In particular, interpreting Random Forests (RFs) [2] and its variants [14, 28, 27, 29, 1, 12] has become an important area of research due to the wide ranging applications of RFs invarious scientific areas, such asgenome-wide association studies (GWAS)[7],gene expression microarray[13,23],andgeneregulatorynetworks[9].

SNR = 10 log10 2 Figure 1: AWGNchannelwithnoisyfeedback (left). Figure 5: Noiseinfirstphasevs. firstparitybit (left) andsecondparitybit (right).

Inductive biases encoding known data symmetries are key to make deep learning models generalize in high-dimensional settings such as computer vision, speech processing and computational neuroscience, just to name a few.

Using a single projection vector, we then project these individual sub-tokens onto a one-dimensional subspace. Importantly, we notice that we can initialize this projection vector cheaply using first-order batch statistics andthen keepitfixedthroughout training. Wethen reconstruct the original tokens using the same vector during the backward pass.

Seide 23] and 25] were reduce accumulation.

Thislinkbetween the two kernels, along with DPP machinery, leads to relatively tight bounds on the quadrature error,that depends onthespectrum oftheRKHS kernel.

Proof of Lemma 5. Suppose M is a matrix then we can write M = UV