Unverified50% confidenceFactExact time
The paper proves that the logarithmic factor appearing in previous risk bounds is not essential and can be completely eliminated, thereby improving the convergence rate to O(1/√N), consistent with the classical law of large numbers.
1
Sources
50%
Confidence
Long-term
Relevance
10/12/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe O(1/√N) convergence rate cannot be further improved in the sense of rates, representing that risk estimation has reached the information-theoretically optimal rate.75% similarUnverifiedThe paper derives that under the softmax retrieval framework, the evidence score margin required to maintain a fixed accuracy must grow at a rate of Ω(√log N), where N is the number of effective distractors rather than the context length.67% similarUnverifiedThe paper identifies the convergence behavior of empirical risk across different regimes: some regimes maintain an O(1/√N) rate, some regimes converge noticeably slower, and in some regimes the empirical risk no longer exhibits consistency.67% similarUnverifiedThe weak law of large numbers only guarantees convergence in probability, whereas the strong law of large numbers guarantees almost sure convergence along sample paths, making the latter stronger66% similarUnverified西尔维斯特-加莱定理依赖于实数域的特殊性质，并非纯粹的组合结论，在复平面上失效65% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/1001352API
curl https://kongchang.com/api/v1/knowledge/claims/1001352MCP
get_claim(id=1001352)