張耀仁

星期日, 3月 02, 2025

晚餐接機大作戰: Part III Standard LLM vs. Reasoning

Scheduling Parallelism in Plans problem (Eng) (from source)

感恩節全家晚餐大作戰

SVG

Why non-reasoning LLM fails (source)

Claude Sonnet 3.5 illustration of solution (happens to be optimum)

ChatGPT o1 reasoning feasible outcome, optimized by human

3.7 Extended

41 s (misinterpreted)

3.7 extended, optimum in 81 s,

4 little experiments in a row (edits)

not always woks (can misinterpret) 85 s

3.7 extended, optimum in 69 s,

3.7 extended, optimum in 78 s,

3.7 extended, optimum in 57 s,

3.7 extended 35 s (misinterpreted)

3.7 Extended, 7 s (misinterpretation), prompt "Use A*"

Grok 3 did it in 79 s

What if Emily arrived at the airport at 4:30

Sonnet 3.5 illustration (attention bias occurs. some constraints forgotten)

ChatGPT o1 feasible (also optimum) at the first try. Solution space is tremendously limited.

What if Emily arrived at the airport at 2:30

Sonnet 3.5 illustration (attention bias occurs. some constraints forgotten)

ChatGPT o1 reasoning feasible outcome, optimized by human

晚餐接機大作戰: Part II A*

Scheduling Parallelism in Plans problem (Eng) (from source)

Try smart search. Prompt Claude to generate A* search Algorithm

Generate Python code base by using Claude Sonnet 4

To run Python, use Google Colab

Visualize results as Python can generate complex states

最佳解最高的平行度，throughput 高，idle time 減少，critical path 短

次佳解因為James 似乎太奔波了，剛從機場回來，馬上得回去剛才的機場接人

在工廠等於也就是機器人來回運動，但是沒有產出

次佳解 Sarah 好忙，先烤火雞，換手給機場回來的 James，然後去機場接Emily，James 接手烤火雞，idle time 過長，而且造成沒有必要的 switchover

星期一, 2月 24, 2025

AI 作為一種實驗科學

AI 求解在數學上是如上圖在一個複雜非線性函數尋找最小誤差的數學過程，

以這張圖為例

每次答案之所以不一樣是因為AI每次啟動都會給予一個新的起始點

以至於每次最後收斂的誤差最低點都不會一樣

直覺式程式設計

出處

ＡＩ很厲害，我們學過的他都會做，他目前唯一缺少的是意圖例如他不會主動說來聊天吧，他也不會突然想寫一支無人機偵測程式當然有一天也許他會有意識，至少目前沒有所以現在做研究就是看你想得到什麼，就做得出什麼不像以前你可能想做也做不出來所以老師跟我的學生們與其說做研究，其實玩得很開心，不像苦命研究生今日的世界，做苦工不一定有收穫，懂的跟ＡＩ溝通，善用ＡＩ，把ＡＩ當作我們的翅膀，任意翱翔天空

星期六, 2月 22, 2025

River crossing puzzle 3

problem statement

17 step solution 黃品勛

17 step solution 王智弘

Use react to illustrate the process

(fails to solve. Helps illustrate.)

even 3.7 Extended mode struggles

Why LLM performs poorly with reasoning and planning

Code gen (Python)

code gen python A* search for ::River Crossing Puzzle ...

Python on colab

Use REACT to visualize the steps

change to js

run js

use React to visualize the steps

I really like ChatGPT o1 reasoning performance.

Monologue is best.

reasoning mode in o1

Talking to itself

Running into difficulties? Cute

hours? Ha Ha Ha

River Crossing Puzzle 2

渡河問題2 (statement)，Problem via 許元銘

結果視覺化

Visualization to verify results

Claude solution non-reasoning (incorrect)

Sonnet 4 extended fails

Reasons: sometimes one of the constraints was disregarded. 2

ChatGPT 5 works 3/5. (Two claimed to use Python code execution. One is correct. The other is not. Therefore, is it true code was generated and then executed?) 1, *2x, 3, 4x, *5

Grok

Even reasoning mode of Grok fails.

