HASKELL: OCAML ACTIVATION FUNCTIONS & DERIVATIVES

REVISED: Wednesday, October 8, 2025

1. OCAML ACTIVATION FUNCTIONS & DERIVATIVES

============================

ocaml C:\AI2025\lesson4.ml

Lesson 4: Activation Functions & Derivatives

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Objective:

1. Implement key activation functions for neural networks

2. Compute their derivatives

3. Prepare for gradient-based learning

(* -----------------------------

1. ReLU (Rectified Linear Unit)

----------------------------- *)

let relu x = if x > 0. then x else 0.

(* ReLU returns x if positive, 0 otherwise *)

let relu_derivative x = if x > 0. then 1. else 0.

(* Derivative of ReLU: 1 if x > 0, else 0 *)

(* -----------------------------

2. Sigmoid

----------------------------- *)

let sigmoid x = 1. /. (1. +. exp (-.x))

(* Sigmoid squashes input to range (0,1) *)

let sigmoid_derivative x =

let s = sigmoid x in

s *. (1. -. s)

(* Derivative of sigmoid: s*(1-s) *)

(* -----------------------------

3. Tanh

----------------------------- *)

let tanh_activation x = tanh x

(* OCaml's built-in tanh *)

let tanh_derivative x =

1. -. (tanh x) ** 2.

(* Derivative of tanh: 1 - tanh^2(x) *)

(* -----------------------------

4. Vectorized application

----------------------------- *)

type vector = float list

let vector_map f v = List.map f v

(* Applies function f to each element of vector v *)

(* -----------------------------

5. Example usage

----------------------------- *)

let inputs = [-2.; -1.; 0.; 1.; 2.]

(* Apply ReLU *)

let relu_outputs = vector_map relu inputs

let relu_derivs = vector_map relu_derivative inputs

let () =

Printf.printf "ReLU outputs: [%s]\n"

(String.concat "; " (List.map string_of_float relu_outputs));

Printf.printf "ReLU derivatives: [%s]\n"

(String.concat "; " (List.map string_of_float relu_derivs))

(* Apply Sigmoid *)

let sigmoid_outputs = vector_map sigmoid inputs

let sigmoid_derivs = vector_map sigmoid_derivative inputs

let () =

Printf.printf "Sigmoid outputs: [%s]\n"

(String.concat "; " (List.map string_of_float sigmoid_outputs));

Printf.printf "Sigmoid derivatives: [%s]\n"

(String.concat "; " (List.map string_of_float sigmoid_derivs))

(* Apply Tanh *)

let tanh_outputs = vector_map tanh_activation inputs

let tanh_derivs = vector_map tanh_derivative inputs

let () =

Printf.printf "Tanh outputs: [%s]\n"

(String.concat "; " (List.map string_of_float tanh_outputs));

Printf.printf "Tanh derivatives: [%s]\n"

(String.concat "; " (List.map string_of_float tanh_derivs))

2. CONCLUSION

Windows PowerShell

Install the latest PowerShell for new features and improvements! https://aka.ms/PSWindows

OCaml version: The OCaml toplevel, version 5.3.0

Coq-LSP version: 0.2.3

Loading personal and system profiles took 4456ms.

PS C:\Users\User> ocaml C:\AI2025\lesson4.ml

ReLU outputs: [0.; 0.; 0.; 1.; 2.]

ReLU derivatives: [0.; 0.; 0.; 1.; 1.]

Sigmoid outputs: [0.119202922022; 0.26894142137; 0.5; 0.73105857863; 0.880797077978]

Sigmoid derivatives: [0.104993585404; 0.196611933241; 0.25; 0.196611933241; 0.104993585404]

Tanh outputs: [-0.964027580076; -0.761594155956; 0.; 0.761594155956; 0.964027580076]

Tanh derivatives: [0.0706508248532; 0.419974341614; 1.; 0.419974341614; 0.0706508248532]

PS C:\Users\User>

3. REFERENCES

Bird, R. (2015). Thinking Functionally with Haskell. Cambridge, England: Cambridge University Press.

Davie, A. (1992). Introduction to Functional Programming Systems Using Haskell. Cambridge, England: Cambridge University Press.

Goerzen, J. & O'Sullivan, B. & Stewart, D. (2008). Real World Haskell. Sebastopol, CA: O'Reilly Media, Inc.

Hutton, G. (2007). Programming in Haskell. New York: Cambridge University Press.

Lipovača, M. (2011). Learn You a Haskell for Great Good!: A Beginner's Guide. San Francisco, CA: No Starch Press, Inc.

Thompson, S. (2011). The Craft of Functional Programming. Edinburgh Gate, Harlow, England: Pearson Education Limited.