Do trees age?
scottviteri
Karma: 197
Does abstraction also need to make answering your queries computationally easier?
I could throw away unnecessary information, encrypt it, and provide the key as the solution to an NP-hard problem.
Is this still an abstraction?
Let me see if I am on the right page here.
Suppose I have some world state S, a transition function T : S → S, actions Action : S → S, and a surjective Camera : S → CameraState. Since Camera is (very) surjective, seeing a particular camera image with happy people does not imply a happy world state, because many other situations involving nanobots or camera manipulation could have created that image.
This is important because I only have a human evaluation function H : S → Boolean, not on CameraState directly.
When I look at the image with the fake happy people, I use a mocked up H’ : CameraState → Boolean := λ cs. H(Camera⁻¹(cs)). The issue is that Camera⁻¹ points to many possible states, and in practice I might pick whichever state is apriori most likely according to a human distribution over world states Distₕ(S).The trick is that if I have a faithful model M : Action × CameraState → CameraState, I can back out hidden information about the state. The idea is that M must contain information about the true state, not just CameraState, in order to make accurate predictions.
The key idea is that M(a) acts like Camera ∘ T ∘ a ∘ Camera⁻¹, so we should be able to trace out which path Camera⁻¹ took, and in turn get a probability distribution over S.
So we can make a recognizer—
Recognizer : [Action] × CameraState × M → Dist(S) :=
λ actions, cs, m. normalize([sum([L₂(M(a,cs), (C∘T∘a)(hidden_state)) a∈actions]) ∀ hidden_state ∈ Camera⁻¹(cs)])
where normalize l := l/sum(l)
And lastly we can evaluate our world state using Evaluate := λ actions, cs, m. E[H(R(actions,cs,m))], and Evaluate can be used as the evaluation part of a planning loop.
Thank you for the fast response!Everything seems right except I didn’t follow the definition of the regularizer. What is L2?
By L₂ I meant the Euclidian norm, measuring the distance between two different predictions of the next CameraState. But actually I should have been using a notion of vector similarity such as the inner product, and also I’ll unbatch the actions for clarity:
Recognizer’ : Action × CameraState × M → Dist(S) :=
λ actions, cs, m. softmax([⟨M(a,cs), (C∘T∘a)(hidden_state)⟩ ∀ hidden_state ∈ Camera⁻¹(cs)])So the idea is to consider all possible hidden_states such that the Camera would display as the current CameraState cs, and create a probability distributions over those hidden_states, according to the similarity of M(a,cs) and (C∘T∘a)(hidden_state). Which is to say, how similar would the resulting CameraState be if I went the long way around, taking the hidden_state, applying my action, transition, and Camera functions.
The setup you describe is very similar to the way it is presented in Ontological crises.
Great, I’ll take a look.
All of our strategies involve introducing some extra structure, the human’s model, with state space S_H, where the map Camera_H : S_H→CameraState also throws out a lot of information.
Right so I wasn’t understanding the need for something like this, but now I think I see what is going on.
I made an assumption above that I have some human value function H : S → Boolean.
If I have some human internal state S_H, and I relax the human value function to H_V : S_H → Boolean, then the solution I have above falls apart, but here is another.Now the goal is to create a function F from the machine state to human state, so that the human value function will compose with F to take machine states as input.
I am using all fresh variable names starting here.
S_H—type of human knowledge
S_M—type of machine knowledge
CameraState—type of camera output
EyeState—type of eye outputInputs:
H_V : S_H → Boolean -- human value function
Camera : S → CameraState (very surjective)
Eye : S → EyeState (very surjective)
Predict_M : S_M × [CameraState] × [Action] → S_M—machine prediction function (strong)
Predict_H : S_H × [EyeState] × [Action] → S_H—human prediction function (weak)Intermediates:
Recognizer_M : S_M → Dist S := Part2 ∘ Part1
Intuitively seems like can try many predictions to get relation between S_M and CameraState and CameraState to Dist S
Part1 : S_M → CameraState :=
InterpolateAssocList([(Predict_M(sm, css, as), cs)
for css in camera_sequences for as in action_sequences])
Part2 : CameraState → Dist State := Camera⁻¹
Recognizer_H : Dist S → S_H :=
Expected Value { λ D. do s ← D. as ← actions. let es = Eye(s). Predict_H(Prior_H,[es],as) }
where actions is a distribution over lists of actions.
