Neumo’s Blogs

Some trivial rambling below; thus, no English. 在高中时由于接触过真正的数学竞赛国家队的成员，知道自己和他们比起来智能水平就像淘宝客服，故在填报志愿时以自己过于愚钝为由放弃了选择数学系。同样是碳基生命，智能竟能如此参差，那如果是能够超脱于生物树桎梏而快速进化的人造智能体，那又将是怎样伟岸的存在？正是抱着这样的想法，我进入了智能科学与工程专业。 随着学习的加深，我发现似乎AGI的实现只需要工程就够了。但脱离了高中的压抑环境后，我的自我价值感逐渐显现，对工程上不求甚解的枚举的容忍度变得更低，于是实现AGI所需要的工程与我对工程的厌恶形成了冲突。再加之我逐渐发现自己的想法其实别人也能想到，无非或早或晚，所以我个人在AGI上的参与其实对于历史车轮而言无足轻重。于是个人偏好的微小叙事与历史进程的宏大叙事都不能够支持我继续在工程上花费时间，所以现在的我离开了工程的赛道（严格来说并不是离开，毕竟我实际上从来没有发过工程论文）。 总结我的大学4年，我会说很多时间是被浪费在工程的细节上的，我看的论文的涉猎面很广，但大部分都是工程。而智能工程专业常规课内的教学也只提供工程实践。（你会说machine learning课程算科学，确实可以这么说，但那涉及的内容太浅显了，几乎是控制论的翻版，而不是真正关于智能的科学。） 一个经典的问题是我会因此后悔吗？但私以为“后悔”本身是个谬论——它假设人能带着现有信息回到过去做出不同选择，这前提就不成立。即便强行假设，如果一个人获得新信息后仍找不到更优解，那或许是由于能力不足，或是因为内在状态未曾更新——用《中国2185》里的话说，“不变就是死了”。所以，只要人还在成长、还在思考，所谓的“后悔”在逻辑上几乎成为恒真命题，反而失去了讨论的意义。 现在我又回到了原点，是选择因自己智力残疾而放弃搞理论AI还是身残志坚。答案已经清晰——我选择后者。在微观层面，这关乎个人的意义坚守；在宏大层面，我盼望能在有生之年，目睹或参与构建AI的大一统理论，将其作为人类献给AGI的一份最后的礼物。在那之后，文明史的主角，就不再是人类了。

What happens when you ssh to a remote machine? This blog will not analyze from a cryptographic way but from an engineering way. We will touch on different components of Linux and how they interact. This blog is a brief introduction. We sacrifice precision for the sake of clarity without compromising the core message. A Quick Tour systemd < root ├─sshd: /usr/sbin/sshd -D [listener] 0 of 10-100 startups < root │ └─sshd: username [priv] < root │ └─sshd: username@pts/0 < user │ └─-fish < user │ └─ other commands └─systemd --user < user ├─(sd-pam) └─other services A root process sshd listens on the configured port (usually 22). Upon connection, it forks a child. This child becomes a privileged monitor process, sshd: <username> [priv], to handle cleanup and audit logs. The monitor forks a net-child that handles network traffic, key exchange, and package parsing as a sandbox user (usually sshd). The net-child receives the key or password and passes it to the privileged root process via a pipe. The monitor runs the PAM stack (/etc/pam.d/sshd) as root, which handles auth, session setup and call pam_systemd.so. pam_systemd.so notifies systemd-logind via D-Bus that a new session is opening. systemd-logind maintains its own database in /run/systemd/sessions and checks if user@<uid>.service is running, If not, it asks PID 1 (system-level systemd) to start it. PID 1 forks a new process to run the service. Because user@.service has PAMName=systemd-user, this new service process initializes the PAM stack (/etc/pam.d/systemd-user), which gathers environment variables and limits. To keep the PAM session alive independent of the service payload, the service process creates a (sd-pam) helper. (sd-pam)’s only job is to wait for the service to die and then call pam_close_session using the parent death signal prctl(PR_SET_PDEATHSIG, SIGTERM). The service process sets its UID to the user and execs the systemd --user binary, passing the PAM-generated environment variables directly. (This explains why we need (sd-pam): after execing the binary, the process that knew how to run pam_close_session() is gone.) Back at step 4, after finishing pam_authenticate, net-child terminates. The sshd monitor calls pam_open_session to gather the environment like step 8 and forks a new child, sshd: <username>@pts/233. The child then sets its UID to the user and forks a new child that sets itself as a session leader using setsid and execs the user’s shell. The shell attaches its IO to the respective pts. This explains why we need the login shell to be a session leader because only a session leader can attach to pts When the user logs out, the ssh monitor detects via SIGCHLD. The monitor performs the final cleanup (recording logout time in wtmp, removing utmp entry, and tearing down the PTY). Note: There is a terminology overload on the word session. The POSIX session (kernel session) is used to manage all the processes belonging to a specific terminal. It can be set using setsid by the process itself. On the other hand, the PAM session in pam_open_session mainly concerns environment and policy management for the convenience of the admin. (Read the following section if you don’t understand.) ...

