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+# Best Practices for Scholar.Optimize Contributions
+
+This document captures key patterns and requirements for implementing optimization algorithms in Scholar, based on review feedback from José Valim (PR #323, #327).
+
+## Core Principle: JIT/GPU Compatibility
+
+**All optimization algorithms must be JIT-compilable and GPU-compatible.**
+
+This means the main entry point must be a `defn` function that can be called with `Nx.Defn.jit_apply/3`.
+
+## Required Patterns
+
+### 1. Use `defn` for Entry Points
+
+```elixir
+# GOOD - JIT compatible
+defn minimize(a, b, fun, opts \\ []) do
+  {tol, maxiter} = transform_opts(opts)
+  minimize_n(a, b, fun, tol, maxiter)
+end
+
+# BAD - NOT JIT compatible
+deftransform minimize(fun, opts) do
+  # This prevents JIT compilation!
+end
+```
+
+### 2. Expose Required Parameters as Function Arguments
+
+Don't bury required parameters in options - expose them as explicit arguments:
+
+```elixir
+# GOOD - bounds as explicit args
+defn minimize(a, b, fun, opts \\ [])
+
+# BAD - bounds buried in options
+deftransform minimize(fun, opts) do
+  {a, b} = opts[:bracket]
+```
+
+**Why?** The `deftransform -> defn` conversion will check the input types automatically, eliminating the need for custom validation logic.
+
+### 3. Use `deftransformp` Only for Option Validation
+
+```elixir
+deftransformp transform_opts(opts) do
+  opts = NimbleOptions.validate!(opts, @opts_schema)
+  {opts[:tol], opts[:maxiter]}
+end
+```
+
+### 4. Use `Nx.select` for Branch-Free Conditionals
+
+Never use Elixir runtime conditionals (`if`, `cond`, `case`) inside `defn` functions:
+
+```elixir
+# GOOD - tensor-based conditional
+new_a = Nx.select(condition, value_if_true, value_if_false)
+
+# BAD - Elixir runtime conditional
+new_a = if Nx.to_number(condition) == 1, do: value_if_true, else: value_if_false
+```
+
+For complex multi-way conditionals, use nested `Nx.select`:
+
+```elixir
+# Four-way conditional
+result = Nx.select(
+  cond1,
+  value1,
+  Nx.select(
+    cond2,
+    value2,
+    Nx.select(cond3, value3, value4)
+  )
+)
+```
+
+### 5. Use `while` Loop (Not Recursion)
+
+```elixir
+# GOOD - while loop
+{final_state, _} =
+  while {state = initial_state, {tol, maxiter}},
+        state.iter < maxiter and state.b - state.a >= tol do
+    # Update state
+    new_state = %{state | iter: state.iter + 1, ...}
+    {new_state, {tol, maxiter}}
+  end
+
+# BAD - recursive call (not JIT-compatible)
+defp loop(fun, state, tol, maxiter) do
+  if converged?(state) do
+    state
+  else
+    loop(fun, update(state), tol, maxiter)
+  end
+end
+```
+
+### 6. Never Use `Nx.to_number` in `defn`
+
+All computation must stay as tensors for JIT compilation:
+
+```elixir
+# GOOD - all tensor operations
+converged = state.b - state.a < tol
+
+# BAD - converts to Elixir number
+converged = Nx.to_number(state.b) - Nx.to_number(state.a) < Nx.to_number(tol)
+```
+
+### 7. Use Unsigned Types for Non-Negative Counters
+
+```elixir
+initial_state = %{
+  iter: Nx.u32(0),      # u32 for iteration count
+  f_evals: Nx.u32(2)    # u32 for function evaluation count
+}
+```
+
+### 8. Let Users Control Precision via Input Types
+
+Don't force type conversions - let the tensor type propagate from inputs:
+
+```elixir
+# GOOD - let user decide precision
+defn minimize(a, b, fun, opts \\ []) do
+  # a and b types propagate through computation
+end
+
+# BAD - forcing f64
+a = Nx.tensor(a, type: :f64)
+```
+
+Document that users can use f64 tensors for higher precision:
+
+```elixir
+@doc """
+For higher precision, use f64 tensors for bounds:
+
+    a = Nx.tensor(0.0, type: :f64)
+    b = Nx.tensor(5.0, type: :f64)
+    result = Brent.minimize(a, b, fun, tol: 1.0e-10)
+"""
+```
+
+### 9. Use Module Constants Directly
+
+```elixir
+# GOOD - use @attr directly in defn
+@phi 0.6180339887498949
+
+defnp minimize_n(a, b, fun, tol, maxiter) do
+  c = b - @phi * (b - a)
+end
+
+# BAD - wrapping in tensor
+defnp minimize_n(a, b, fun, tol, maxiter) do
+  phi = Nx.tensor(@phi)
+  c = b - phi * (b - a)
+end
+```
+
+### 10. Self-Contain Modules
+
+Keep NimbleOptions validation in the same module - don't create wrapper modules:
+
+```elixir
+defmodule Scholar.Optimize.Brent do
+  opts = [
+    tol: [...],
+    maxiter: [...]