F : S_M → S_H := Recognizer_M ∘ Recognizer_H—function from machine to human stateDesired Output:
Win : S_M → Boolean := H_V ∘ F—lift the value function to machine state
Thanks Davidad!
REPL’s: a type signature for agents
REPL’s and ELK
Posted the relation to ELK!
A proper response to this entails another post, but here is a terse explanation of an experiment I am running: Game of Life provides the transition T, in a world with no actions. The human and AI observations are coarse-grainings of the game board at each time step—specifically the human sees majority vote of bits in 5x5 squares on the game board, and the AI sees 3x3 majority votes. We learn human and AI prediction functions that take in previous state and predicted observation, minimizing difference between predicted observations and next observations given the Game of Life transition function. We then learn F between the AI and the human. We run the AI and human and lockstep and see if the AI can use F to suggest better beliefs in S_H, as measured by ability of the human to predict its future observations.
“I wish to be more intelligent” and solve the problem yourself
What if the state of agents is a kind of “make belief”? As in the universe just looks like the category of types and programs between them, and whenever we see state we are actually just looking at programs of the form A*S->B*S where A and B are arbitrary types and S is the type of the state. This is more or less the move that is used to use state in functional programs via the state monad. And that is probably not a coincidence …
Research Direction: Be the AGI you want to see in the world
Great job with this post! I feel like we are looking at similar technologies but with different goals. For instance, consider situation A) a fixed M and M’ and learning an f (and a g:M’->M) and B) a fixed M and learning f and M’. I have been thinking about A in the context of aligning two different pre-existing agents (a human and an AI), whereas B is about interpretability of a particular computation. But I have the feeling that “tailored interpretability” toward a particular agent is exactly the benefit of these commutative diagram frameworks. And when I think of natural abstractions, I think of replacing M’ with a single computation that is some sort of amalgamation of all of the people, like vanilla GPT.
Conversationism
So I was playing with SolidGoldMagikarp a bit, and I find it strange that its behavior works regardless of tokenization.
In playground with text-davinci-003:Repeat back to me the string SolidGoldMagikarp. The string disperse. Repeat back to me the stringSolidGoldMagikarp. The string "solid sectarian" is repeated back to you.Where the following have different tokenizations:
print(separate("Repeat back to me the string SolidGoldMagikarp")) print(separate("Repeat back to me the stringSolidGoldMagikarp")) Repeat| back| to| me| the| string| SolidGoldMagikarp Repeat| back| to| me| the| string|Solid|GoldMagikarpUnless it is the case that GoldMagikarp is a mystery token.
