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Notes on AI, language models and software engineering.

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2026-10-07Sequence PackingYou are teaching a model to write short customer responses: “Thank you”, “No”, and “Yes”. After division into pieces of text, or tokens, the examples illustratively occupy 3, 2, and 2 positions, including each text's end
2026-10-05Reinforcement LearningYou want to teach a program to win a small game. At a fork, it can choose route A, collect two coins immediately, and finish the second turn without any new coins. Route B gives nothing on the first turn but leads to fiv
2026-09-20Predicting command outputs helps with later agent trainingAn agent working in a terminal tries to run a program. It sends a command, reads an error message and chooses its next action. In doing so, it must connect the output to the earlier command: recognize whether a file, mem
2026-09-20Loss maskingYou are training an agent on records of conversations with tools. A record contains its commands and the tools' responses. You want to assess selected parts while still letting it read the rest as context for its next ac
2026-09-20pass@kThe model produced ten programs, and one passed the tests. Does that mean a single response is likely to succeed? You need to distinguish “it worked on the first attempt” from “we found a success among many attempts”. pa
2026-09-20Continuous BatchingA server generates two responses at once. One finishes quickly; the other is long. If the next user must wait for the entire pair to finish, the freed slot is wasted for many steps. Continuous Batching allows the group o
2026-09-20PagedAttentionA server handles conversations of different lengths. If it reserves a large contiguous memory region in advance for each entire future response, some space remains unused. You want to allocate smaller pieces as needed. P
2026-09-20Prefix CachingYou ask five questions about the same long document. Each input starts with the same instruction and document text; only the ending contains a new question. Computing the same beginning again would repeat work. Prefix Ca
2026-09-20Time to First TokenYou click “Send” and stare at an empty chat. For the user's comfort, it matters when the beginning of the response appears, even if writing the rest takes much longer. You need to measure that initial wait. Time to First
2026-09-18DecodeThe first piece of the response has appeared. The next must account for what was just written: after “Today I drink tea” the model has a different context than after “Today I drink water”. This changing text must be exte
2026-09-18FlashAttentionAttention compares many pairs of text fragments. Saving all intermediate results to a computing card's large memory can make data transfers expensive. You want to perform the same calculation while reducing movement and
2026-09-18PrefillYou send a long question to a chat and wait for the first word. Before the model appends a response, it must process the content it has already received. This initial stage can require considerable work, especially for a
2026-09-18Speculative DecodingA large model generates text correctly but slowly. A smaller model can quickly propose several following pieces. You want to use its work while keeping the large model in control of the final result. Speculative Decoding
2026-09-18Beam SearchWhen choosing the first piece of a response, you may reject too early a path that would later turn out better. Checking all possible sequences is too expensive, however. You need a limited pool of alternatives. Beam Sear
2026-09-18Greedy DecodingThe model could append several different pieces. The simplest choice is always to take the most likely one. This saves consideration of alternatives, but does the best first step lead to the best entire sequence? Greedy
2026-09-18Grouped-Query AttentionThe model reads earlier text in several ways in parallel. Each such computation is an attention head. You want to reduce the memory these heads occupy, but sharing a single data set completely may constrain the model too
2026-09-18Multi-Query AttentionThe model connects the current piece of text to the earlier conversation through several parallel computations. These computations are called attention heads. If each head stores its own descriptions of the entire preced
2026-09-18Rotary Position EmbeddingThe model compares pieces of text, but also needs to know how far apart they are. “Yesterday” beside a verb can play a different role from the same word in a distant quotation. How can position be included when comparing
2026-09-16KL DivergenceTwo models divide probabilities differently among the same answers. One assigns 90% to A and 10% to B; the other gives each 50% . You want to measure how well the second reproduces the first model's predictions. KL Diver
2026-09-16Knowledge DistillationA large model performs a task well but is too expensive for everyday use. A smaller model could try to reproduce its behavior. It needs examples or assessments showing more than just a list of correct labels, however. Kn
2026-09-16KV CacheThe model appends a response piece by piece. It has already computed much information about earlier text, so computing it from scratch at every step would repeat work. You want to retain results that remain valid. KV Cac
