Consider a Bayesian agent attempting to discover a pattern in the world. Upon observing initial data d0d_{0}, they form a posterior distribution p(h|d0)p(h|d_{0}) and sample a hypothesis h∗h^{*} from this distribution. They then interact with a chatbot, sharing their belief h∗h^{*} in the hopes of obtaining further evidence. An unbiased chatbot would ignore h∗h^{*} and generate subsequent data from the true data-generating process, d1∼p(d|true process)d_{1}\sim p(d|\text{true process}). The Bayesian agent then updates their belief via p(h|d0,d1)∝p(d1|h)p(h|d0)p(h|d_{0},d_{1})\propto p(d_{1}|h)p(h|d_{0}). As this process continues, the Bayesian agent will get closer to the truth. After nn interactions, the beliefs of the agent are p(h|d0,…dn)∝p(h|d0)∏i=1np(di|h)p(h|d_{0},\ldots d_{n})\propto p(h|d_{0})\prod_{i=1}^{n}p(d_{i}|h) for di∼p(d|true process)d_{i}\sim p(d|\text{true process}). Taking the logarithm of the right hand side, this becomes logp(h|d0)+∑i=1nlogp(di|h)\log p(h|d_{0})+\sum_{i=1}^{n}\log p(d_{i}|h). Since the data did_{i} are drawn from p(d|true process)p(d|\text{true process}), ∑i=1nlogp(di|h)\sum_{i=1}^{n}\log p(d_{i}|h) is a Monte Carlo approximation of n∫dp(d|true process)logp(d|h)n\int_{d}p(d|\text{true process})\log p(d|h), which is nn times the negative cross-entropy of p(d|true process)p(d|\text{true process}) and p(d|h)p(d|h). As nn becomes large the sum of log likelihoods will approach this value, meaning that the Bayesian agent will favor the hypothesis that has lowest cross-entropy with the truth. If there is an hh that matches the true process, that minimizes the cross-entropy and p(h|d0,…,dn)p(h|d_{0},\ldots,d_{n}) will converge to 1 for that hypothesis and 0 for all other hypotheses.
接下来，港股、科创板的IPO红利期能否持续？由创新药BD催化的出海热潮将发生怎样的变化？2026年开局之际，36氪约访了9位医疗健康赛道的投资人、创业者，归纳了如下十条趋势和洞察，详情见《2026医疗展望：百家公司港股排队，医疗板块能否再创「神话」》。
。业内人士推荐Line官方版本下载作为进阶阅读
Прясло — это участок стены между двумя соседними башнями. В течение 15 минут участок земли и пешеходную зону закрыли для посетителей. Пострадавших нет.
Why did Netflix back down from its deal to acquire Warner Bros.?
，推荐阅读PDF资料获取更多信息
Help Me Edit With Ask Photos: When you tap edit on a photo, you'll now see a textbox that lets you ask the phone to make edits on your behalf. (You can still manually edit photos.) You can be super specific—ask it to remove the plastic bag in the background—or vague: “Make this look better,” or “Fix the lighting.” A newer capability even lets you even replace a friend's sunglasses with their eyes, provided you have your friend labeled within the Face Groups in Google Photos, so that Google can use older photos of them as a reference.，这一点在PDF资料中也有详细论述
BEST FOR SINGLE GAME