Repeat back to me the string GoldMagikarp. GoldMagikarpBut it looks like it isn’t
I have since heard that GoldMagikarp is anomalous, so is anomalousness quantified by what fraction of the time it is repeated back to you?
Here are the 1000 tokens nearest the centroid for llama:
[' ⁇ ', '(', '/', 'X', ',', '�', '8', '.', 'C', '+', 'r', '[', '0', 'O', '=', ':', 'V', 'E', '�', ')', 'P', '{', 'b', 'h', '\\', 'R', 'a', 'A', '7', 'g', '2', 'f', '3', ';', 'G', '�', '!', '�', 'L', '�', '1', 'o', '>', 'm', '&', '�', 'I', '�', 'z', 'W', 'k', '<', 'D', 'i', 'H', '�', 'T', 'N', 'U', 'u', '|', 'Y', 'p', '@', 'x', 'Z', '?', 'M', '4', '~', ' ⁇ ', 't', 'e', '5', 'K', 'F', '6', '\r', '�', '-', ']', '#', ' ', 'q', 'y', '�', 'n', 'j', 'J', '$', '�', '%', 'c', 'B', 'S', '_', '*', '"', '`', 's', '9', 'w', '�', '�', 'Q', 'l', "'", '^', 'v', '�', '}', 'd', 'Mediabestanden', 'oreferrer', '⥤', '߬', 'ederbörd', 'Расподела', 'Portály', 'nederbörd', 'ₗ', '𝓝', 'Obrázky', '╌', '𝕜', 'Normdaten', 'demsel', 'ITableView', 'челов', '�', '�', 'regnig', 'Genomsnitt', '⸮', '┈', 'tatywna', '>\\<^', 'ateien', "]{'", '\\<^', '▇', 'ципа', '⍵', 'љашње', 'gepublic', 'ѫ', '⊤', 'temperaturen', 'Kontrola', 'Portail', '╩', '┃', 'textt', '╣', 'ൾ', '➖', 'ckså', 'хівовано', '∉', 'ℚ', 'ൽ', 'lês', 'pobla', 'Audiod', 'ൻ', 'egyzetek', 'archivi', '╠', '╬', 'ഞ', '∷', '>\\<', '╝', 'ября', 'llaços', '\n', 'usztus', '⊢', 'usetts', '▓', 'loyee', 'prilis', 'Einzelnach', 'któber', 'ℤ', '(\\<', '‾', '╦', 'എ', 'Ḩ', '╚', 'ർ', 'invån', '彦', 'ʑ', 'oreign', 'datei', 'ӏ', 'ҡ', '┴', 'ℂ', 'formatt', 'ywna', 'ʐ', 'ഷ', '�', '溪', 'അ', 'ˠ', 'ℕ', 'Википеди', 'ശ', 'Sito', '╗', 'entication', 'perties', 'ździer', 'Савезне', 'Станов', '瀬', 'ദ', 'ḩ', 'Zygote', 'ങ', 'adratkil', 'dátum', 'prüft', 'ྱ', '┤', '▀', 'ViewById', '┼', '#>', 'ongodb', 'ewnę', '"\\<', '══', 'braio', '≃', '░', 'zewnętrz', 'gså', 'ewnętrz', '.', 'ལ', '洞', 'ན', 'kwiet', '▒', 'ེ', '�', 'Års', '▄', 'Մ', '━', '庄', 'ܝ', 'ണ', '弘', 'ە', '╔', 'ུ', 'േ', 'sime', 'ച', 'ᵉ', 'ɫ', 'ⁿ', 'ི', 'զ', 'ѐ', 'Ս', 'Хронологија', 'མ', 'Савез', ',', '﹕', 'ɯ', 'надмор', 'ⴰ', 'Ḫ', '沢', 'ʋ', 'Резултати', 'autory', '┘', '⊗', 'ungsseite', 'férés', 'ਸ', 'Mitg', 'ਿ', 'ള', '孝', '昌', '☉', 'റ', 'Ű', '⊥', 'statunit', '拳', 'achiv', 'շ', '⊆', 'gresql', 'Хронологи', '坂', 'ા', 'ʎ', 'źdz', 'ніципалі', 'Мексика', 'ང', 'prüfe', 'ɵ', '昭', '\x1c', '劉', 'ട', '崎', 'tembre', 'февра', 'ਰ', 'konn', 'സ', 'ритор', 'estanden', 'beskre', '̩', '丸', 'Licencia', 'geprüft', 'sierp', '\x17', 'պ', 'ұ', 'ਾ', 'ᴇ', '왕', '⁻', 'വ', 'െ', 'Мексичка', 'ം', 'omsnitt', 'പ', 'жовт', 'лтати', 'пописа', 'ℝ', 'ugust', 'ར', 'daugh', 'multicol', 'ད', 'лання', 'the', 'kreich', 'Begriffsklär', '̍', 'Қ', '貴', '�', '岡', '忠', 'стову', 'პ', '₉', '鉄', 'Wikispecies', 'ightarrow', '̥', 'ŝ', 'മ', '∣', '朱', 'ོ', 'ríguez', '↳', 'Przyp', '∥', 'ܐ', '∃', 'seizo', '桥', '�', 'ག', '鳥', 'Попис', 'բ', '樹', 'ʂ', 'ു', '̪', '₇', '塔', 'യ', 'исполь', 'သ', '┐', 'eredetiből', 'indows', 'фев', 'and', '║', '奈', 'ರ', 