AI WITH PROF. WHITAKER PARAMETERS What is ONE parameter?

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Why it worked

The video effectively breaks down a complex AI concept (parameters) into understandable analogies and visual aids, starting from a simple neuron and building up to large models. This step-by-step approach, combined with clear explanations of training and optimization, makes the information accessible and engaging for a broad audience interested in AI.

Summary

This video explains the concept of parameters in AI models, starting from a single neuron and scaling up to large language models. It details how parameters, which are learned numerical values (weights and biases), are used in computations and how they are adjusted during training to improve model performance. The video also touches upon the storage requirements and efficiency gains from techniques like quantization.

Structure

1Introduction to AI parameters and their scale
2Explaining parameters as learned numbers in a neuron
3The role of weights and bias in calculations
4How parameters change influence and are not hand-tuned
5Parameters as matrices in transformers and their function
6The training process: prediction, loss, backpropagation, and updates
7The impact of parameter count and architecture
8

Original caption

AI models can have billions — even trillions — of parameters. But what does that actually mean? They aren’t facts. They aren’t memories. And they definitely aren’t billions of lines of code. Parameters are the learned numbers that control how a neural network transforms information — tiny weights and biases, repeated across an enormous mathematical system. Prof. Whitaker breaks down what a “parameter” actually is, starting with a single artificial neuron and scaling all the way up to modern LLMs. Once you understand this, model sizes like 7B, 70B, or 1T parameters finally start to make sense. #AI #ArtificialIntelligence #MachineLearning #LLM #NeuralNetworks