2026-09-16Top-k SamplingWhen sampling the next piece, the model allows many extremely unlikely options. You want to keep some diversity but remove the long tail of candidates. You can admit only a specified number of leaders. Top k Sampling sam
2026-09-16Top-p SamplingSometimes the model has one clear leader; sometimes it has many continuations with similar scores. Always admitting five candidates ignores this difference. You want to choose the group's size according to where the prob
2026-09-15Cross-entropyTwo models identify the same word as the best continuation, but the first gives it 80% probability and the second only 20% . Checking only the winner misses this difference. Training needs a measure of how strongly the m
2026-09-15LoRAYou have a large model and want to adapt it to the style of your documents. Training all its weights — the numbers controlling its computations — requires a lot of memory. Can you train only a smaller correction to what
2026-09-15Masked Language ModelingYou want to teach the model to use the entire sentence. You hide a fragment in “Alice has a MASK ” or “Alice MASK a cat” and ask it to reconstruct the original. Information on both sides of the gap may be needed for the
2026-09-15PerplexityYou compare two models on the same text. You want to know which predicts its successive fragments better, rather than merely which guessed more individual winners. You need a number summarizing the probabilities assigned
2026-09-15TemperatureThe model usually chooses similar continuations, and you want to regulate sampling diversity. You do not change its knowledge or weights. You change only how strongly the best scoring candidates' lead affects their proba
2026-09-14Autoregressive Language ModelingYou start a sentence: “Today I drink…”. After appending “tea”, possible continuations differ from those after “water”. The model must account for the text already chosen at every next step, rather than guess all position
2026-09-14Byte Pair EncodingA vocabulary containing every possible word would be enormous and would continually lack new names. A vocabulary of individual characters is small but turns text into a very long sequence. You need a compromise: frequent
2026-09-14Fine-tuningA trained model can process language, but you want it to classify company messages as “return”, “delivery”, or “payment”. General ability does not yet provide the way of working you expect. You prepare examples of messag
2026-09-14Pre-trainingYou want the model to recognize relationships in language before adapting it to a specific job, such as classifying customer messages. Manually preparing answers for all the text would be impractical. The text itself, ho
2026-09-14SoftmaxThe model scored three possible sentence continuations with the numbers 2 , 1 , and 0 . You want to sample a response according to their probabilities. Raw scores are not probabilities: they can be negative and do not su
2026-09-14Causal MaskingYou are teaching the model to append “cat” after “Alice has a”. The word “cat” already exists in the complete example. If the model could look at it while predicting, the task would appear easy but would not resemble cre
2026-09-14Cross-attentionIn translation, the model has two different texts: the original and the response still being created. When appending another translation word, it needs information from the original. Mixing only the response already writ
2026-09-14Layer NormalizationOne fragment's description enters the next layer with numbers 2, 4 , another with 20, 40 . The signal magnitude can differ considerably. You want to aid computation by converting numbers within each description to a comp
2026-09-14Position-wise Feed-Forward NetworkThe model gathered information from the rest of the sentence for a particular fragment. It now needs to process that description: combine features and compute a new representation. Reading other positions again is not th
2026-09-14Token EmbeddingThe computer receives a number identifying a text fragment. The number 17 itself does not tell it what the fragment is or how it relates to others. It needs a useful numerical description that can be transformed during c
2026-09-13Quantization errors partly cancel out across model layersYou want to run a language model on your own graphics card, but its weights take up too much memory. One solution is post training quantization: you replace numbers stored in the finished model with values from a smaller
2026-09-13Post-training quantizationYou already have a trained model, but it occupies too much memory to run on your chosen computer. Much of that space stores the numbers controlling computation. Can they be stored less precisely to shrink the model? Post
2026-09-13Residual connectionThe model processes a text description through many layers. If every layer had to rebuild all the information, forwarding it could easily become difficult. Retaining the input and adding only the computed change is helpf
2026-09-13LM headThe model has processed “Today I drink” and has an internal description of this content as a list of numbers. The user, however, is waiting for text. We need a transition from the description hidden in the model to score
2026-09-13Multi-Head AttentionOne combination of information can mix different sentence relationships too strongly. In translation, relationships involving people, time, and grammatical form may all be useful. We want to let the model compute several