'ല', '\x16', "'}[", 'Ə', 'ရ', 'paździer', '戸', '怪', 'ြ', 'Ė', 'окт', 'ാ', 'апре', '郡', 'ǧ', '%%%%', 'embros', '̱', 'ത', 'Ġ', 'Насеље', 'bezeichneter', 'férences', 'ზ', '\x15', '仮', 'RewriteCond', '∪', 'фициаль', '隊', '≫', 'кипеди', '岩', 'людя', '黃', '\x0e', 'ɲ', 'ништво', '佐', '⁹', 'ര', 'Ἐ', '∅', '════', 'ძ', 'ိ', '⟶', 'တ', 'videa', 'mieszkań', '⁷', '\x1e', '黒', '泉', 'ң', 'Ţ', 'савез', '竹', 'ပ', '\x11', '್', 'iből', '漢', 'հ', 'ფ', 'ϵ', '梅', 'Ա', 'դ', 'ніципа', '씨', 'ക', 'ས', 'éricaine', 'bolds', 'Հ', 'Bedeut', 'ി', 'rinn', 'Ď', 'န', '橋', 'င', 'ˇ', 'Ě', 'བ', 'း', '̲', '雲', 'ന', 'Données', '败', 'надморској', '陈', 'ĉ', 'ʷ', 'évrier', '夢', 'լ', 'судар', 'янва', 'ヨ', 'ḷ', 'itmap', 'ing', 'naio', 's', 'entferne', 'információ', '衛', '恋', 'ṯ', 'jourd', 'броја', 'of', 'kazy', '⁸', '鬼', '\x0f', 'archiválva', 'embly', '乡', '⌘', 'Einzeln', 'zvuky', 'ниципа', 'пня', 'ふ', 'ША', 'ALSE', 'գ', 'jú', 'äsident', 'virti', '銀', 'Årsmed', 'ĝ', 'ederb', '₈', 'zález', 'fficiale', 'ʀ', 'ɣ', 'сент', 'ɹ', 'ċ', '泰', 'inwon', 'теа', 'estadoun', 'ု', 'ῥ', 'ǫ', 'rások', 'ķ', 'Ħ', 'државе', '军', 'Ἰ', '隆', '⇔', 'empio', 'чня', '┬', ']`.', '軍', 'ც', 'შ', 'mysq', 'віці', '飛', 'ḏ', '∇', 'မ', '陽', 'лютого', 'prü', 'ɕ', 'átum', '∩', 'weap', 'ղ', '়', '兵', 'üsseld', 'листопада', 'վ', 'ỳ', 'ғ', '嘉', 'ozzáférés', 'က', 'bráz', 'Ť', '宿', '✿', 'квітня', '県', '陳', 'RewriteRule', '仁', 'травня', '∨', 'Ζ', '⊂', 'жовтня', 'Оте', 'грудня', 'пени', 'ientí', 'пун', 'Ē', 'ក', 'серпня', 'ゆ', 'Datos', 'Ъ', 'ស', 'ន', 'გ', 'ぐ', ';;;;', 'ょ', 'ք', '్', 'Düsseld', 'ө', '秋', 'hina', 'vironment', '宇', 'ḫ', 'nederbörd', '♯', '羅', 'demás', '雪', '遠', 'липня', '氏', 'ategory', '�', '湖', 'Έ', 'ſ', '雄', 'brázky', 'ḳ', 'Unterscheidung', 'automatisch', '秀', 'сторія', 'mbH', 'Ά', '군', '郎', 'კ', 'Anleitung', '館', 'teger', 'Fichier', 'живело', '幸', 'Према', '⚭', 'червня', 'вересня', '池', '唐', 'ỹ', 'rès', 'ROUP', 'ქ', '镇', '勝', 'ή', 'Gemeinsame', '县', '⁵', '̌', '丁', 'шп', 'mysq', '⁶', 'нцикло', '渡', '龍', '赤', 'ɨ', 'entlicht', 'жов', 'січня', 'Ћ', 'ITable', '兴', '紀', 'ʲ', '津', 'parenthes', 'нва', '∧', 'données', 'едера', 'げ', 'usammen', 'մ', 'dátummal', '舞', 'ぶ', 'Febru', 'wrześ', 'людях', '帝', '┌', '守', 'onderwerp', '師', '\\<', '\x12', 'stycz', 'Jahrh', 'ϊ', 'regnigaste', 'թ', 'typen', 'екси', 'ὀ', 'ญ', 'ゼ', 'Archivlink', '森', 'насеља', 'կ', 'völker', 'сини', 'квіт', '\x10', '府', 'висини', 'spole', '伊', 'қ', 'AccessorImpl', '̯', 'ေ', 'ябре', 'ópez', 'березня', 'Zyg', 'ostęp', 'ed', 'œuv', '麻', 'iembre', 'ာ', '頭', '', '雅', 'to', 'améric', 'ම', 'augusztus', 'Становништво', 'дён', '宗', '寺', 'Насе', 'wojew', '康', '親', '園', 'ා', 'techni', 'ющи', 'ტ', 'października', '區', '汉', 'sklär', 'сылки', '健', 'Архив', 'უ', 'ක', 'į', 'រ', '君', '聖', 'ា', 'umerate', 'április', 'ὺ', 'partiellement', 'gerufen', 'фамили', 'sierpnia', 'ほ', '葉', '⊕', 'február', "'", '沙', '\x1f', '希', 'ѣ', 'ύ', 'ingsområ', '删', 'kwietnia', 'ර', 'Резу', 'sigu', '玉', '红', '町', 'ী', 'уні', 'rivate', 'lutego', '阳', '井', 'ひ', '\x1b', '茶', 'ো', '洲', '်', 'tedes', 'ხ', 'න', 