9 problems

Effective Lipschitz concentration. The effective Lipschitz constant satisfies $\Lambda_{\mathrm{eff}}\ll\Lambda(W)$, specifically $\Lambda_{\mathrm{eff}}=O(\mathrm{poly}(H))$, whil…

A verifiable task is one in which a judge model can enforce the legality of player moves and score their plausibility, thereby providing a continuous reward signal for search optim…

Let $(X_t)_{t\in\mathbb{Z}}$ be a stationary stochastic process on a finite alphabet $\mathcal{A}$. Write $H(X_1^n)=H(X_1,\ldots,X_n)$ for its block entropy and let $h$ be its Shan…

A probability vector is sparsified by solving an $\ell_0$-regularized separable Bregman projection problem over the simplex; the resulting primitive admits exact and efficient opti…

Let $(\mathbb{R}^N)^n$ be the phase space associated with a language-model geometrization, and let … be a differentiable extension of the language-model entropy function. The entro…

Let $\mathcal{W}$ be the vocabulary, let $\mathcal{S}_n=\mathcal{W}^n$ be the finite set of sentences of length $n$, and let a geometrization consist of an embedding…

Let $\mathcal{S}$ be the set of sentences, let $\mathscr{L}$ be a causal language model, and let … be its entropy function. The AGI finite-determination conjecture. If a causal lan…

Let $\mathcal{S}$ be the set of sentences, let $\mathscr{L}$ be a causal language model, and let … map each sentence to its output-probability distribution, where…

A language model has a key-value-query structure associated with its attention mechanism. Key-value-query approximation conjecture. The key-value-query structure in language models…