Prerequisite Basic knowledge of the structure of Transformer and RNN Understand how to train AI models in NLP Notations: Symbol Meaning $x_t$ token at time $t$ $x_{:t}$ tokens before time $t$ $x_{a:b}$ tokens after time $a$ (included) and before time $b$ (excluded) $p$ the distribution of ground truth $q$ model’s prediction $v$ vocabulary size (# of different tokens) $d$ embedding dimension (dimension of hidden states) Main This blog will explore some potential factors contributing to the distinction between text generated by LLMs and human’s text. ...

Puzzle Play music “Pascual: España Cañí Pasodoble” to set the vibe. In a bullring, a brave matador is engaged in a splendid fight with a furious bull. The matador is agile, meaning that he can change his velocity immediately (even at accelerations up to 100g), but he has a maximum velocity. In contrast, the bull has no upper limit on its velocity, but it has a maximum acceleration due to its massive build. The bull wants to gore the matador while the matador wants to dodge the bull’s charge. Can the bull knock down the matador in a finite time? Or can the matador always dodge the bull’s charge for as long as he wants? Note: we model both the matador and the bull as a point without volume. ...

The transition from the Lagrangian to the Hamiltonian formulation can be viewed as an operation that reduces a higher-order dynamical system to a first-order one. Specifically, given the Euler–Lagrange equation \[ \frac{d}{dt}\left(\frac{\partial L}{\partial \dot{q}_i}\right) - \frac{\partial L}{\partial q_i} = 0, \] let \[ p_i = \frac{\partial L}{\partial \dot{q}_i}. \] Then we have \[ \dot{p}_i = \frac{\partial L}{\partial q_i}. \] We would also like to introduce an equation that describes the evolution of \( q_i \): ...

