Figure 1 shows screenshots from our online psychophysical critical band masking experiment. Accuracy heatmaps computed for different observers in our experiment showed little individual difference (Figure 1) and an even smaller difference in terms of threshold noise SD for 50% accuracy. Table 1 shows the value of each channel property computed from Gaussian fits to the averaged human data versus those found by summarizing Gaussian fits to individual human data. Given that they are similar for all channel properties, we use the former for all reported human data in the main paper. Our existing method for computing thresholds and fitting the Gaussian function to them is difficult to apply to observers that have very high noise sensitivity (low efficiency) since it relies on good performance for the baseline (zero-noise) condition.

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel") that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise.

Combination therapy refers to the use of multiple treatments - such as surgery, medication, and behavioral therapy - to cure a single disease, and has become a cornerstone for treating various conditions including cancer, HIV, and depression. All possible combinations of treatments lead to a collection of treatment regimens (i.e., policies) with mixed scopes, or what physicians could observe and which actions they should take depending on the context. In this paper, we investigate the online reinforcement learning setting for optimizing the policy space with mixed scopes. In particular, we develop novel online algorithms that achieve sublinear regret compared to an optimal agent deployed in the environment. The regret bound has a dependency on the maximal cardinality of the induced state-action space associated with mixed scopes. We further introduce a canonical representation for an arbitrary subset of interventional distributions given a causal diagram, which leads to a non-trivial, minimal representation of the model parameters.

Inference Suppose S: X R is a continuous set function w.r.t Hausdorff distance dH(,).

Y-axis: Cross Entropy Loss on validation set. Figure 1 shows the validation loss changes with respect to training time for 50k steps as supplementary results for the experiments in Section 5. In general, Skyformer converges faster and finishes 50k steps earlier than vanilla Attention and Kernelized Attention over all tasks. We further remark that on Text Classification, all models quickly fall into over-fitting, and thus the validation losses rise quickly. On Pathfinder, due to the difficulty of training, in the trial shown in the figure vanilla Attention fails to reach the best long-time limit under a certain setting. Figure 2 shows the singular value distribution of attention output from the second layer of a trained vanilla transformer.