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Softmax Function Explained: From Raw Scores to Probabilities

TLDR: Softmax converts a vector of raw scores (logits) into a valid probability distribution by exponentiating each value and dividing by the total. Subtracting the max before exponentiating prevents

·23 min read·81 views
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HyperLogLog Explained: Counting Billions of Unique Items with 12 KB

TLDR: HyperLogLog estimates the number of distinct elements in a dataset using ~12 KB of memory regardless of cardinality — with ±0.81% error. The insight: if you hash every element to a random bit st

·18 min read·4 views
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Count-Min Sketch Explained: Frequency Estimation at Streaming Scale

TLDR: Count-Min Sketch (CMS) is a fixed-size d × w counter matrix that estimates how often any element has appeared in a stream. Insert: hash the element with each of the d hash functions to get one c

·22 min read·2 views
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Clock Skew and Causality Violations: Why Distributed Clocks Lie

TLDR: Physical clocks on distributed machines cannot be perfectly synchronized. NTP keeps them within tens to hundreds of milliseconds in normal conditions — but under load, across datacenters, or aft

·19 min read·8 views
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Stale Reads and Cascading Failures in Distributed Systems

TLDR: Stale reads return superseded data from replicas that haven't yet applied the latest write. Cascading failures turn one overloaded node into a cluster-wide collapse through retry storms and redi

·25 min read
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Split Brain Explained: When Two Nodes Both Think They Are Leader

TLDR: Split brain happens when a network partition causes two nodes to simultaneously believe they are the leader — each accepting writes the other never sees. Prevent it with quorum consensus (at lea

·22 min read·10 views
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