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AI WITH PROF. WHITAKER PARAMETERS What is ONE parameter? GPT-6 ASTRO 2,055,844,907,407 PARAMETERS? Hypothesis -- not an official specification Start with one learned value. FutureWithAI 01 / 31 AI WITH PROF. WHITAKER PARAMETERS AI with Prof. Whitaker PARAMETERS Unfortunately, mathematics. FutureWithAI 02 / 31 X1w1 + X2w2 + X3w3 + b A short course in learned numbers. FutureWithAI 03 / 31 First, a correction. A = B FACT FILE [ ] MEMORY </> CODE ≠ PARAMETER A parameter is a learned number. FutureWithAI 04 / 31 A mathematical function. Input. Computation. Prediction. TEXT VECTORS TRANSFORM TRANSFORM PROBABILITIES MAT 72% FLOOR 14% CHAIR 6% Illustrative; other tokens omitted FutureWithAI 05 / 31 One tiny neuron. Σ neuron Three inputs. One computation. FutureWithAI 06 / 31 Weights. And bias. X1 X2 X3 w1 w2 w3 b Σ neuron The x values are inputs. The w values and b are learned. FutureWithAI 07 / 31 Numbers change influence. X1 X2 X3 w1 = +1.00 w2 = +1.00 w3 = +1.00 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +3.00 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 08 / 31 X1 X2 X3 w1 = +2.14 w2 = +1.00 w3 = +1.00 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +4.14 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 09 / 31 X1 X2 X3 w1 = +2.40 w2 = +1.00 w3 = +1.00 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +4.40 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 10 / 31 X1 X2 X3 w1 = +2.40 w2 = +0.50 w3 = +1.00 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +3.90 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 11 / 31 X1 X2 X3 w1 = +2.40 w2 = +0.01 w3 = +1.00 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +3.41 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 12 / 31 X1 X2 X3 w1 = +2.40 w2 = +0.01 w3 = -1.30 b Σ neuron Hold x1 = x2 = x3 = 1, b = 0 Weighted sum = +1.11 Illustrative input and weight values Same inputs. Different influence. FutureWithAI 13 / 31 Not hand-tuned. w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28 NOT MANUALLY PROGRAMMED Thankfully. We have weekends. FutureWithAI 14 / 31 From weights to matrices. W1 +0.310 W2 W3 One reusable idea, at a much larger scale. FutureWithAI 15 / 31 W1 +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 WEIGHT MATRIX vector X W new vector FutureWithAI 16 / 31 Inside a transformer. TOKEN → EMBEDDING ATTENTION Learned values throughout the computation. FutureWithAI 17 / 31 TOKEN → EMBEDDING ATTENTION FEED-FORWARD OUTPUT SCORES MAT 72% FLOOR 14% CHAIR 6% Illustrative; other tokens omitted Learned values throughout the computation. FutureWithAI 18 / 31 70 billion... what? 70B PARAMETERS learned numerical values +0.310 Values used in computation. FutureWithAI 19 / 31 +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 Values used in computation. FutureWithAI 20 / 31 The wrong mental model. WRONG MENTAL MODEL #8,482,193 There is no one-fact-per-slot map. FutureWithAI 21 / 31 #8,482,193 Earth orbits Sun #15,821,992 Python uses indentation FutureWithAI 22 / 31 Distributed influence. PARIS / FRANCE Conceptual illustration, not a mechanistic map Many values. Overlapping effects. FutureWithAI 23 / 31 GRAMMAR Conceptual illustration, not a mechanistic map Many values. Overlapping effects. FutureWithAI 24 / 31 GRAMMAR GEOGRAPHY Conceptual illustration, not a mechanistic map Many values. Overlapping effects. FutureWithAI 25 / 31 Where do the numbers come from? +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 TRAINING Training. FutureWithAI 26 / 31 Start almost at random. +0.012 INITIAL WEIGHTS Small values. An untrained function. FutureWithAI 27 / 31 +0.012 -0.033 +0.006 +0.043 +0.001 -0.016 +0.000 -0.001 +0.001 +0.009 +0.029 -0.004 +0.013 +0.000 -0.003 +0.001 +0.017 -0.021 +0.008 +0.027 INITIAL WEIGHTS Then: predict text. Small values. An untrained function. FutureWithAI 28 / 31 A prediction. The capital of France is... Other tokens: 30% (not shown) The training data supplies the target. FutureWithAI 29 / 31 London 35% Paris 20% Rome 15% Other tokens: 30% (not shown) TARGET: PARIS The training data supplies the target. FutureWithAI 30 / 31 Measure the error. PREDICTION TARGET: PARIS COMPARE