Meta tags:
Headings (most frequently used words):
attention, alternative, transformer, training, architecture, embedding, positional, encoder, decoder, encodings, deep, learning, contents, history, full, subsequent, work, applications, see, also, notes, references, further, reading, predecessors, with, seq2seq, parallelizing, ai, boom, era, methods, for, stabilizing, pretrain, finetune, tasks, tokenization, un, encoding, overview, feedforward, network, scaled, dot, product, sublayers, pseudocode, terminology, activation, functions, normalizations, efficient, implementation, sub, quadratic, transformers, multimodality, head, multihead, masked, rope, alibi, relative, position, kv, caching, flashattention, multi, query, speculative, decoding, graphs, random, feature,
Text of the page (most frequently used words):
the (634), and (208), displaystyle (188), attention (186), for (162), text (140), transformer (130), #learning (93), from (91), are (91), model (80), that (76), encoder (73), decoder (73), original (70), arxiv (69), with (68), language (64), tokens (64), each (63), neural (60), 2024 (59), sequence (58), token (57), this (56), layer (54), edit (51), archived (48), retrieved (47), models (47), query (47), transformers (46), machine (44), embedding (41), 2023 (41), network (40), output (40), all (39), used (39), matrix (39), input (38), which (38), z_d (37), vector (36), one (36), into (36), can (36), architecture (33), vectors (33), was (32), gpt (32), 2020 (32), key (32), then (32), head (31), 2022 (30), information (30), z_e (29), training (28), masked (28), positional (28), not (28), layers (28), google (27), processing (27), self (27), value (27), where (27), mechanism (27), large (26), translation (26), networks (26), first (25), 2026 (24), 2021 (24), length (23), only (23), encoding (22), 2017 (21), 2019 (21), doi (21), linear (21), but (21), rope (21), image (20), softmax (20), its (20), size (20), context (19), bert (19), long (19), also (19), using (18), decoding (18), such (18), they (18), data (17), vision (17), systems (17), other (17), more (17), series (17), mathrm (17), than (17), feedforward (17), based (16), function (16), multi (16), have (16), end (16), ffn (16), emb (16), generation (15), seq2seq (15), pre (15), flashattention (15), natural (15), has (15), like (15), example (15), two (15), begin (15), theta (15), deep (14), use (14), artificial (14), speculative (14), 2018 (14), time (14), right (14), cos (14), sin (14), over (14), aligned (14), called (14), may (13), articles (13), research (13), generative (13), rnn (13), lstm (13), 2016 (13), big (13), autoregressive (13), causal (13), left (13), these (13), heads (13), when (13), you (12), architectures (12), inference (12), small (12), computational (12), recurrent (12), liu (12), fast (12), some (12), standard (12), sigma (12), varphi (12), following (12), multiheadattention (12), dots (12), vocabulary (12), wikipedia (11), memory (11), weights (11), trained (11), proceedings (11), conference (11), modeling (11), random (11), efficient (11), position (11), words (11), alternative (11), applied (11), same (11), frac (11), article (11), there (11), matrices (11), any (11), sublayer (11), search (10), short (10), different (10), noam (10), shazeer (10), recognition (10), gradient (10), weight (10), activation (10), representation (10), see (10), 2025 (10), 2014 (10), lee (10), zhang (10), via (10), full (10), learn (10), how (10), uses (10), computed (10), tasks (10), multihead (10), sum (10), would (10), vdots (10), paper (10), last (9), multiple (9), june (9), openai (9), applications (9), supervised (9), word (9), computer (9), david (9), speech (9), normalization (9), need (9), uszkoreit (9), wang (9), without (9), new (9), representations (9), encodings (9), between (9), many (9), during (9), sqrt (9), while (9), probability (9), tilde (9), dimension (9), allows (9), infty (9), dot (9), module (9), sublayers (9), convention (9), because (9), consists (9), intelligence (8), ilya (8), sutskever (8), aidan (8), deepseek (8), llm (8), algorithm (8), functions (8), history (8), jakob (8), advances (8), methods (8), better (8), prediction (8), association (8), relative (8), units (8), their (8), developed (8), later (8), langle (8), rangle (8), mathbb (8), both (8), forward (8), block (8), since (8), generate (8), through (8), main (8), before (8), well (8), ell (8), pmatrix (8), product (8), were (8), prefixlm (8), bmatrix (8), typically (8), task (8), toggle (7), issues (7), andrew (7), ashish (7), vaswani (7), christopher (7), gomez (7), open (7), prompt (7), tuning (7), nlp (7), list (7), video (7), state (7), general (7), reinforcement (7), bias (7), loss (7), algorithms (7), sebastian (7), further (7), chen (7), peter (7), feature (7), wei (7), faster (7), work (7), what (7), part (7), them (7), times (7), parallel (7), within (7), had (7), followed (7), just (7), usually (7), distribution (7), processed (7), similarly (7), number (7), final (7), another (7), entire (7), dimensional (7), xw_ (7), cross (7), attend (7), second (7), process (7), produce (7), three (7), tokenizers (7), modelling (7), sentence (7), additional (6), inc (6), page (6), references (6), software (6), bengio (6), source (6), vllm (6), agent (6), gemini (6), chatgpt (6), parameter (6), tokenization (6), window (6), linguistics (6), john (6), diffusion (6), human (6), post (6), method (6), kaiser (6), scale (6), yang (6), kevin (6), outputs (6), isbn (6), gqa (6), still (6), michael (6), pdf (6), order (6), multimodal (6), found (6), parameters (6), written (6), steps (6), takes (6), concat (6), include (6), practice (6), implemented (6), alibi (6), masking (6), prefix (6), referred (6), tokenizer (6), z_d_copy (6), feed (6), after (6), commonly (6), projection (6), 768 (6), seq (6), code (5), about (5), non (5), hidden (5), contain (5), reliable (5), chatbots (5), chatbot (5), boom (5), alec (5), radford (5), manning (5), geoffrey (5), yoshua (5), datasets (5), unit (5), gpu (5), claude (5), xlnet (5), muse (5), engineering (5), instruction (5), fine (5), reasoning (5), residual (5), convolutional (5), gated (5), term (5), james (5), alphago (5), audio (5), regression (5), future (5), zero (5), niki (5), parmar (5), pmid (5), 978 (5), hao (5), blog (5), curran (5), associates (5), zheng (5), chung (5), speed (5), calculation (5), improve (5), analysis (5), transfer (5), translate (5), every (5), rnns (5), empirical (5), here (5), version (5), theory (5), max (5), avoid (5), positions (5), related (5), real (5), instead (5), next (5), generated (5), cdots (5), been (5), pass (5), similar (5), larger (5), run (5), 512 (5), must (5), specifically (5), thus (5), caching (5), multiplication (5), defined (5), mask (5), integer (5), complex (5), layernorm (5), subsequent (5), previous (5), copy (5), layer_norm (5), given (5), case (5), relevance (5), delta (5), converts (5), identifier (5), published (5), remove (5), subsection (5), languages (4), contents (4), policy (4), september (4), february (4), links (4), style (4), org (4), impact (4), hinton (4), hugging (4), face (4), detection (4), evaluation (4), llama (4), tensorflow (4), palm (4), optimization (4), chain (4), multimodality (4), scaling (4), pagedattention (4), knowledge (4), hyperparameter (4), visual (4), art (4), autoencoder (4), gru (4), quoc (4), oriol (4), vinyals (4), jürgen (4), schmidhuber (4), dall (4), robotics (4), 2015 (4), llion (4), jones (4), alexander (4), reading (4), ieee (4), partitioning (4), han (4), jong (4), quality (4), pretrained (4), computation (4), free (4), sequences (4), generating (4), range (4), windows (4), international (4), łukasz (4), report (4), narang (4), sharan (4), roberts (4), adam (4), exact (4), online (4), eds (4), 1910 (4), improving (4), square (4), variants (4), pretraining (4), understanding (4), colin (4), bidirectional (4), november (4), statistical (4), connections (4), type (4), variant (4), graphs (4), perform (4), autoregressively (4), converted (4), down (4), lstms (4), finding (4), queries (4), rather (4), might (4), log (4), factor (4), changes (4), several (4), gpus (4), implementation (4), operations (4), intermediate (4), form (4), step (4), applies (4), sinusoidal (4), being (4), represent (4), paid (4), numbers (4), etc (4), causally (4), described (4), z_e_copy (4), rate (4), proposed (4), individually (4), introduced (4), numerical (4), norm (4), embeddings (4), encoderlayer (4), means (4), scaled (4), most (4), create (4), contextualized (4), transformations (4), encoded (4), 10000 (4), even (4), out (4), conditional (4), authors (4), early (4), message (4), help (4), sources (4), hide (4), move (4), sidebar (4), table (3), view (3), safety (3), foundation (3), wayback (3), needing (3), description (3), wikidata (3), category (3), liang (3), yann (3), people (3), meta (3), common (3), set (3), content (3), benchmark (3), benchmarks (3), high (3), hardware (3), pytorch (3), coding (3), protocol (3), vicuna (3), phi (3), chinchilla (3), engine (3), thought (3), alignment (3), rlhf (3), mixture (3), experts (3), cache (3), llms (3), jan (3), stephen (3), von (3), walter (3), cognitive (3), world (3), alphafold (3), synthesis (3), implementations (3), weak (3), automated (3), symbolic (3), latent (3), gating (3), convolution (3), backpropagation (3), descent (3), clustering (3), modern (3), formal (3), 1109 (3), science (3), luong (3), thang (3), aditya (3), shot (3), pieter (3), phenaki (3), domain (3), textual (3), parti (3), baptiste (3), perceiver (3), structured (3), inputs (3), 2103 (3), eess (3), march (3), aaai (3), song (3), longer (3), sparse (3), reformer (3), dehghani (3), mostafa (3), pham (3), joshua (3), generalized (3), 2305 (3), reverse (3), together (3), tri (3), dao (3), parallelism (3), dan (3), mixed (3), zhuang (3), serving (3), computing (3), press (3), ofir (3), train (3), levy (3), pmlr (3), 1162 (3), overview (3), mean (3), 1906 (3), 18653 (3), does (3), keras (3), raffel (3), katherine (3), matena (3), zhou (3), yanqi (3), exploring (3), limits (3), unified (3), cheng (3), inside (3), built (3), finetune (3), now (3), english (3), october (3), library (3), era (3), approaches (3), 1409 (3), specific (3), classification (3), gulcehre (3), caglar (3), cho (3), kyunghyun (3), emnlp (3), icml (3), 1992 (3), memories (3), dynamic (3), december (3), level (3), chess (3), decision (3), stabilizing (3), 1997 (3), weighted (3), issue (3), sub (3), beyond (3), expressed (3), writing (3), predict (3), signal (3), treated (3), composed (3), way (3), compute (3), approx (3), independent (3), quadratic (3), 100 (3), performs (3), however (3), verified (3), suppose (3), those (3), take (3), 4t_ (3), taking (3), could (3), quickly (3), low (3), generally (3), grouped (3), pair (3), increases (3), increase (3), revealed (3), reduction (3), improved (3), support (3), dimensions (3), loop (3), per (3), always (3), produced (3), generic (3), absolute (3), plugged (3), others (3), write (3), learned (3), itself (3), examples (3), often (3), replaced (3), significantly (3), less (3), rarely (3), cited (3), variations (3), terminology (3), output_distributions (3), pseudocode (3), modules (3), vanishing (3), adding (3), diagram (3), contains (3), again (3), rows (3), attends (3), major (3), components (3), fashion (3), relevant (3), should (3), allow (3), will (3), far (3), find (3), fixed (3), subword (3), vocabularization (3), pretoken (3), known (3), package (3), unk (3), string (3), important (3), preprocessor (3), produces (3), mapping (3), predicts (3), dataset (3), pretrain (3), recurrence (3), parallelize (3), local (3), problem (3), allowing (3), multiplicative (3), note (3), predecessors (3), field (3), please (3), citations (3), tools (3), contact (2), privacy (2), available (2), terms (2), apply (2), site (2), commons (2), categories (2), lacking (2), title (2), workplace (2), healthcare (2), education (2), risk (2), ethics (2), regulation (2), environmental (2), competition (2), psychosis (2), arms (2), race (2), anthropomorphism (2), slop (2), bubble (2), social (2), economic (2), lecun (2), andrej (2), karpathy (2), demis (2), hassabis (2), sam (2), machines (2), lab (2), technology (2), minimax (2), mistral (2), microsoft (2), deepmind (2), labs (2), test (2), pile (2), corpus (2), perplexity (2), humanity (2), exam (2), center (2), infrastructure (2), virtual (2), assistant (2), summarization (2), question (2), answering (2), vibe (2), agent2agent (2), autogpt (2), intelligent (2), com (2), sparrow (2), kimi (2), grok (2), word2vec (2), lamda (2), glm (2), gemma (2), hallucination (2), adversarial (2), rag (2), prompting (2), mechanistic (2), interpretability (2), autoregression (2), concepts (2), companies (2), effect (2), principle (2), act (2), graph (2), gan (2), variational (2), mamba (2), multilayer (2), perceptron (2), vit (2), turing (2), françois (2), chollet (2), daniel (2), alex (2), fei (2), paul (2), joseph (2), shaw (2), rule (2), semantic (2), programs (2), engines (2), control (2), muzero (2), alphazero (2), ibm (2), project (2), genie (2), veo (2), sora (2), stable (2), imagen (2), whisper (2), wavenet (2), alexnet (2), hypothetical (2), playing (2), actor (2), critic (2), approach (2), neuro (2), improvement (2), sarsa (2), double (2), variance (2), tradeoff (2), projects (2), glossary (2), timeline (2), quantum (2), brain (2), raschka (2), comparison (2), look (2), design (2), lukasz (2), illia (2), polosukhin (2), transduction (2), assigned (2), 2405 (2), phuong (2), mary (2), hutter (2), marcus (2), 2207 (2), 09238 (2), rush (2), group (2), april (2), issn (2), service (2), william (2), eric (2), zhu (2), pmc (2), journal (2), jiahui (2), goh (2), gabriel (2), gray (2), scott (2), 2102 (2), chang (2), jiang (2), ming (2), mohammad (2), pathways (2), jaegle (2), borgeaud (2), jean (2), ionescu (2), catalin (2), brock (2), 03206 (2), kim (2), wook (2), tao (2), brockman (2), greg (2), mcleavey (2), christine (2), robust (2), supervision (2), 2212 (2), 04356 (2), vol (2), 7138 (2), 52202 (2), lmsys (2), grover (2), abbeel (2), mordatch (2), igor (2), 1609 (2), choromanski (2), krzysztof (2), likhosherstov (2), valerii (2), dohan (2), xingyou (2), gane (2), andreea (2), sarlos (2), tamas (2), hawkins (2), davis (2), jared (2), linearly (2), 2006 (2), peng (2), pappas (2), nikolaos (2), smith (2), noah (2), kong (2), zhai (2), huang (2), reversible (2), january (2), tay (2), bahri (2), dara (2), rao (2), arena (2), interspeech (2), 2203 (2), septr (2), spectrogram (2), lin (2), cao (2), swin (2), hierarchical (2), iccv (2), technical (2), lopez (2), accelerating (2), towards (2), stack (2), feng (2), bei (2), ainslie (2), thorp (2), michiel (2), zemlyanskiy (2), yury (2), lebrón (2), federico (2), sanghai (2), sumit (2), checkpoints (2), 13245 (2), devlin (2), jacob (2), hyung (2), won (2), introducing (2), crfm (2), stanford (2), ermon (2), stefano (2), rudra (2), atri (2), 16359 (2), 16344 (2), awareness (2), maxim (2), downstream (2), zhuohan (2), woosuk (2), kwon (2), siyuan (2), sheng (2), ying (2), lianmin (2), cody (2), gonzalez (2), stoica (2), ion (2), easy (2), york (2), usa (2), management (2), tie (2), yan (2), rethinking (2), lewis (2), biases (2), rotary (2), ram (2), omer (2), jonas (2), root (2), 1606 (2), 2002 (2), chao (2), clark (2), august (2), wolf (2), xavier (2), paradigms (2), huggingface (2), 10683 (2), patrick (2), flow (2), christoph (2), pattern (2), cvpr (2), yonghui (2), pang (2), conformer (2), thomas (2), sylvain (2), 1706 (2), story (2), unsupervised (2), recent (2), almost (2), tensor2tensor (2), americas (2), volume (2), linguistic (2), anthony (2), quentin (2), rwkv (2), decomposable (2), great (2), system (2), minh (2), hieu (2), effective (2), 1508 (2), 04025 (2), 3215 (2), cells (2), sensitive (2), bahdanau (2), springer (2), neco (2), 131 (2), 1987 (2), feldman (2), 1982 (2), biological (2), chapter (2), pages (2), 119 (2), optics (2), books (2), foundations (2), properties (2), julien (2), tim (2), grandmaster (2), samples (2), aravind (2), 1735 (2), space (2), reduced (2), notes (2), designed (2), family (2), alone (2), achieved (2), traditional (2), success (2), named (2), document (2), variety (2), including (2), unlike (2), generates (2), processes (2), unmasked (2), iteration (2), until (2), 114 (2), 115 (2), turning (2), patches (2), turned (2), breaking (2), images (2), either (2), finetuned (2), adapted (2), modalities (2), approximation (2), precise (2), sampled (2), normal (2), consequently (2), ordinary (2), require (2), grows (2), behavior (2), single (2), arbitrarily (2), costs (2), greedy (2), smaller (2), simple (2), few (2), four (2), discarded (2), values (2), verify (2), indeed (2), largest (2), mla (2), minimizes (2), needs (2), cached (2), rank (2), showing (2), figure (2), groups (2), mqa (2), maximal (2), multiqueryattention (2), whereas (2), amount (2), necessary (2), developments (2), types (2), added (2), computes (2), keys (2), making (2), communication (2), avoiding (2), careful (2), blocks (2), caches (2), slow (2), multiplications (2), prefilling (2), performed (2), directly (2), idea (2), direction (2), ddots (2), location (2), angle (2), equivalently (2), provides (2), normalizations (2), combination (2), relu (2), much (2), columns (2), correspond (2), though (2), mathbf (2), architectural (2), t_e (2), t_d (2), shape (2), positional_embedding (2), multihead_attention (2), final_layer_norm (2), third (2), unembed (2), warm (2), starts (2), easier (2), requiring (2), convergence (2), conceptually (2), object (2), probabilities (2), schematically (2), maskedmultiheadattention (2), decoderlayer (2), current (2), cannot (2), yet (2), stacked (2), producing (2), row (2), combine (2), entries (2), permutation (2), iteratively (2), calculated (2), link (2), maskedattention (2), mechanisms (2), theoretically (2), possible (2), owned (2), individual (2), whole (2), passed (2), scope (2), relationships (2), dependencies (2), humans (2), computations (2), counts (2), due (2), divided (2), stabilizes (2), necessarily (2), cdot (2), learns (2), neurons (2), layered (2), earlier (2), difference (2), neighbors (2), happens (2), easily (2), diag (2), distance (2), shift (2), ldots (2), dog (2), bites (2), man (2), illustration (2), top (2), temperature (2), hot (2), bpe (2), ulm (2), segmentation (2), python (2), latter (2), sentences (2), retrieval (2), pretokenization (2), special (2), segments (2), characters (2), strings (2), segmented (2), although (2), depending (2), pretokens (2), finite (2), back (2), result (2), section (2), parts (2), classes (2), thank (2), your (2), party (2), week (2), warmup (2), compared (2), recommended (2), publication (2), became (2), public (2), contribute (2), led (2), intra (2), parallelizing (2), took (2), develop (2), global (2), higher (2), sequential (2), operate (2), widely (2), curve (2), net (2), forest (2), anomaly (2), bayes (2), dimensionality (2), challenged (2), removed (2), talk (2), appearance (2), upload (2), file (2), read (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, conduct, legal, contacts, disclaimers, under, agree, registered, trademark, profit, organization, wikimedia, creative, attribution, sharealike, license, rendered, parsoid, edited, utc, webarchive, template, maintenance, https, index, php, transformer_, deep_learning, oldid, 