+  ]
+
+  @opts_schema NimbleOptions.new!(opts)
+
+  # Validation happens here, not in a separate module
+end
+```
+
+## Module Structure Template
+
+```elixir
+defmodule Scholar.Optimize.AlgorithmName do
+  @moduledoc """
+  Description of the algorithm.
+
+  ## Algorithm
+  ...
+
+  ## Convergence
+  ...
+
+  ## References
+  ...
+  """
+
+  import Nx.Defn
+
+  @derive {Nx.Container, containers: [:x, :fun, :converged, :iterations, :fun_evals]}
+  defstruct [:x, :fun, :converged, :iterations, :fun_evals]
+
+  @type t :: %__MODULE__{
+          x: Nx.Tensor.t(),
+          fun: Nx.Tensor.t(),
+          converged: Nx.Tensor.t(),
+          iterations: Nx.Tensor.t(),
+          fun_evals: Nx.Tensor.t()
+        }
+
+  # Constants
+  @some_constant 0.123456789
+
+  # Options schema
+  opts = [
+    tol: [
+      type: {:custom, Scholar.Options, :positive_number, []},
+      default: 1.0e-5,
+      doc: "..."
+    ],
+    maxiter: [
+      type: :pos_integer,
+      default: 500,
+      doc: "..."
+    ]
+  ]
+
+  @opts_schema NimbleOptions.new!(opts)
+
+  @doc """
+  Main entry point documentation...
+  """
+  defn minimize(a, b, fun, opts \\ []) do
+    {tol, maxiter} = transform_opts(opts)
+    minimize_n(a, b, fun, tol, maxiter)
+  end
+
+  deftransformp transform_opts(opts) do
+    opts = NimbleOptions.validate!(opts, @opts_schema)
+    {opts[:tol], opts[:maxiter]}
+  end
+
+  defnp minimize_n(a, b, fun, tol, maxiter) do
+    # Implementation using while loop and Nx.select
+  end
+end
+```
+
+## Test Requirements
+
+Every optimization module must include:
+
+1. **Basic functionality tests** - Verify correct results on standard test functions
+2. **Option handling tests** - Test tolerance and maxiter options
+3. **JIT compatibility test** - Critical! Must pass:
+
+```elixir
+test "works with jit_apply" do
+  fun = fn x -> Nx.pow(Nx.subtract(x, 3), 2) end
+  opts = [tol: 1.0e-5, maxiter: 500]
+
+  result = Nx.Defn.jit_apply(&AlgorithmName.minimize/4, [0.0, 5.0, fun, opts])
+
+  assert Nx.to_number(result.converged) == 1
+end
+```
+
+4. **Tensor bounds test** - Accept both numbers and tensors
+5. **Precision test** - Higher precision with f64 bounds
+
+## Validation Against SciPy
+
+When implementing algorithms, validate results against SciPy:
+
+```python
+from scipy.optimize import minimize_scalar
+
+result = minimize_scalar(func, bracket=(a, b), method='brent')
+print(f"x: {result.x}, f(x): {result.fun}, iterations: {result.nit}")
+```
+
+Use these reference values in tests with appropriate tolerance (typically `atol: 1.0e-4` to `1.0e-6`).
+
+## References
+
+- PR #323: https://github.com/elixir-nx/scholar/pull/323 (original comprehensive optimizer)
+- PR #327: https://github.com/elixir-nx/scholar/pull/327 (merged Golden Section)
+- SciPy optimize: https://docs.scipy.org/doc/scipy/tutorial/optimize.html