We show that GWG exhibits strong convergence guarantees.

We use decision trees to convey this reasoning information, as they can be easily represented in natural language, effectively providing knowledge from prior experiments ( i.e., the impact of the generated features on performance) to

Points were sampled uniformly in the bands denoted by dashed lines. We posit that these barriers are due, at least in part, to the sensitivity of decision trees to transformations of the input resulting from greedy construction and simple decision rules. Of these, key limitation is the latter; even if we replace greedy construction with a perfect tree learner, simple distributions can nonetheless require an arbitrarily large axis-aligned tree to fit.

By analyzing the loss landscape of a single Transformer layer using Softmax and Gaussian attention kernels, our work provides concrete answers to these questions.

From the three-points identity of the Bregman divergence (Lemma 3.1 of [9]), KL (x y) KL ( x y) = KL (x x) + ln x ln y,x x (12) The first term in (12) can be bounded by KL (x x) = By the Hölder's inequality, the second term in (12) is bounded as ln x ln y,x x ln x ln y Lemma 5. Consider a block diagonal matrix We prove the lemma via induction on N . This completes the induction proof.Lemma 6. We introduce one more notation before presenting the proof. This leads us to the initialization-dependent convergence rate of Algorithm 1, which we re-state and prove as follows. In addition, if we initialize the players' policies to be uniform policies, i.e., The rest of the proof follows by putting all the aforementioned results together.

We further provide numerical simulations to corroborate our theoretical findings.

This bias becomes particularly noticeable when the study's endpoint can be inferred from the