Natural-log cross-entropy A number the training system can minimize. FutureWithAI 31 / 31 Follow the gradient. WEIGHTS LAYERS LOSS +0.310 -0.820 +0.140 Backprop computes gradients. The optimizer updates weights. FutureWithAI 32 / 31 GRADIENTS +0.310 -0.820 +0.140 +0.312 -0.817 +0.139 OPTIMIZER: SMALL UPDATE Backprop computes gradients. The optimizer updates weights. FutureWithAI 33 / 31 Repeat. PREDICTION LOSS BACKPROP GRADIENTS UPDATE Many small updates. FutureWithAI 34 / 31 PREDICTION STEP 1 Illustrative iteration counter Many small updates. FutureWithAI 35 / 31 PREDICTION STEP 10,000 Illustrative iteration counter Many small updates. FutureWithAI 36 / 31 PREDICTION STEP 1,000,000 Illustrative iteration counter Many small updates. FutureWithAI 37 / 31 Training changes numbers. MEMORY SLOT #4,000,000 PARIS +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 SMALL NUMERICAL UPDATES Paris 20% → Paris ↑ Better predictions through small adjustments. FutureWithAI 38 / 31 +0.312 -0.817 +0.139 +1.072 +0.033 -0.411 +0.008 -0.025 +0.012 +0.227 +0.718 -0.103 +0.335 +0.012 -0.075 SMALL NUMERICAL UPDATES Paris 20% → Paris ↑ Better predictions through small adjustments. FutureWithAI 39 / 31 Patterns take shape. Conceptual illustration, not a mechanistic map Distributed patterns, not separate filing cabinets. FutureWithAI 40 / 31 GRAMMAR Conceptual illustration, not a mechanistic map Distributed patterns, not separate filing cabinets. FutureWithAI 41 / 31 GRAMMAR FACTUAL ASSOCIATIONS Conceptual illustration, not a mechanistic map Distributed patterns, not separate filing cabinets. FutureWithAI 42 / 31 STYLE CONCEPTS Conceptual illustration, not a mechanic map Distributed patterns, not separate filing cabinets. FutureWithAI 43 / 31 STYLE RELATIONSHIPS CONCEPTS PATTERNS Conceptual illustration, not a mechanistic map Distributed patterns, not separate filing cabinets. FutureWithAI 44 / 31 Capacity. FEWER CONTROLS MORE CONTROLS Illustration of flexibility, not a performance test More adjustable degrees of freedom. FutureWithAI 45 / 31 Bigger ≠ better. 500B > 100B Parameter count is not a performance score. FutureWithAI 46 / 31 500B ≠ 100B ARCHITECTURE DATA OPTIMIZATION COMPUTE POST-TRAINING INFERENCE CONTEXT COUNT ≠ PERFORMANCE Parameter count is not a performance score. FutureWithAI 47 / 31 Mixture of Experts. TOKEN ROUTER EXPERT A EXPERT B EXPERT C EXPERT D EXPERT E EXPERT F EXPERT G EXPERT H ILLUSTRATIVE EXAMPLE Some models route tokens through selected components. FutureWithAI 48 / 31 Total ≠ active. 500B TOTAL ILLUSTRATIVE EXAMPLE Wonderful. Another number. FutureWithAI 49 / 31 500B TOTAL TOTAL PARAMETERS ≠ ACTIVE PARAMETERS ILLUSTRATIVE EXAMPLE Wonderful. Another number. FutureWithAI 50 / 31 Numbers need storage. Before runtime overhead, KV cache, etc. Raw weights only. Runtime needs more memory. FutureWithAI 51 / 31 70B parameters × 16 bits 16 bits = 2 bytes 70B × 2 bytes ≈ 140 GB of weights Before runtime overhead, KV cache, etc. Raw weights only. Runtime needs more memory. FutureWithAI 52 / 31 Less precision. PARAMETERS = 70B 16-BIT 1 0 1 0 1 0 1 0 1 0 1 0 1 0 4-BIT 1 0 1 0 fewer precision levels QUANTIZATION The number of parameters stays the same. FutureWithAI 53 / 31 Same count. Less storage. 70B 16-bit ≈ 140 GB SAME COUNT: 70B Weight storage approximation. 70B 4-bit ≈ 35 GB FutureWithAI 54 / 31 Return to the number. 70,000,000,000 PARAMETERS FACT? FACT? FACT? FACT? FACT? FACT? Transform → Predict Numbers shaping a mathematical function. FutureWithAI 55 / 31 +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 +0.016 +0.415 -0.521 +0.197 +0.682 TRANSFORM → PREDICT Numbers shaping a mathematical function. FutureWithAI 56 / 31 Learned numbers. LEARNED NUMBERS SHAPE COMPUTATION SHAPE BEHAVIOR Parameter count ≠ fact count. A rough measure of learned capacity. Parameter count ≠ fact count. FutureWithAI 57 / 31 PARAMETER COUNT ≠ FACT COUNT A rough measure of learned capacity. Parameter count ≠ fact count. FutureWithAI 58 / 31 A great many knobs. +0.310 -0.820 +0.140 +1.070 +0.030 -0.410 +0.006 -0.028 +0.013 +0.225 +0.715 -0.102 +0.333 +0.009 -0.074 +0.016 +0.415 -0.521 +0.197 +0.682 A GREAT MANY KNOBS. AI with Prof. Whitaker FutureWithAI 59 / 31