1376232609, existential, dependency, gaid, deaths, linked, copyright, governance, mira, murati, arthur, mensch, wenfeng, percy, dario, amodei, altman, xai, thinking, innovation, institute, stepfun, sarvam, openrouter, nvidia, moonshot, eleutherai, cohere, baidu, anthropic, alibaba, ai21, organizations, validation, sets, synthetic, web, scraping, crawl, undetectable, gptzero, metric, judge, lmarena, mmlu, tpu, bandwidth, cuda, chromadb, database, openvino, onnx, tensorrt, sglang, ollama, studio, cpp, codex, manus, langchain, crewai, agents, copilot, lumo, ernie, bot, doubao, character, amazon, assistants, qwen, nemotron, glimmer, spark, mixtral, minerva, mimo, laguna, jais, inkling, granite, pangu, glove, dbrx, bloom, apertus, glitch, stochastic, parrot, injection, constitutional, law, distillation, compression, moe, nlg, warfare, military, games, marketing, fiction, explainable, winter, literacy, opposition, centers, propaganda, politician, precautionary, nationalism, elections, takeover, government, cold, war, political, gnn, vae, highway, cnn, mlp, echo, differentiable, kokotajlo, leike, mustafa, suleyman, schulman, silver, ian, goodfellow, krizhevsky, goodnight, graves, grossberg, lotfi, zadeh, hopfield, werbos, seppo, linnainmaa, seymour, papert, weizenbaum, bernard, widrow, frank, rosenblatt, oliver, selfridge, herbert, simon, cliff, allen, newell, nathaniel, rochester, mccarthy, marvin, minsky, takeo, kanade, kunihiko, fukushima, shun, ichi, amari, shannon, neumann, pitts, warren, sturgis, mcculloch, alan, yago, dbpedia, conceptnet, bases, opencog, lida, clarion, soar, reasoners, procedural, logic, expert, deductive, classifiers, robot, action, selection, driving, car, five, decisional, watsonx, watson, debater, oasis, udio, suno, riffusion, music, seedance, kling, hailuo, runway, gen, dream, recraft, midjourney, ideogram, flux, firefly, aurora, facial, elevenlabs, ocr, hwr, physical, superintelligence, asi, agi, lethal, autonomous, weapons, laws, companion, nmt, game, theorem, proving, situated, sovereign, blended, recursive, reflection, uncanny, valley, adversary, imitation, augmentation, regularization, initialization, rectifier, sigmoid, batchnorm, conjugate, quasi, newton, sgd, overfitting, constraint, satisfaction, planning, lists, proprietary, institutions, workspace, summit, antigravity, vids, notebooklm, dreambooth, videopoet, nano, banana, tensor, gato, efficientnet, mobilenet, inception, alphagenome, alphaevolve, alphaproof, alphageometry, funsearch, alphadev, alphatensor, alphastar, popular, culture, jie, sedol, fan, hui, competitions, master, versions, magazine, nicholas, mieczyslaw, owen, teku, issued, llc, patent, 10452978, leech, gavin, argmin, gravitas, ferrando, javier, sarti, gabriele, bisazza, arianna, costa, jussà, marta, primer, inner, workings, 00208, harvard, annotated, hsu, cyril, shih, huan, dalgkitsis, anestis, grosso, paola, papagianni, chrysa, 9264, 2327, 4697, tnse, 3689920, 9247, transactions, empowered, aware, kariampuzha, alyea, gioconda, sue, sanjak, jaleal, mathé, ewy, sid, chatelaine, haley, yadaw, arjun, yanji, qian, 157, 36855134, 9972634, 1186, s12967, 023, 04011, translational, medicine, precision, extraction, rare, disease, epidemiology, yuanzhong, koh, jing, baid, gunjan, zirui, vasudevan, vijay, yinfei, rich, 2206, 10789, ramesh, pavlov, mikhail, voss, chelsea, mark, 12092, huiwen, barber, jarred, maschinot, lezama, jose, murphy, freeman, 2301, 00704, hsuan, villegas, ruben, babaeizadeh, kindermans, moraldo, hernan, saffar, taghi, castro, santiago, kunze, julius, erhan, dumitru, variable, descriptions, 2210, 02399, sites, alayrac, doersch, carl, ding, koppula, skanda, zoran, shelhamer, evan, hénaff, olivier, 2107, 14795, gimeno, felix, zisserman, carreira, joao, perception, iterative, haotian, chunyuan, qingyang, yong, jae, 34916, 9911, 075280, 1516, 34892, impressing, 7636, 2374, 3468, v36i7, 20729, 7628, frozen, universal, belanger, colwell, lucy, weller, adrian, proteins, scalable, 03555, yogatama, dani, schwartz, roy, lingpeng, 02143, shuangfei, talbott, srivastava, nitish, hanlin, ruixiang, susskind, josh, 2105, 14103, constructing, child, rewon, 1904, 10509, ren, mengye, urtasun, raquel, grosse, roger, 1707, 04585, storing, activations, abnar, samira, shen, yikang, philip, jinfeng, ruder, metzler, donald, 2011, 04006, ristea, nicolaea, radu, tudor, khan, fahad, shahbaz, isca, 4107, 21437, 249, 09581, 4103, separable, yutong, yue, yixuan, guo, baining, shifted
Text of the page (random words):