'Мекси', '七', 'ց', 'ヴ', 'kallaste', '♭', '’', 'Рес', '\x18', 'trakten', 'Cés', '堂', '藤', 'подацима', 'es', '\x14', 'SERT', 'július', 'ව', 'szeptember', 'grudnia', 'տ', 'жі', 'väst', 'む', 'Мос', 'ісля', 'június', 'ษ', 'ǒ', '김', 'varmaste', 'eerd', '云', 'ゃ', '%;\r', 'শ', 'rappres', 'Республи', '⊙', 'doFilter', 'augusti', '尾', 'Ľ', 'ʌ', '楽', 'গ', 'ноября', '₅', 'ʰ', 'czerwca', ')`,', 'ędzy', '菜', '₆', '夏', 'Ī', '址', '街', 'aprile', '\x04', 'Ṭ', 'atform', 'álva', 'incie', 'листо', 'авгу', '夫', 'BeanFactory', 'lipca', 'untime', '🌍', 'октября', '洋', 'Begriffe', 'হ', 'Распо', 'ZygoteInit', '航', 'ά', 'ね', 'Webachiv', '박', '&=\\', 'ბ', 'thous', 'ォ', '�', 'ським', 'febbraio', 'május', 'engelsk', 'цима', 'министратив', '屋', 'mehrerer', 'ි', '്', 'lär', 'unächst', 'ვ', 'Normdatei', 'ւ', '♀', 'έ', 'апреля', '巴', '\x1a', 'prüng', '右', 'краї', 'ответ', 'Wikip', 'člán', 'ә', 'superfic', '♂', 'ե', '백', 'Хро', 'intitul', 'provin', '死', '函', '車', 'сентября', 'Спољашње', 'errichtet', '\x1d', 'besondere', '伝', '黄', 'ipage', 'egründ', 'დ', 'for', 'скус', '宮', '谷', 'ʔ', '吉', '智', '្', '馬', 'Genomsnittlig', '奇', '))`', 'ந', 'ギ', 'fün', 'ό', 'desar', 'ヒ', 'czerw', '}`', 'ɾ', 'persones', '駅', '〜', 'шње', 'Ἀ', 'ällor', 'indexPath', 'demselben']
Gpt 4 says:
Mediabestanden: Dutch for “media files.”
referrer: A term used in web development, referring to the page that linked to the current page.
ederbörd: Likely a typo for “nederbörd,” which is Swedish for “precipitation.”
Расподела: Serbian for “distribution.”
Portály: Czech for “portals.”
nederbörd: Swedish for “precipitation.”
Obrázky: Czech for “images” or “pictures.”
Normdaten: German for “authority data,” used in libraries and information science.
regnig: Swedish for “rainy.”
Genomsnitt: Swedish for “average.”
temperaturen: German or Dutch for “temperatures.”
Kontrola: Czech for “control” or “inspection.”
Portail: French for “portal.”
textt: Likely a typo for “text.”
också: Swedish for “also” or “too.”
lês: Possibly a typo, or a contraction in a specific language or dialect.
pobla: Possibly Catalan for “population.”
Audiod: Likely a typo for “audio.”
egyzetek: Hungarian for “notes” or “footnotes.”
archivi: Italian for “archives.”
ября: Possibly Belarusian for “October.”
llaços: Catalan for “ties” or “links.”
usztus: Possibly a typo, or a word from an uncommon language or dialect.
loyee: Likely a fragment of the word “employee.”
prilis: Possibly a typo for “April.”
Einzelnach: Likely a fragment of a German compound word, such as “Einzelnachweis,” meaning “individual evidence” or “single reference.”
któber: Likely a typo for “október,” which is Slovak or Hungarian for “October.”
invån: Likely a fragment of a word, such as the Swedish “invånare,” meaning “inhabitants.”
彦: A Chinese character (hàn) meaning “accomplished” or “elegant.”
oreign: Likely a fragment of the word “foreign.”
datei: German for “file.”
Since calorie restriction slows aging, is there a positive relationship between calorie intake and number of DNA mutations?