Shorts
Single-idea notes drawn from the longer pieces. 1-2 minutes each. Use the search to narrow by topic, tag, or track — or browse the full feed →.
31 shorts
A matrix turns and stretches every arrow in space — except for a few special directions it only stretches. Those are eigenvectors, the natural grain of the transformation.
Once you know a matrix's un-turnable directions, you can rewrite the whole thing as three simple moves: rotate, stretch, rotate back. That's eigendecomposition.
Eigenvectors are beautiful on paper. Computing them for a 100,000×100,000 matrix is an engineering problem — and the tool that does it, iteratively, is an eigensolver.
Supervised fine-tuning is the imitation step of post-training: show the model (prompt → ideal answer) pairs and minimize cross-entropy on the target tokens. It teaches the format of being an assistant — and hits a ceiling that preference learning exists to break.
Reinforcement Learning from Human Feedback is how a model is bent from optimizing likelihood to optimizing preference: an SFT base, a reward model trained on human comparisons, and a policy optimized against that reward under a KL leash.
Reinforcement Learning from AI Feedback swaps the human labeler for a model: a capable model judges which of two responses is better, and those AI preferences train the reward. Constitutional AI is its most influential form — and the values don't disappear, they move and become explicit.
GQA sits between full multi-head attention and MQA: query heads are partitioned into a small number of groups, and each group shares one K/V set. Most of the KV-cache savings of MQA, most of the head diversity of MHA — and a cheap conversion path from existing checkpoints.
Why long context costs memory, not flops. The KV-cache size formula has six factors — once you can read it, every attention-variant design choice falls into place.
The most famous LLM bug — miscounting letters in a word — is not a reasoning failure. It is a representation failure. The model isn't fed letters, it's fed tokens. Once you know what a token actually is, the bug is the only outcome that could have happened.
Three sampling knobs, three different operations on the same next-token distribution. Temperature reshapes; top_k truncates by count; top_p truncates by cumulative probability. They are not interchangeable.
The graph that turned vector search from O(N) into O(log N). A hierarchy of small-world graphs, three tunable parameters, and the recall/latency trade-off underneath every production vector database.
Two retrieval philosophies — lexical evidence vs learned geometry — fail in exactly opposite ways. That's why production retrieval is rarely pure dense, and why Reciprocal Rank Fusion ended up everywhere.
A bi-encoder encodes query and document independently; a cross-encoder reads them together. One is cheap and slightly dumb, the other is expensive and much sharper. Modern retrieval uses both — and the two-stage cascade is the whole point.
The same data, two layouts on disk. For analytical queries that touch a few columns out of many, Parquet reads tens of times less from disk than CSV — and that gap is structural, not a benchmark artifact.
Partition count is the ceiling on parallel consumption. Ordering is a per-partition guarantee, not a per-topic one. Two facts that decide most Kafka architecture questions.
Random k-fold CV reshuffles time. On time series that means training on the future to predict the past — and quietly inflating every metric. The correct alternatives are expanding-window and rolling-window CV.
Three components, one additive identity. STL splits a series into trend, seasonality, and residual so you can see what's actually in it before modeling — and the same decomposition idea propagates into modern deep architectures like N-BEATS.
Everyone trains classifiers with cross-entropy, far fewer can say why that loss and not another. It isn't a design choice — it falls out of one principle: maximize the probability the model assigns to the data. Cross-entropy, log-loss, MSE, and KL are the same idea wearing four different hats.
KL divergence turns up in cross-entropy training, VAEs and variational inference, knowledge distillation, and the RLHF leash. That isn't a coincidence — a huge fraction of ML is secretly the sentence 'make distribution q close to distribution p,' and KL is what that sentence reduces to.
Everyone knows attention is softmax(QKᵀ/√d)V. Fewer notice it's structurally the same thing as kernel regression — Nadaraya-Watson smoothing from 1964, with a learned similarity. Seeing the kernel underneath tells you immediately how to make attention linear.
The evidence lower bound looks like a formula handed down from on high. It isn't invented — it's forced. When the evidence integral is intractable but you still want maximum likelihood, there is essentially one move available, and the ELBO is what it produces.
Three different similarity measures that, on normalized embeddings, all rank the same. Why cosine is the convention, why dot is the implementation, and when the choice actually matters.
TCN stands for Temporal Convolutional Network — a causal CNN with dilated convolutions that gives sequence models exponential receptive field for the cost of linear depth.
Univariate is one signal over time. Multivariate is many signals over time. The decision between them is about whether the extra signals actually carry information about the target.
ARIMA in three letters: AutoRegression, Integration, Moving Average. SARIMA adds seasonal versions of each. Together they handle the linear, stationary case — which covers a surprising amount of forecasting.
Why production LLM decoders share K and V across attention heads — and the 8–32× memory cut that follows.
An LLM agent is an LLM wrapped in a loop that gives it tools, state, and a stopping rule. The architecture is the shape of that loop.
MLA stores a low-rank latent representation for each token and uses learned projections to produce the K/V information needed by attention at decode time. A different way to attack the KV-cache problem than MQA or GQA — trading a sharing bottleneck for a rank one.
Each interpolation method makes a different assumption about what was happening between known measurements. The right method depends on what the signal actually does between samples, not on what's the default.
TS preprocessing is a pipeline, not a checklist. The order of steps changes the result — scaling before handling missing values is the common trap.
Time series is one entity over time. Panel data is many entities over time. The new dimension — unit-level heterogeneity — is what panel methods exist to handle.