activation the number of neurons in the middle layer is called intermediate size gpt 60 filter size bert 38 or feedforward size bert 38 it is typically larger than the embedding size for example in both gpt 2 series and bert series the intermediate size of a model is 4 times its embedding size d ffn 4 d emb displaystyle d_ text ffn 4d_ text emb scaled dot product attention edit main article dot product attention attention head edit scaled dot product attention block diagram exact dimension counts within an attention head module the attention mechanism used in the transformer architecture are scaled dot product attention units for each unit the transformer model learns three weight matrices the query weights w q displaystyle w q the key weights w k displaystyle w k and the value weights w v displaystyle w v the module takes three sequences a query sequence a key sequence and a value sequence the query sequence is a sequence of length ℓ seq query displaystyle ell _ text seq query and each entry is a vector of dimension d emb query displaystyle d_ text emb query similarly for the key and value sequences for each vector x i query displaystyle x_ i text query in the query sequence it is multiplied by a matrix w q displaystyle w q to produce a query vector q i x i query w q displaystyle q_ i x_ i text query w q the matrix of all query vectors is the query matrix q x query w q displaystyle q x_ text query w q similarly we construct the key matrix k x key w k displaystyle k x_ text key w k and the value matrix v x value w v displaystyle v x_ text value w v it is usually the case that all w q w k w v displaystyle w q w k w v are square matrices meaning d emb query d query displaystyle d_ text emb query d_ text query etc attention weights are calculated using the query and key vectors the attention weight a i j displaystyle a_ ij from token i displaystyle i to token j displaystyle j is the dot product between q i displaystyle q_ i and k j displaystyle k_ j the attention weights are divided by the square root of the dimension of the key vectors d k displaystyle sqrt d_ k which stabilizes gradients during training and passed through a softmax which normalizes the weights the fact that w q displaystyle w q and w k displaystyle w k are different matrices allows attention to be non symmetric if token i displaystyle i attends to token j displaystyle j i e q i k j displaystyle q_ i cdot k_ j is large this does not necessarily mean that token j displaystyle j will attend to token i displaystyle i i e q j k i displaystyle q_ j cdot k_ i could be small the output of the attention unit for token i displaystyle i is the weighted sum of the value vectors of all tokens weighted by a i j displaystyle a_ ij the attention from token i displaystyle i to each token the attention calculation for all tokens can be expressed as one large matrix calculation using the softmax function which is useful for training due to computational matrix operation optimizations that quickly compute matrix operations the matrices q displaystyle q k displaystyle k and v displaystyle v are defined as the matrices where the i displaystyle i th rows are vectors q i displaystyle q_ i k i displaystyle k_ i and v i displaystyle v_ i respectively then we can represent the attention as attention q k v softmax q k t d k v displaystyle begin aligned text attention q k v text softmax left frac qk mathrm t sqrt d_ k right v end aligned where the softmax is applied over each of the rows of the matrix the number of dimensions in a query vector is query size d query displaystyle d_ text query and similarly for the key size d key displaystyle d_ text key and value size d value displaystyle d_ text value the output dimension of an attention head is its head dimension d head displaystyle d_ text head the attention mechanism requires the following three equalities to hold ℓ seq key ℓ seq value d query d key d value d head displaystyle ell _ text seq key ell _ text seq value d_ text query d_ text key d_ text value d_ text head but is otherwise unconstrained if the attention head is used in a self attention fashion then x query x key x value displaystyle x_ text query x_ text key x_ text value if the attention head is used in a cross attention fashion then usually x query x key x value displaystyle x_ text query neq x_ text key x_ text value it is theoretically possible for all three to be different but that is rarely the case in practice multihead attention edit multihead attention block diagram exact dimension counts within a multihead attention module one set of w q w k w v displaystyle left w q w k w v right matrices is called an attention head and each layer in a transformer model has multiple attention heads while each attention head attends to the tokens that are relevant to each token multiple attention heads allow the model to do this for different definitions of relevance specifically the query and key projection matrices w q displaystyle w q and w k displaystyle w k which are involved in the attention score computation defines the relevance meanwhile the value projection matrix w v displaystyle w v in combination with the part of the output projection matrix w o displaystyle w o determines how the