2026-09-13Positional EncodingYou read “BMW overtook Volvo” and “Volvo overtook BMW”. They contain exactly the same words, but changing their order reverses the cars' roles. If the model sees only word descriptions and compares them as an unordered s
2026-09-13Scaled Dot-Product AttentionThe model needs to combine information from several sentence fragments. One is more useful, another less so. It needs a specific way to compute their contributions and then assemble the information into one result. Scale
2026-09-13Self-attentionIn “Anna put the book down because it was heavy”, the word “it” alone explains little. It must connect to earlier fragments. A model processing text needs a way for one position's description to incorporate information f
2026-09-13TransformerYou want to translate “The train will arrive tomorrow”. Translating each word separately is insufficient: the correct form depends on other words and their order. The model needs a way to combine information from text, e
2026-08-30The same ranking yields different decisions after reorderingA system answering questions from documents often operates in four steps. A search engine finds candidates, a scorer assigns each one a number indicating its usefulness, a threshold rejects low scores, and a reader model
2026-08-30Batched pointwise scoringYou have a question and three retrieved documents. You want to score each one's usefulness, but three separate model calls repeat the same instruction and question. You can show all three together and ask for three score
2026-08-30nDCG@10A search engine returns ten results. Good documents may be on the list, but if the most useful is only tenth, the reader may never reach it. You need a measure accounting for both relevance and position. nDCG@10 measures
2026-08-30Order-consistency SFTYou show the model the same documents in two orders. One document's score changes from 0.70 to 0.60 . If you then discard documents below a threshold, shuffling alone can change the system's answer. You want to limit thi
2026-08-29Causal circuitA large model contains thousands of elements, but a smaller network of dependencies may lead to a particular answer. You want to check whether retaining only the relevant computational path can still reproduce the behavi
2026-08-29Interchange ablationYou suspect that a model connection carries information about the book's recipient. Replacing its value with zero may create a situation unlike normal computation. You want to change the information in a more controlled
2026-08-29Mechanistic interpretabilityThe model identified Mary as the book's recipient in “John gave Mary a book”. The correct answer does not yet explain how it obtained it. You want to check which internal computations actually caused this result. Mechani
2026-08-28Action chunkA robot moving through a crowd needs more than a single “turn now” command. A short plan of several movements can better describe its intent: slow down, avoid the obstacle, and return to the route. An action chunk is a s
2026-08-28Behavioral cloningYou want to teach a robot to avoid obstacles, but finding behaviors from scratch would be expensive. You have records of what a good controller did in different situations. You can begin by imitating those examples. Beha
2026-08-28CREATE-pathAn agent finds someone else's script as an example and writes its own tool based on it. The example contains a dangerous operation that the agent copies. A new filename and author may lead the system to treat the same co
2026-08-28Diffusion policyA robot needs to avoid a person. Both the left and right routes may be good, but their average would lead straight into the obstacle. You need a model capable of proposing different coherent behaviors, rather than just o
2026-08-28GRPOThe model creates several solutions to the same task. Some get better scores, others worse. You want to increase the chances of better behaviors by comparing responses within this group, without building an additional mo
2026-08-28On-policy self-distillationYou want to improve a model but do not have a separate, stronger teacher. The same model can receive an additional hint, such as the answer in the task text. Can its better informed version teach the version without that
2026-08-28Pseudo-labelYou have many training examples, but nobody supplied correct answers. You ask the model to estimate them and use those estimates as guidance for further learning. What actually enters the data then? A pseudo label is a l
2026-08-28Receding-horizon controlYou plan several steps, but the environment changes faster than you can execute the whole plan. A robot sees that a pedestrian suddenly turned. Completing the old sequence could be dangerous. Receding horizon control cre
2026-08-28Self-evolving agentAn agent wrote a useful script for checking a project. On the next similar task, it starts from scratch even though the earlier procedure could save work. You want experience from one task to help with later ones. A self
2026-08-28Signed quarantineAn agent saves a new tool in a library. If it immediately becomes an example for later tasks, a copied bug or malicious code can spread further. You need to separate permission to save a file from considering it trusted.
