Ishaan Sandhwar — writingDerivations and notes on machine learning, deployment and GATE CS.https://ishaansandhwar.netlify.app/en-gbThe master theorem, and the recurrences it refuses to solvehttps://ishaansandhwar.netlify.app/writing/master-theorem-recurrences/https://ishaansandhwar.netlify.app/writing/master-theorem-recurrences/The three cases with the comparison that decides them, worked on merge sort, binary search and Strassen — plus the GATE favourite that falls in the gap.Tue, 01 Sep 2026 00:00:00 GMTAlgorithmsGATEComplexityNormalisation up to BCNF, and the dependency you have to give uphttps://ishaansandhwar.netlify.app/writing/normalisation-to-bcnf/https://ishaansandhwar.netlify.app/writing/normalisation-to-bcnf/Attribute closure, candidate keys, and 1NF through BCNF on one small relation — including the standard example where BCNF costs you a functional dependency.Tue, 01 Sep 2026 00:00:00 GMTDBMSGATENormalisationThe split is the experiment — five ways data leakshttps://ishaansandhwar.netlify.app/writing/leakage-and-the-split/https://ishaansandhwar.netlify.app/writing/leakage-and-the-split/Why fitting a scaler before splitting inflates your score, plus the group, temporal and duplicate leaks that survive a correct train_test_split.Sat, 29 Aug 2026 00:00:00 GMTEvaluationscikit-learnMethodologyBias, variance, and what L1 and L2 actually do to the weightshttps://ishaansandhwar.netlify.app/writing/bias-variance-and-regularisation/https://ishaansandhwar.netlify.app/writing/bias-variance-and-regularisation/The decomposition derived in four lines, then why ridge shrinks everything and lasso sets coefficients to exactly zero.Wed, 26 Aug 2026 00:00:00 GMTRegularisationModel selectionStatisticsBackpropagation by hand — one forward pass, one backward pass, real numbershttps://ishaansandhwar.netlify.app/writing/backpropagation-by-hand/https://ishaansandhwar.netlify.app/writing/backpropagation-by-hand/A two-layer network worked end to end with arithmetic you can check, including the update and the loss afterwards to prove it went down.Sat, 22 Aug 2026 00:00:00 GMTBackpropagationNeural networksChain ruleSoftmax without overflow — the max-subtraction trick, provedhttps://ishaansandhwar.netlify.app/writing/softmax-without-overflow/https://ishaansandhwar.netlify.app/writing/softmax-without-overflow/Why exp() overflows at around 709, why subtracting the max changes nothing mathematically, and how log-sum-exp keeps the whole thing finite.Tue, 18 Aug 2026 00:00:00 GMTNumerical stabilitySoftmaxFundamentalsLogistic regression, and why the gradient is just (p − y)https://ishaansandhwar.netlify.app/writing/logistic-regression-cross-entropy/https://ishaansandhwar.netlify.app/writing/logistic-regression-cross-entropy/Deriving the sigmoid's derivative, the cross-entropy loss, and the one-line gradient that falls out — plus why squared error is the wrong loss for classification.Fri, 14 Aug 2026 00:00:00 GMTClassificationCross-entropyOptimisationLinear regression two ways — closed form and gradient descenthttps://ishaansandhwar.netlify.app/writing/linear-regression-two-ways/https://ishaansandhwar.netlify.app/writing/linear-regression-two-ways/Deriving the normal equation from the gradient, solving a three-point dataset by hand, and the cost analysis that says when to give up on the exact answer.Tue, 11 Aug 2026 00:00:00 GMTRegressionLinear algebraOptimisationFrom one derivative to gradient descent, with numbershttps://ishaansandhwar.netlify.app/writing/derivative-to-gradient-descent/https://ishaansandhwar.netlify.app/writing/derivative-to-gradient-descent/What a derivative actually tells you, why the update rule subtracts it, and the exact learning rate at which the whole thing blows up.Fri, 07 Aug 2026 00:00:00 GMTCalculusOptimisationFundamentalsShapes first — vectors, matrices, and why matmul is the whole gamehttps://ishaansandhwar.netlify.app/writing/shapes-first-matmul/https://ishaansandhwar.netlify.app/writing/shapes-first-matmul/The linear algebra you need before any of the rest makes sense, written as the shape rules I check before running anything.Tue, 04 Aug 2026 00:00:00 GMTLinear algebraNumPyFundamentalsAttention, derived rather than quotedhttps://ishaansandhwar.netlify.app/writing/attention-from-scratch/https://ishaansandhwar.netlify.app/writing/attention-from-scratch/Most explanations hand you softmax(QKᵀ/√d) and move on. Here is where each piece comes from, why the scaling factor is a square root, and what breaks without it.Sat, 14 Feb 2026 00:00:00 GMTTransformersAttentionFrom first principlesYour model is not wrong, it is overconfidenthttps://ishaansandhwar.netlify.app/writing/calibration-not-accuracy/https://ishaansandhwar.netlify.app/writing/calibration-not-accuracy/Accuracy tells you how often the label is right. Calibration tells you whether the confidence means anything — and for anything with a human downstream, the second matters more.Thu, 22 Jan 2026 00:00:00 GMTCalibrationEvaluationDeploymentFine-tuning a 7B model on a 12GB cardhttps://ishaansandhwar.netlify.app/writing/qlora-on-one-gpu/https://ishaansandhwar.netlify.app/writing/qlora-on-one-gpu/The memory arithmetic that decides whether a fine-tune fits, and the four settings that actually move the number. No A100 required.Mon, 08 Dec 2025 00:00:00 GMTQLoRAPEFTTutorialPage replacement, and the GATE trap in Belady's anomalyhttps://ishaansandhwar.netlify.app/writing/page-replacement-gate/https://ishaansandhwar.netlify.app/writing/page-replacement-gate/FIFO, LRU and Optimal worked end to end on one reference string, plus the question pattern that catches people every year.Mon, 03 Nov 2025 00:00:00 GMTOperating systemsGATEMemory managementIn a RAG system, retrieval is the modelhttps://ishaansandhwar.netlify.app/writing/retrieval-is-the-model/https://ishaansandhwar.netlify.app/writing/retrieval-is-the-model/Three weeks of fine-tuning bought six points. Two days of fixing chunking bought nineteen. Here is why that keeps happening.Sun, 19 Oct 2025 00:00:00 GMTRAGRetrievalLLM engineering