attended tokens influence what information is passed to subsequent layers and ultimately the output logits in addition the scope of attention or the range of token relationships captured by each attention head can expand as tokens pass through successive layers this allows the model to capture more complex and long range dependencies in deeper layers many transformer attention heads encode relevance relations that are meaningful to humans for example some attention heads can attend mostly to the next word while others mainly attend from verbs to their direct objects 61 the computations for each attention head can be performed in parallel which allows for fast processing the outputs for the attention layer are concatenated to pass into the feedforward neural network layers concretely let the multiple attention heads be indexed by i displaystyle i then we have multiheadattention q k v concat i n heads attention x w i q x w i k x w i v w o displaystyle text multiheadattention q k v text concat _ i in n_ text heads text attention xw_ i q xw_ i k xw_ i v w o where the matrix x displaystyle x is the concatenation of word embeddings and the matrices w i q w i k w i v displaystyle w_ i q w_ i k w_ i v are projection matrices owned by individual attention head i displaystyle i and w o displaystyle w o is a final projection matrix owned by the whole multihead attention head it is theoretically possible for each attention head to have a different head dimension d head displaystyle d_ text head but that is rarely the case in practice as an example in the smallest gpt 2 model there are only self attention mechanisms it has the following dimensions d emb 768 n head 12 d head 64 displaystyle d_ text emb 768 n_ text head 12 d_ text head 64 since 12 64 768 displaystyle 12 times 64 768 its output projection matrix w o r 12 64 768 displaystyle w o in mathbb r 12 times 64 times 768 is a square matrix masked attention edit the transformer architecture is constructed to calculate output tokens iteratively assuming t 0 displaystyle t 0 refers to the calculation of the first output token i 0 displaystyle i 0 for step t 0 displaystyle t 0 the output token i 0 displaystyle i 0 shall remain constant this ensures properties of the model similar to autoregressive models 1 therefore at every time step t displaystyle t the calculation for all outputs i displaystyle i should not have access to tokens at position j displaystyle j for j i displaystyle j i as it naturally is the case for time step t i displaystyle t i when tokens j t displaystyle j t are not yet calculated this behavior may be accomplished before the softmax stage by adding a mask matrix m displaystyle m that is displaystyle infty at entries where the attention link must be cut and 0 displaystyle 0 at other places maskedattention q k v softmax m q k t d k v displaystyle begin aligned text maskedattention q k v text softmax left m frac qk mathrm t sqrt d_ k right v end aligned the following matrix is commonly used in decoder self attention modules called causal masking m causal 0 0 0 0 0 0 0 0 0 0 displaystyle m_ text causal begin bmatrix 0 infty infty dots infty 0 0 infty dots infty 0 0 0 dots infty vdots vdots vdots ddots vdots 0 0 0 dots 0 end bmatrix in words it means that each token can pay attention to itself and every token before it but not any after it a non masked attention module can be thought of as a masked attention module where the mask has all entries zero as an example of an uncommon use of mask matrix the xlnet considers all masks of the form p m causal p 1 displaystyle pm_ text causal p 1 where p displaystyle p is a random permutation matrix 62 encoder edit one encoder layer an encoder consists of an embedding layer followed by multiple encoder layers each encoder layer consists of two major components a self attention mechanism and a feed forward layer it takes an input as a sequence of input vectors applies the self attention mechanism to produce an intermediate sequence of vectors then applies the feed forward layer for each vector individually schematically we have given input vectors h 0 h 1 combine them into a matrix h h 0 h 1 encoderlayer h ffn multiheadattention h h h 0 ffn multiheadattention h h h 1 displaystyle begin aligned text given input vectors h_ 0 h_ 1 dots text combine them into a matrix h begin bmatrix h_ 0 h_ 1 vdots end bmatrix text encoderlayer h begin bmatrix text ffn text multiheadattention h h h _ 0 text ffn text multiheadattention h h h _ 1 vdots end bmatrix end aligned where ffn displaystyle text ffn stands for feed forward network we can more succinctly write it as encoderlayer h ffn multiheadattention h h h displaystyle text encoderlayer h text ffn text multiheadattention h h h with the implicit convention that the ffn displaystyle text ffn is applied to each row of the matrix individually the encoder layers are