Happening Faster Than Ever? Yes, It Is • AI User + Usage + CapEx Growth = Unprecedented • AI Model Compute Costs High / Rising + Inference Costs Per Token Falling = Performance Converging + Developer Usage 4/25 75% 60% 10% 21% 15% 0% Details on Page 293 USA – LLM #1 China USA – LLM #2 AI Model Compute Costs High / Rising + Inference Costs Per Token Falling = Performance Converging + Developer Usage Leading USA-Based AI LLM Revenue vs. Compute Expense Note: Figures are estimates. Source: The Information, public estimates 2022 2024 Revenue (Blue) & Compute Expense (Red) +$3.7B -$5B Details

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs to give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A,B] .⊗ [C,D] will compute [A⊗C, B⊗D] with no additional coding.CHAPTER 5. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 5.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs to give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A,B] .⊗ [C,D] will compute [A⊗C, B⊗D] with no additional coding.CHAPTER 5. MATHEMATICAL OPERATIONS AND ELEMENTARY FUNCTIONS "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 5.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.8 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies

Moreover, like all vectorized "dot calls," these "dot operators" are fusing. For example, if you compute 2 .* A.^2 .+ sin.(A) (or equivalently @. 2A^2 + sin(A), using the @. macro) for an array A, it performs give a convenient infix syntax A ⊗ B for Kronecker products (kron), then [A, B] .⊗ [C, D] will compute [A⊗C, B⊗D] with no additional coding. Combining dot operators with numeric literals can be ambiguous "vectorized" fashion to arrays and other collections with the dot syntax f.(A), e.g. sin.(A) will compute the sine of each element of an array A. 6.7 Operator Precedence and Associativity Julia applies