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Concepts532

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📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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📚TheoryIntermediate

Temporal Convolutions

Temporal (causal) convolution computes each output at time t using only the current and past inputs, ensuring no future information leakage.

#temporal convolution#causal convolution#fir filter+12
📚TheoryAdvanced

Mamba & Selective State Spaces

Mamba uses a state-space model whose parameters are selected (gated) by the current input token, letting the model adapt its memory dynamics at each step.

#mamba
12345
#selective state space
#ssm
+12
∑MathIntermediate

State Space Models (SSM)

A State Space Model (SSM) describes a dynamical system using a state vector x(t) that evolves via a first-order matrix differential equation and produces outputs y(t).

#state space#matrix exponential#controllability+12
📚TheoryIntermediate

LSTM & Gating Mechanisms

Long Short-Term Memory (LSTM) networks use gates (forget, input, and output) to control what information to erase, write, and reveal at each time step.

#lstm#forget gate#input gate+11
📚TheoryIntermediate

Recurrent Neural Network Theory

A Recurrent Neural Network (RNN) processes sequences by carrying a hidden state that is updated at every time step using h_t = f(W_h h_{t-1} + W_x x_t + b).

#recurrent neural network#rnn#backpropagation through time+12
📚TheoryIntermediate

Multi-Task Loss Balancing

Multi-task loss balancing aims to automatically set each task’s weight so that no single loss dominates training.

#multi-task learning#uncertainty weighting#homoscedastic uncertainty+12
∑MathIntermediate

Surrogate Loss Theory

0-1 loss directly measures classification error but is discontinuous and non-convex, making optimization computationally hard.

#surrogate loss#0-1 loss#hinge loss+12
📚TheoryIntermediate

Knowledge Distillation Loss

Knowledge distillation loss blends standard hard-label cross-entropy with a soft distribution match from a teacher using a temperature parameter.

#knowledge distillation#kd loss#temperature scaling+12
📚TheoryAdvanced

CTC Loss (Connectionist Temporal Classification)

CTC loss trains sequence models when you do not know the alignment between inputs (frames) and outputs (labels).

#ctc loss#connectionist temporal classification#forward backward+12
📚TheoryIntermediate

Perceptual Loss & Feature Matching

Perceptual loss compares images in a deep network's feature space rather than raw pixels, which aligns better with human judgment of similarity.

#perceptual loss#feature matching#gan+12
📚TheoryIntermediate

Triplet Loss & Contrastive Loss

Triplet loss and contrastive loss are metric-learning objectives that teach a model to map similar items close together and dissimilar items far apart in an embedding space.

#triplet loss#contrastive loss#metric learning+12
📚TheoryIntermediate

Focal Loss

Focal Loss reshapes cross-entropy so that hard, misclassified examples get more focus while easy, well-classified ones are down-weighted.

#focal loss#class imbalance#cross-entropy+11