Code Gen

Use ChatGPT 5 to generate BFS search

search that works

Use Claude second time to generate A*

it takes 15 steps. (thanks to the python code generated by Claude)

python code

another 15-step solution

yet another 15-step

one more 15-step

last 15-step

River Crossing with Alice and her company (River Crossing Puzzle 1)

Five people - Alice, Bob, Carlos, Diana, and Elena - must cross a river in a small boat. The boat can only hold three people at a time. The following conditions apply:

* Alice refuses to be in the boat with Carlos

* Bob and Diana must travel together if either one is in the boat

* Elena can only operate the boat when Carlos is not present

* At least one person in each crossing must know how to operate the boat

* Only Bob, Carlos, and Elena know how to operate the boat

Infer an efficient plan.

Try ChatGPT o1 reasoning, verified by Claude using REACT (it works.)

Try ChatGPT 4o, failure verified by Claude

晚餐接機大作戰: Part I Exploring the Problem

Dinner Operation vs. Semiconductor Fab Scheduling Optimization

Scheduling Parallelism in Plans problem (Eng) (from source)

From python to svg

Try ChatGPT o1, Claude

verify the schedule by flow template

Part II

星期五, 2月 21, 2025

增強AI的能力

ＡＩ的能力來自哪裡？

Given 19, 36, 55, 7, can you give an equation that equals 622?

educated guess ChatGPT 5

Hand trial-and-error ChatGPT 5

Brute force Program execution ChatGPT 5

推理模式 Claude Sonnet 4 Thinking process

直覺 Claude Sonnet 4

推理模式Gemini 2.5 Pro 推理模式

Hand trial-and-error Grok 4

Given 1,2,3,4,5,6 can you give an equation that equals -38?

Grok 4 直覺，hand trial-and-error, too many errors, stop

Sonnet 4 (直覺) hand trial-and-error, too many errors, stop

ChatGPT 5 直覺 hand trial-and-error, deemed nontrivial, stop and ask for brute force

Gemini 2.5 Pro *

半導體廠製程情境

晚餐接機大作戰(半導體廠製程排程)

Gemini 2.5 Pro 推理，Claude Sonnet 4 流程圖 feasible, not optimal

Claude Sonnet 4 直覺模式流程圖，no feasible

Claude Sonnet 4 推理模式 (extended thinking)，流程圖 no feasible，＊

ChatGPT 5, 流程圖 feasible, not optimal，＊

Grok 4 ，流程圖＊

AI 自言自語什麼（Gemini 2.5 pro 為例）

好的，這是在繁體中文中的翻譯： **探究方程式的可能性** 我已經開始使用各種數學運算來嘗試組合 19、36、55 和 7。最初，我的目標是找到一個能直接得出 622 的方程式。我將探索加、減、乘、除等可能性，評估其有效性並進行迭代。這是一個探索無數種可能數學組合的問題。

**計算潛在的組合

** 我現在完全投入於測試不同算術運算的過程中。最初，我專注於直接的方法：將這四個給定的數字進行加、減、乘、除。我的目標是找到一個能得出目標值 622 的組合。如果這證明具有挑戰性，我計劃加入更複雜的運算。目標是得出一個具體的方程式。

**研究數學關係** 我一直在尋找一個使用 19、36、55 和 7 來得出 622 的方程式，但初步的結果沒有幫助。搜尋結果非常籠統，只著重於數學中的運算順序。我需要調整我的搜尋，以專門針對這些數字和目標結果。

**推導方程式** 我已經使用提供的數字構建了一個等於 622 的方程式。我的策略是從乘法開始，以快速接近目標值，然後減去剩餘數字的總和。我驗證了 (19 * 36) - (55 + 7) = 622。我現在可以自信地將此解決方案視為完整的。

**優化方程式策略** 我現在正在制定一個計劃，以使用指定的數字生成得出目標數字的方程式。我目前的方法是利用乘法來接近答案，然後嘗試使用加法和減法使其相等。在我發現 (19 * 36) 是最接近 622 的結果後，我使用剩餘的數字來產生確切的差值，以獲得正確的結果。方程式 (19 * 36) - (55 + 7) = 622 是我經過這次分析後得出的解決方案。