Transcript

OpenAI says their new model GPT-6 Astra has 2,055,844,907,407 parameters. Hypothesis -- not an official specification. Start with one learned value. AI with Prof. Whitaker. Parameters. Unfortunately, mathematics. X1w1 + X2w2 + X3w3 + b. A short course in learned numbers. First, a correction. A = B. FACT. FILE. [ ]. MEMORY. </>. CODE. ≠ PARAMETER. A parameter is a learned number. A mathematical function. Input. Computation. Prediction. TEXT. VECTORS. TRANSFORM. TRANSFORM. PROBABILITIES. MAT 72%. FLOOR 14%. CHAIR 6%. Illustrative; other tokens omitted. One tiny neuron. Σ neuron. Three inputs. One computation. Weights. And bias. X1 w1. X2 w2. X3 w3. b. Σ neuron. The x values are inputs. The w values and b are learned. Numbers change influence. X1 w1 = +1.00. X2 w2 = +1.00. X3 w3 = +1.00. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +3.00. Illustrative input and weight values. Same inputs. Different influence. X1 w1 = +2.14. X2 w2 = +1.00. X3 w3 = +1.00. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +4.14. Illustrative input and weight values. Same inputs. Different influence. X1 w1 = +2.40. X2 w2 = +1.00. X3 w3 = +1.00. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +4.40. Illustrative input and weight values. Same inputs. Different influence. X1 w1 = +2.40. X2 w2 = +0.50. X3 w3 = +1.00. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +3.90. Illustrative input and weight values. Same inputs. Different influence. X1 w1 = +2.40. X2 w2 = +0.01. X3 w3 = +1.00. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +3.41. Illustrative input and weight values. Same inputs. Different influence. X1 w1 = +2.40. X2 w2 = +0.01. X3 w3 = -1.30. b. Σ neuron. Hold x1 = x2 = x3 = 1, b = 0. Weighted sum = +1.11. Illustrative input and weight values. Same inputs. Different influence. Not hand-tuned. w1 w2 w3 w4 w5 w6 w7 w8 w9 w10 w11 w12 w13 w14 w15 w16 w17 w18 w19 w20 w21 w22 w23 w24 w25 w26 w27 w28. NOT MANUALLY PROGRAMMED. Thankfully. We have weekends. From weights to matrices. W1 +0.310. W2. W3. One reusable idea, at a much larger scale. W1 +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. WEIGHT MATRIX. vector X W new vector. Inside a transformer. TOKEN → EMBEDDING. ATTENTION. Learned values throughout the computation. TOKEN → EMBEDDING. ATTENTION. FEED-FORWARD. OUTPUT SCORES. MAT 72%. FLOOR 14%. CHAIR 6%. Illustrative; other tokens omitted. Learned values throughout the computation. 70 billion... what? 70B PARAMETERS. learned numerical values. +0.310. Values used in computation. +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. Values used in computation. The wrong mental model. WRONG MENTAL MODEL. #8,482,193. There is no one-fact-per-slot map. #8,482,193 Earth orbits Sun. #15,821,992 Python uses indentation. Distributed influence. PARIS / FRANCE. Conceptual illustration, not a mechanistic map. Many values. Overlapping effects. GRAMMAR. Conceptual illustration, not a mechanistic map. Many values. Overlapping effects. GRAMMAR. FACTUAL ASSOCIATIONS. Conceptual illustration, not a mechanistic map. Many values. Overlapping effects. STYLE. CONCEPTS. Conceptual illustration, not a mechanistic map. Many values. Overlapping effects. STYLE. RELATIONSHIPS. CONCEPTS. PATTERNS. Conceptual illustration, not a mechanistic map. Many values. Overlapping effects. Where do the numbers come from? +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. TRAINING. Training. Start almost at random. +0.012. INITIAL WEIGHTS. Small values. An untrained function. +0.012 -0.033 +0.006 +0.043 +0.001. -0.016 +0.000 -0.001 +0.001 +0.009. +0.029 -0.004 +0.013 +0.000 -0.003. +0.001 +0.017 -0.021 +0.008 +0.027. INITIAL WEIGHTS. Then: predict text. Small values. An untrained function. A prediction. The capital of France