stacked the first encoder layer takes the sequence of input vectors from the embedding layer producing a sequence of vectors this sequence of vectors is processed by the second encoder and so on the output from the final encoder layer is then used by the decoder as the encoder processes the entire input all at once every token can attend to every other token all to all attention so there is no need for causal masking decoder edit one decoder layer a decoder consists of an embedding layer followed by multiple decoder layers followed by an un embedding layer each decoder consists of three major components a causally masked self attention mechanism a cross attention mechanism and a feed forward neural network the decoder functions in a similar fashion to the encoder but an additional attention mechanism is inserted which instead draws relevant information from the encodings generated by the encoders this mechanism can also be called the encoder decoder attention 1 59 like the first encoder the first decoder takes positional information and embeddings of the output sequence as its input rather than encodings the transformer must not use the current or future output to predict an output so the output sequence must be partially masked to prevent this reverse information flow 1 this allows for autoregressive text generation for decoding all to all attention is inappropriate because a token cannot attend to tokens not yet generated thus the self attention module in the decoder is causally masked in contrast the cross attention mechanism attends to the output vectors of the encoder which is computed before the decoder starts decoding consequently there is no need for masking in the cross attention mechanism schematically we have h maskedmultiheadattention h h h decoderlayer h ffn multiheadattention h h e h e displaystyle begin aligned h text maskedmultiheadattention h h h text decoderlayer h text ffn text multiheadattention h h e h e end aligned where h e displaystyle h e is the matrix with rows being the output vectors from the encoder the last decoder is followed by a final un embedding layer to produce the output probabilities over the vocabulary then one of the tokens is sampled according to the probability and the decoder can be run again to produce the next token etc autoregressively generating output text full transformer architecture edit sublayers edit a one encoder layer and one decoder layer b two encoder layers and two decoder layers the sublayers are labelled as well each encoder layer contains 2 sublayers the self attention and the feedforward network each decoder layer contains 3 sublayers the causally masked self attention the cross attention and the feedforward network transformer encoder with norm first and norm last transformer decoder with norm first and norm last block diagram for the full transformer architecture schematic object hierarchy for the full transformer architecture in object oriented programming style the final points of detail are the residual connections and layer normalization denoted as layernorm or ln in the following which while conceptually unnecessary are necessary for numerical stability and convergence the residual connections are introduced to avoid vanishing gradient issues and stabilize the training process they can be expressed by x f x x displaystyle x mapsto f x x where f displaystyle f is a given component of the transformer adding the input x displaystyle x can preserve the input information and avoid issues when the gradient of f x displaystyle f x is close to zero similarly to how the feedforward network modules are applied individually to each vector the layernorm is also applied individually to each vector there are two common conventions in use the post ln and the pre ln convention in the post ln convention the output of each sublayer is l a y e r n o r m x s u b l a y e r x displaystyle mathrm layernorm x mathrm sublayer x where s u b l a y e r x displaystyle mathrm sublayer x is the function implemented by the sublayer itself in the pre ln convention the output of each sublayer is x s u b l a y e r l a y e r n o r m x displaystyle x mathrm sublayer mathrm layernorm x the original 2017 transformer used the post ln convention it was difficult to train and required careful hyperparameter tuning and a warm up in learning rate where it starts small and gradually increases the pre ln convention proposed several times in 2018 63 was found to be easier to train requiring no warm up leading to faster convergence 51 pseudocode edit the following is the pseudocode for a standard pre ln encoder decoder transformer adapted from formal algorithms for transformers 64 input encoder input t_e decoder input t_d output array of probability distributions with shape decoder vocabulary size x length decoder output sequence encoder z_e encoder tokenizer t_e for e...
|
