Saddle Points in the Wild
A saddle point is a stationary point with both upward and downward curvature, and its escape routes lie along the negative-curvature directions revealed by the Hessian's eigenvalues.
14 min 7 scenes
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Technology & Computing
AI, programming, data, computing, and the internet.
When the Central Limit Theorem Wobbles
The bell-shaped limit survives mild dependence but changes shape — width, tail weight, and even symmetry — as correlation length and strength grow, and a single correlation time scale controls the transition.
16 min 8 scenes
What Really Moves the Weights?
Effective step size is the product of learning rate and gradient magnitude, so step length scales with both knob and slope.
18 min 9 scenes
Learning Rate or Bad Model? Diagnosing Training Failure
A trained eye reads loss curves, gradient norms, and weight updates to separate learning-rate failure from architectural or data failure — and knows which knob to turn next.
14 min 7 scenes
When a Learning Rate Diverges
A learning rate that worked can diverge when the loss landscape shifts under it — when gradients spike, curvature grows, or accumulated updates push the model into a steeper region — and you can read early warning signs before the explosion.
24 min 12 scenes
Why Gradient Descent Slows Near Saddle Points
A saddle point stalls gradient descent because the gradient itself nearly vanishes, and the surrounding curvature decides whether the algorithm escapes or gets stuck.
20 min 10 scenes
Why Stochastic Gradient Descent Beats Full-Batch
Gradient noise in SGD is not a bug to fix but a feature to exploit: it provides implicit regularization that helps the optimizer escape saddle points, traverse flat regions, and prefer wide minima that generalize.
18 min 9 scenes
How Can We Trust an Unsupervised Model?
Unsupervised models are evaluated by measurable properties of the structure they produce — internal consistency, stability under perturbation, and downstream usefulness — rather than by matching a hidden ground truth.
14 min 7 scenes
Hidden Dimensions in Data
How unsupervised learning reveals latent structure — clusters, low-dimensional manifolds, and anomalies — hidden inside high-dimensional data.
26 min 13 scenes
Is Modern AI Actually Unsupervised?
A clear separation between the textbook meaning of 'unsupervised learning' and the hybrid training pipelines behind modern AI, supported by concrete examples of each stage.
18 min 9 scenes
Can a Machine Discover Hidden Groups?
How an unsupervised algorithm like k-means turns feature vectors into discrete clusters, and why its verdict is real for some shapes and unreliable for others.
16 min 8 scenes
How Can a Machine Learn Without Answers?
Unsupervised learning works by turning raw inputs into compressed, similarity-based representations — clusters, dimensions, and patterns — that the model itself defines as 'consistent.'
16 min 8 scenes
How Machines Judge Similarity
Machines judge similarity by representing items as numerical vectors and computing the distance between them in a feature space.
8 min 4 scenes
TikTok FYP vs Instagram Explore
TikTok's For You Page learns you from pure watch behavior on strangers' videos, while Instagram's Explore learns you from likes and saves blended with your social graph — that's why they feel different.
8 min 4 scenes
有限域上模运算为何难逆
有限域上的模乘法本身是双射、结构完全确定，可一旦把多次乘法叠成幂，求逆就退化为遍历整个乘法群，规模随域大小指数膨胀。
8 min 4 scenes
Why the 7th Scale Degree Pulls Up
The raised 7th resolves up to tonic because a half step is smaller than a whole step, so upward motion covers the shortest distance to a stable pitch.
8 min 4 scenes
Photoshop Foundations
How the core Photoshop tools — selections, layers, masks, and adjustments — work together to transform and refine images.
24 min 12 scenes
Claude Architect Foundations
How to design, configure, and troubleshoot Claude-based agentic systems by reasoning about the agentic loop, MCP tool design, Claude Code workflows, structured prompting, and context management.
28 min 14 scenes
Blur Detective: Focus vs. Shake
Out-of-focus blur softens every edge uniformly into disc-like smears that ignore motion, while camera-shake blur smears every point in a single direction; inspecting edge shape and smear direction separates the two.
16 min 8 scenes
Why Photos Look Sharp or Blurry
A photo is sharp when light from each point converges to a single point on the sensor, and blur appears when focus error or subject motion spreads that light into a disc during exposure.
8 min 4 scenes
哈希函数抗碰撞的奥秘
抗碰撞性是指没有任何比穷举更快的方法能故意制造碰撞,哈希的安全性建立在计算不可行而非数学不可能之上。
8 min 4 scenes
When Rumors Die Out
A rumor dies out when fewer than one new person is infected per infected person before that person stops spreading — so survival depends on the reproduction ratio, not on how interesting the rumor is.
8 min 4 scenes
What Is a Filter Bubble?
A filter bubble is the personalized, algorithmically narrowed slice of information a platform shows you, and the clearest sign you're in one is when your feed feels uniformly agreeable and missing opposing views.
8 min 4 scenes
The Lost Tomb of Cleopatra
Cleopatra's tomb is most likely submerged beneath the ancient harbor of Alexandria because the city has been sinking for centuries.
8 min 4 scenes