is... Other tokens: 30% (not shown). The training data supplies the target. London 35%. Paris 20%. Rome 15%. Other tokens: 30% (not shown). TARGET: PARIS. The training data supplies the target. Measure the error. PREDICTION. TARGET: PARIS. COMPARE. Natural-log cross-entropy. A number the training system can minimize. LOSS = 1.61. -ln(0.20) = 1.61. Natural-log cross-entropy. A number the training system can minimize. Follow the gradient. WEIGHTS. LAYERS. LOSS. +0.310 -0.820 +0.140. Backprop computes gradients. The optimizer updates weights. GRADIENTS. +0.310 -0.820 +0.140. +0.312 -0.817 +0.139. OPTIMIZER: SMALL UPDATE. Backprop computes gradients. The optimizer updates weights. Repeat. PREDICTION. LOSS. BACKPROP. GRADIENTS. UPDATE. Many small updates. PREDICTION. STEP 1. Illustrative iteration counter. Many small updates. PREDICTION. STEP 10,000. Illustrative iteration counter. Many small updates. PREDICTION. STEP 1,000,000. Illustrative iteration counter. Many small updates. Training changes numbers. MEMORY SLOT #4,000,000. PARIS. +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. SMALL NUMERICAL UPDATES. Paris 20% → Paris ↑. Better predictions through small adjustments. +0.312 -0.817 +0.139 +1.072 +0.033. -0.411 +0.008 -0.025 +0.012 +0.227. +0.718 -0.103 +0.335 +0.012 -0.075. SMALL NUMERICAL UPDATES. Paris 20% → Paris ↑. Better predictions through small adjustments. Patterns take shape. Distributed patterns, not separate filing cabinets. GRAMMAR. Distributed patterns, not separate filing cabinets. GRAMMAR. FACTUAL ASSOCIATIONS. Distributed patterns, not separate filing cabinets. STYLE. CONCEPTS. Distributed patterns, not separate filing cabinets. STYLE. RELATIONSHIPS. CONCEPTS. PATTERNS. Distributed patterns, not separate filing cabinets. Capacity. FEWER CONTROLS. MORE CONTROLS. Illustration of flexibility, not a performance test. More adjustable degrees of freedom. Bigger ≠ better. 500B > 100B. Parameter count is not a performance score. 500B ≠ 100B. ARCHITECTURE. DATA. OPTIMIZATION. COMPUTE. POST-TRAINING. INFERENCE. CONTEXT. COUNT ≠ PERFORMANCE. Parameter count is not a performance score. Mixture of Experts. TOKEN. ROUTER. EXPERT A. EXPERT B. EXPERT C. EXPERT D. EXPERT E. EXPERT F. EXPERT G. EXPERT H. ILLUSTRATIVE EXAMPLE. Some models route tokens through selected components. Total ≠ active. 500B TOTAL. ILLUSTRATIVE EXAMPLE. Wonderful. Another number. 500B TOTAL. TOTAL PARAMETERS ≠ ACTIVE PARAMETERS. ILLUSTRATIVE EXAMPLE. Wonderful. Another number. Numbers need storage. Before runtime overhead, KV cache, etc. Raw weights only. Runtime needs more memory. 70B parameters × 16 bits. 16 bits = 2 bytes. 70B × 2 bytes ≈ 140 GB of weights. Before runtime overhead, KV cache, etc. Raw weights only. Runtime needs more memory. Less precision. PARAMETERS = 70B. 16-BIT. 1 0 1 0 1 0 1 0. 1 0 1 0 1 0 1 0. 4-BIT. 1 0 1 0. fewer precision levels. QUANTIZATION. The number of parameters stays the same. Same count. Less storage. 70B 16-bit ≈ 140 GB. SAME COUNT: 70B. Weight storage approximation. 70B 4-bit ≈ 35 GB. Return to the number. 70,000,000,000 PARAMETERS. FACT? FACT? FACT? FACT? FACT? FACT? TRANSFORM → PREDICT. Numbers shaping a mathematical function. +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. TRANSFORM → PREDICT. Numbers shaping a mathematical function. Learned numbers. LEARNED NUMBERS. SHAPE COMPUTATION. SHAPE BEHAVIOR. Parameter count ≠ fact count. A rough measure of learned capacity. Parameter count ≠ fact count. PARAMETER COUNT ≠ FACT COUNT. A rough measure of learned capacity. Parameter count ≠ fact count. A great many knobs. +0.310 -0.820 +0.140 +1.070 +0.030. -0.410 +0.006 -0.028 +0.013 +0.225. +0.715 -0.102 +0.333 +0.009 -0.074. +0.016 +0.415 -0.521 +0.197 +0.682. A GREAT MANY KNOBS. AI with Prof. Whitaker.