How do we prove $x^2+2x+1 \geq 0$ by sum of squares(SOS)? Quite trivial $\text{LHS} = (x+1)^2 \geq 0$ Then, how to prove this by SOS? $$1024 x^{12} + 1024 x^{11} - 2304 x^{10} - 2304 x^9 + 1856 x^8 + 1856 x^7 - 672 x^6 - 688 x^5 + 96 x^4 + 120 x^3 + x^2 - 8 x + 21 > 0$$Note that $$ \begin{align*} & 1024 x^{12} + 1024 x^{11} - 2304 x^{10} - 2304 x^9 + 1856 x^8 + 1856 x^7 - 672 x^6 - 688 x^5 + 96 x^4 + 120 x^3 + x^2 - 8 x + 21 \\ =& \frac{953178310898788044405634417898675810098347314821670074294737731307329417300202257499761536478657283822781507633364642416166327278492431062378651278370657928662612204203551165032096670314311671897547870594071651961090916102146117367523334512377797063623918959641854483477219062452053117354701873293279721322207383101430406097244237282245639156393092313795413669142611049 x^{12}}{855628317881711343628447665505529353642205279926550721248508119951156125518248969209845948736002719280414541370639384443936720924614544681187805334420694749567400421129263862969704529965010066154381893028055449128137526516108909143872797671529580790648030301664407011259998219690161313333579998909002703175128634549361882868091571588610793879524527809926169868860955417600} \\ & +\frac{20730892603614552086030236791584376390584458016906737607737484410976414001063114786504571319170688941259188382102808494189006085284963556422616888222898922617541385760899893376535242468971667371887252593392744651799829664240827458028060434738895363938051839773370848251341085723828176528969737296885610550104284856922624395816262451042617170959861753944569051610115364975096073666531052259740236406867828388007841283785939762576367433335933838418591322151049217429629270341561448035039752629166572755121441300348424582513530988930032979543430868119319256707428034767673 \left(x^6-\frac{537192259959723196414608024276178584105895770740349990419864409450146859446360918141274261404347215931631797055464128276914916157874933032752787127367563050763626059546908325367179084235774333657723622129680953103417722133971649513536014377636992875729296614390814113462253672326830450300193835 x^5}{573436804488876102142203069716235581838573141198680442118406207394949540289519077190803351051243463518468145511138665086473396444014968827035817391723483821802914447475306468210874522306578884970990388833275010785029852472999820007452095481245595738959406070890816673619069129251781055609514481}\right)^2}{6206525292964998561634089879171420703703077222813245725237731062283243057781605384272715894893115688039561739976314528141440276348710982794310284305563578483338134927900379708528960238116906764065435465250988664286812424413087069804415610909501395560804213981736329016091614450301007081812989768771400716805356955326219422447174363315272321570725848811409107568938852180691630516174689224926595786145141068421753037366221895943861317367364438368687862455344412538507280470763541217796022531535278362226193304037113002012436942592035108049513404198504622679784592044800} \\ & +\frac{89049395936672352040168549073731104935508445899958191436161862318618887575473347824917288559803543779125075800645083670230091642794205786249413530141184376511491703526443536337740075607815663586644005996838313922814771433710991249266480332814634194309626307993872905338940207675367318393363919505638197260130676409010048261104018415934500084622706963281661906523350259253983921638707587 \left(x^6+\frac{1250035259177316292055552469386970079830476326367794092844767479864825753282605141675706859648589867835412955837749840441264047429340506451409551822678359781540767273795999093416096481298696046487871220 x^5}{8622143587826850910117502112533330587731675813130997925666043593533539304265371562476845710341277127329332016845355859683327927946544194588985145498192793223955868643181370645313715205428657738385563819}-\frac{250068555521657649046677562622926995400361492206054337746046763604698328360725525321979519080245347110841949526008580342735436820548070105753437244690660363635344349057576996446918551957050730363661467736795517432 