2026-08-28Test-time trainingA trained model receives a task unlike those it handled well. You can give it more attempts with the same settings, or try to adapt its weights while it works on the new task. These are two different operations. Test tim
2026-08-28Voting lies. Disagreement usually does notOn AIME 2026, the pseudo label from Qwen3 1.7B voting is wrong for about 85% of tasks. It is still possible to learn from this, because among the responses that disagree with the cluster, about 79% are also wrong. You wa
2026-08-27Attention sinkImagine a model reading a conversation for many hours. To limit memory, we retain only the latest fragments. In some models, discarding a few initial pieces of text can degrade performance even when their content seems u
2026-08-27Sliding windowThe model is creating a long response. It compares each next piece with earlier text, so computation and memory grow. What if we let it use only the latest part of the conversation? Sliding Window Attention restricts a p
2026-08-27Test-time scalingThe model answers a difficult task incorrectly. Instead of immediately building a larger model, you give it more time: it can prepare several solutions, compare them, or perform extra verification. Will a larger work bud
2026-08-26Delayed accelerationYou compare two training runs. In the first, you constrain weight growth; in the second, you do not. Initially the first performs worse, so it looks like a poor choice. Near the end, the situation reverses: it catches up
2026-08-26Frobenius normYou have a weight table with thousands of numbers and want one number describing their overall magnitude. A simple sum is misleading: 3 and −3 cancel even though both are large. You need a measure accounting for all entr
2026-08-26HyperballDuring training, not only which connections matter changes, but also the overall magnitude of their weights — numbers controlling how connections influence the result. You want to separate changes in the direction of the
2026-08-26RMSNormOne layer receives a list of large numbers, another much smaller values. These scale differences can complicate computation and learning. You want to standardize the signal's overall magnitude while preserving proportion
2026-08-26Scale invarianceYou double every number in part of a model. Does the answer change? Sometimes a following normalization removes the shared scale and the result stays the same. In other arrangements, this rescaling changes behavior. Scal
2026-08-26Weight decayThe model fits the data increasingly well, while its weights — numbers controlling computation — move away from zero. You want to constrain this growth without manually correcting millions of values. You need a rule oper
2026-04-26Critical Batch SizeCritical Batch Size You want to speed learning by showing the model more examples at once. Initially this helps. Beyond a point, however, you process much more data while the number of steps needed for a given result dec
2026-04-26Edge of StabilityEdge of Stability During learning, a model improves its weights in small steps. You expect its error to decrease smoothly. Yet in some experiments, results oscillate, local conditions appear unstable, and training still
2026-04-26GrokkingGrokking The model answers training tasks perfectly but makes mistakes on new examples of the same kind. It looks as though it memorized a table of answers. Training continues, and only much later do results on new examp
2026-04-26Implicit Regularization Through HyperparametersImplicit Regularization Through Hyperparameters Two models train on the same examples and reach similar training error, but one handles new data better. Only their training procedures differed. Where can the difference c
2026-04-26Neural Feature AnsatzNeural Feature Ansatz A model recognizes an image, but we do not know which input changes actually affect the answer. Do learned weights amplify precisely the directions of change to which the result is most sensitive? T
2026-04-26Scaling LawsScaling Laws You have a budget for model training. You can build a larger model or show a smaller one more text. Fully testing every combination would be expensive. You need a way to estimate what extra scale provides be
2026-04-26µP and Hyperparameter TransferµP and Hyperparameter Transfer Choosing a good learning step requires trials. For an enormous model, each trial is expensive. Can good settings be found in a small network and used after increasing its width, the number
2026-04-16Token EconomicsToken Economics Token Economics in LLMs Large Language Models is a set of principles, strategies, and models describing how the costs, management, and use of tokens — the basic units of text processing — affect the opera
2026-04-15Test-time ComputeTest time Compute The model needs to solve a difficult problem. You can request one short attempt or devote more work to proposals and checking them. Describing this cost requires a computation budget after training ends
2026-01-26Neural CollapseNeural Collapse You train a model to recognize cats, dogs, and birds in photos. Inside it, each photo gets a list of numbers describing features. After successful training, do these descriptions remain chaotic or form a
2025-01-01Types of tokens in LLMsTokens are the basic units of text processing in language models. They can be divided by role, visibility, and function. 1. Classification by processing flow Type Description Counted toward costs? Example Input Tokens fr
2024-01-01TokenToken You paste one sentence into a chat, and the counter shows a dozen or so units. Why not as many as there are words? A computer needs a defined way to divide text that also handles rare names, punctuation, and code f