competence, were evaluated using an ordinal scale and used as input features. After thorough preprocessing and outlier removal, multiple ML algorithms were trained and compared. The K-Nearest Neighbors (KNN), Gradient Boosting (GB), Random Forest (RF), XGBoost, and Decision Tree (DT) algorithms showed the highest explanatory power (Test R2 ~ 0.85), effectively modeling the complex, non-linear relationships involved in qualitative sampling decisions. Feature importance analysis confirmed the vital roles of research design type and information power, providing quantitative validation of key theoretical assumptions in qualitative methodology. The study concludes by proposing a conceptual framework for a web-based computational application designed to serve as a decision support system for qualitative researchers, journal reviewers, and thesis advisors. This model represents a significant step toward standardizing sample size justification, enhancing transparency, and strengthening the epistemological foundation of qualitative inquiry through evidence-based, systematic decision-making.

Structured pruning removes entire neurons or channels, but its effectiveness depends on how importance is distributed across the representation space. Change-of-basis (CoB) pruning addresses this challenge by applying orthogonal linear transformations that concentrate importance within certain dimensions. However, many standard deep learning architectures are not inherently invariant to such transformations. To enable compatibility, we introduce two-subspace radial activations (TSRAs): an activation family that is invariant to orthogonal linear transformations applied independently within its two activation subspaces. This invariance allows CoB transformations to be merged into surrounding weights without incurring extra parameters. We position this work as a proof-of-concept that a rotationally invariant design may offer a principled approach towards change-of-basis pruning. We do not provide an analysis of multiple TSRA candidates nor do we explore weight initialization for any TSRAs. These limitations, combined with other necessary modifications we make to permit rotational invariance, result in a slight accuracy drop of $4.52\%$ compared to a ReLU-based control. However, using activation-magnitude importance, VGG-16 implementing our CoB+TSRA framework shows encouraging results on CIFAR-10. Under fixed-ratio structured pruning, CoB improves accuracy over a TSRA baseline at all pruning ratios and extends reliable pruning frontier from roughly $30\%$ to $70\%$ of parameters without post-prune fine tuning. Under threshold-based pruning strategies, CoB prunes $90-96\%$ of parameters while maintaining $1-6\%$ accuracy drop after fine-tuning. Together, these results indicate that rotationally invariant architectures may offer a promising path towards CoB pruning.

Note that this safe RL problem is less general than the standard formulation of safe RL. The authors introduce a teacher-student hierarchy. To learn the teacher's policy the following constraints are followed: a1 The unsafe set is contained in the intervention set D D The teacher learns when to intervene and to switch between different interventions. A1.2 RL with probability one constraints We have introduced the safety state to the environment as follows: s First, we discuss our design for the PI controller and discuss the necessary parts for it. The proportional part delivers brute force control by having a large control magnitude for large errors, but it is not effective if the instantaneous error values become small.

We thank all the reviewers for their time and comments. Our work builds directly on GLUE and maintains the same general structure. Our benchmark does have a less uniform API than GLUE, but we view this as both a pro and a con. WSC is a coreference task but is designed to require commonsense reasoning to solve. COP A explicitly tests systems' causal reasoning ability (somewhat related to commonsense reasoning).

Figure 2: (a) Real data covers five modes (1-5) and the generated data is expanded, one mode at a time, to cover the real modes (1-5) and five extraneous modes (6-10). Both metrics were evaluated using 20k real and generated samples. We thank the reviewers for their comments and remarks, and will gladly implement the suggested clarifications. Finally, Figure 1c shows that our metric behaves similarly to FID as the number of samples increases. Furthermore, we thank the reviewer for bringing [2] to our attention, and will cite it as parallel work.

Batch Normalization is commonly located in front of activation functions, as proposed by the original paper.