x^4}{247000887631547219650362262267498217114359645814025727199754456680281704352551452248260792050311392387975177735397802907626080272289713051779703241439169224797693110058833779475283650861940201841910326516809614621}\right)^2}{341822602918637684462759803331862949268521644937598626784273477398092190810659753651937927998386651744723163423943913812097353506749855595813602901610410889636152000488013806377115269602857144079515823849827076508204604117044432065154126771800620953408005355692583886319844446768050888556173228514949931617518643948118914444108098243115937619771018949965589413350297216046547214310400} \\ & +\frac{114110582938612998704158659404514255051669057393030752659470219065049417311463468557376015892172386233408723378189272123039495190457682922779027347858586303115779007600668186892567924675431960334050645546500616838293445049 \left(x^6+\frac{170372215743602129824191290442816200114290980759432737980698537578762149431655574586767607141481342217936642217045286295 x^5}{79198978232815290130528655478941018199689976888747889206980181686545761334890064169317612189500341634270976992383855892}-\frac{10203953103929899682581976196753751277654908019629863829295675407122586862724024696782342783750780067856543386194463907683978113 x^4}{13451588692120113302853290112643611602282673701089314990715540684831684684396619555438945669199900573439855658045046218504735514}-\frac{1156921360237789757302485482040694552188225079328629147544405729241765179914524617193983587603792399575398269867536010269771984801215 x^3}{579480989267842360973616884762574144214735300369226600485034777161864144519121973828754340483462516803215541892922546046965501207606}\right)^2}{1366111482246106172696369013109580206661129472861465130693169324770543975649855414453178742347115059279451705556403540118352861235205455721219880514785580582513596385591992213465538746668601219072613820297212205392956700}\\ & +\frac{855170648996299453282826318597469637692688774342377279122588090583182914361725138849041618786410014540391013069612470521 \left(x^6+\frac{208824848701751946066177483431560679149593637501714562853898328 x^5}{1622430576418306376968793749919537014833913740547776937187465121}-\frac{1102891048931550800774133577726231389446852281283462307407302195510467736 x^4}{551125008995526254989473607432028592184518611427649841031577162693270089}-\frac{61451711586630000225725826920536158859746855484781118310242171140952718523128 x^3}{593547856562956888467288338364108993067921931542293187544982814791584554100775}+\frac{232473948787618155607377486386406989276269768205862051739439363838088892436 x^2}{237921979767491444391645439166417035735774063213781213491056607955450278625}\right)^2}{1734819496159721395301097762699887999566121344999250931454978497836495899386698353810674840031645076695859122690108416}\\ & +\frac{152625114303613097562970499342414182175024924456131965 \left(x^6+\frac{28563189249509387706470170536420805 x^5}{9315046557962779041251696063459844}-\frac{6454490216193107995064656609442859126128240 x^4}{6064787888379130847288192308311499387086309}-\frac{16732721532793552664373217343255126836816 x^3}{3553024507622509278691554818253293871345}+\frac{2619886181080527170645281731667006 x^2}{10684687385267909341688179834740825}+\frac{879726740067337452506895818594 x}{518598620844921096038838025275}\right)^2}{2087473500409210051198263446146771163219546655799312} \\ & +\frac{79747153878767503695019075279803 \left(x^6+\frac{740175552623215917780704 x^5}{8159383732850597703519153}-\frac{334868393274810914740397696 x^4}{120845381198458989757409079}-\frac{1582860475816375677208 x^3}{7966887686614702087275}+\frac{19812948366188776778252 x^2}{9085183041159657600375}+\frac{1284036836607616 x}{15467432289695097}-\frac{2247064464063328}{5155810763231699}\right)^2}{721328386522315927536627776512} \\ \gt &0 \end{align*} $$ ...

Notation $[n]$ denotes $\{1,2,\cdots,n\}$. $[m:n]$ denotes $\{m,m+1,\cdots,n\}$ if $m\geq n$. It’s an empty set otherwise. $a_{m:n}$ denotes $a_m,a_{m+1},\cdots,a_n$. $\{\{1,1,2^{(3)}\}\}$ denotes the multiset with two 1s and three 2s in it. The Problem Given several positive integers $a_{1:n}$, what’s the maximum value that can be achieved by four basic operations, additions, subtractions, multiplications and divisions? Every number is used exactly once. (Provider: 雷伊布是真的狗 aka 雷狗) For example, given 1,1,2,3, a possible result is $4/3=(1+1)\times 2/3$ but the largest result is $12=(1+1)\times 2\times3$. ...

Given the Euclidean distances between N points, what’s the minimum dimension where these N points exist? More formally, given a positive integer $N \geq 2$ and positive numbers $a_{ij}$ for any $1\leq i, j\leq N$(and $a_{ij}=a_{ji}$), how to determine whether there exist $N$ points in the K-dimensional Euclidean space such that the distance between point $i$ and point $j$ is $a_{ij}$ for for any $1 \leq i, j\leq N$? Yes. Adding new points iteratively to the construction solves this problem easily because the distances between the newly added point and the points in our current construction uniquely determine its position in the space. But here is a more linear-algebraic solution. ...

Scroll down to read the English version. 问题 你真的理解侦测器吗？ 问题1： 为什么两个面对面的侦测器，如果是用活塞推上去的， 获得的就是4gt周期的1/2占空比的方波；而如果是手动放置的， 则是6gt周期的1/3占空比的方波？ 上面一行的朝右侧的侦测器是手动放置的，而下面一行的朝右侧的侦测器是由活塞放置的 问题2： 来看下面这个机械，BUD活塞会活动吗？ 如果是这样呢？BUD活塞还会活动吗？ 如果你无法回答这两个问题，那么这篇文章就是你所找的。 这篇博文将会从源代码的层面刨根问底去解释侦测器的微时序行为。 文中的源代码是用DecompilerMC 默认配置生成的1.21.4的代码。 在读之前，你应该先对微时序有初步了解。肥啾的这个视频 和 佛冷的博客都是不错的中文相关材料。 注意由于mapping与源代码的差异，在这些资料中对某个微时序称谓可能与本博客不同。 在本文关心的微时序中，命名差异见下表 上述材料中的命名 本文的命名 NTE(Next Tick Entry) TT(Tile Tick) NU(Network Update) PA(Player Action) 代码基础 太长不看版： 计划刻不包含“要让侦测器变亮”或“要让中继器暗掉”这样的信息， 计划刻的行为逻辑是每个方块根据当前状态自己决定的。 例如同样是计划刻，亮的中继器执行则是熄灭，暗的中继器执行则是亮起。 如果当前时刻有计划刻则侦测器首先会改变自己的状态， 之后给出对自己的毗邻方块给出PP更新， 再判断(如果新状态是亮起来，那么添加一个两个游戏刻后的计划刻；如果是暗掉，则不添加)， 然后NC更新自己屁股对着的方块， 之后对自己屁股对着的方块为中心的一阶邻域（不包括侦测器自己和屁股对着的方块）给出一个NC更新。 详细版： 如果侦测器在当前游戏刻有一个计划刻需要执行，则在Tile Tick阶段将会执行以下代码 // net/minecraft/world/level/block/ObserverBlock.java protected void tick(BlockState blockState, ServerLevel serverLevel, BlockPos blockPos, RandomSource randomSource) { if (blockState.getValue(POWERED).booleanValue()) { serverLevel.setBlock(blockPos, (BlockState)blockState.setValue(POWERED, false), 2); } else { serverLevel.setBlock(blockPos, (BlockState)blockState.setValue(POWERED, true), 2); serverLevel.scheduleTick(blockPos, this, 2); } this.updateNeighborsInFront(serverLevel, blockPos, blockState); } 这里数字2对应的是UPDATE_CLIENTS ...

Does IQ matter in terms of test score? Yes. But recently, upon deeper reflection, I come to realize that IQ is not the only factor that affects one’s exam performance. My Childhood When I was in the third year of junior high school, I stumbled upon the Math olympics by chance. It was then that I realized that all the math I had learned was so naive and boring up to that point seemed – it felt like it was only for test, for scoring higher rather than for challenging human’s talent and intelligence. I’ve always loved puzzle games like Sokoban, Cut the Rope, Where’s My Water, etc. For me, the visual effects in video games matter far less than the ingenious level design and mechanics. You might guess that I am a fan of redstone mechinery in Minecraft. – and you’d be right. In my perspective, Math felt like the perfect game: no flashy or gaudy visuals, just clever, sometimes obscure tricks to solve problems. I’d often sit for an entire day trying to crack a tough problem. And when I finally solved it, it was a sheer bliss. ...