class Predict(Module, Parameter):
    def __init__(self, signature, callbacks=None, **config)
    def forward(self, **kwargs) -> Prediction
    def reset(self) / dump_state(self) / load_state(self)
    def _forward_preprocess(self, **kwargs)
    def _forward_postprocess(self, completions, signature, **kwargs)

# lib/dspex/program.ex - Enhanced with streaming and concurrency
defmodule DSPEx.Program do
  @moduledoc """
  Enhanced program behaviour with streaming, concurrency, and fault tolerance.
  
  Supports both traditional batch execution and modern streaming patterns
  with built-in supervision, backpressure, and adaptive execution.
  """
  
  @type program :: struct()
  @type inputs :: map()
  @type outputs :: map()
  @type options :: keyword()
  @type stream_options :: %{
    optional(:buffer_size) => pos_integer(),
    optional(:max_demand) => pos_integer(),
    optional(:flow_control) => :push | :pull,
    optional(:timeout) => pos_integer()
  }
  
  # Core execution callbacks
  @callback forward(program(), inputs(), options()) :: 
    {:ok, outputs()} | {:error, term()}
  
  # Streaming execution callbacks
  @callback stream_forward(program(), Stream.t(), stream_options()) :: 
    {:ok, GenStage.stage()} | {:error, term()}
    
  # Concurrent execution callbacks  
  @callback concurrent_forward(program(), [inputs()], options()) ::
    {:ok, [outputs()]} | {:error, term()}
    
  # Adaptive execution callbacks
  @callback adaptive_forward(program(), inputs(), options(), adaptation_state()) ::
    {:ok, outputs(), adaptation_state()} | {:error, term()}
    
  @optional_callbacks [
    stream_forward: 3,
    concurrent_forward: 3, 
    adaptive_forward: 4
  ]
  
  # Enhanced execution functions
  def forward(program, inputs, opts \\ []) do
    case opts[:execution_mode] do
      :streaming -> stream_forward(program, inputs, opts)
      :concurrent -> concurrent_forward(program, inputs, opts)
      :adaptive -> adaptive_forward(program, inputs, opts)
      _ -> traditional_forward(program, inputs, opts)
    end
  end
  
  def stream_forward(program, input_stream, opts \\ []) do
    # Create supervised GenStage pipeline
    with {:ok, supervisor} <- start_prediction_supervisor(program, opts),
         {:ok, producer} <- start_stream_producer(input_stream, supervisor),
         {:ok, consumer} <- start_stream_consumer(program, supervisor, opts) do
      
      # Link producer and consumer
      GenStage.sync_subscribe(consumer, to: producer, opts)
      {:ok, consumer}
    end
  end
  
  def concurrent_forward(program, input_list, opts \\ []) do
    # Parallel execution with configurable concurrency
    concurrency = Keyword.get(opts, :max_concurrency, System.schedulers_online())
    timeout = Keyword.get(opts, :timeout, 30_000)
    
    # Use Task.async_stream for managed concurrency
    results = 
      input_list
      |> Task.async_stream(
        fn inputs -> forward(program, inputs, opts) end,
        max_concurrency: concurrency,
        timeout: timeout,
        on_timeout: :kill_task
      )
      |> Enum.map(fn
        {:ok, result} -> result
        {:exit, reason} -> {:error, {:task_exit, reason}}
      end)
    
    {:ok, results}
  end
end

# lib/dspex/predict/stream_predict.ex
defmodule DSPEx.Predict.StreamPredict do
  @moduledoc """
  Stream-based prediction with GenStage integration.
  
  Provides real-time prediction processing with backpressure,
  adaptive batching, and automatic error recovery.
  """
  
  use GenStage
  
  alias DSPEx.Predict.StreamPredict.{Producer, Processor, Consumer}
  
  defstruct [
    :signature,
    :client, 
    :adapter,
    :buffer_size,
    :batch_size,
    :flow_control,
    :error_strategy
  ]
  
  @type t :: %__MODULE__{
    signature: module(),
    client: atom(),
    adapter: module(),
    buffer_size: pos_integer(),
    batch_size: pos_integer(),
    flow_control: :push | :pull,
    error_strategy: :retry | :skip | :fail_fast
  }
  
  def start_link(program, opts \\ []) do
    GenStage.start_link(__MODULE__, {program, opts})
  end
  
  def init({program, opts}) do
    state = %__MODULE__{
      signature: program.signature,
      client: program.client,
      adapter: program.adapter,
      buffer_size: Keyword.get(opts, :buffer_size, 1000),
      batch_size: Keyword.get(opts, :batch_size, 10),
      flow_control: Keyword.get(opts, :flow_control, :pull),
      error_strategy: Keyword.get(opts, :error_strategy, :retry)
    }
    
    {:producer_consumer, state, subscribe_to: [], buffer_size: state.buffer_size}
  end
  
  def handle_events(input_batches, _from, state) do
    # Process inputs in parallel with adaptive batching
    processed_batches = 
      input_batches
      |> Enum.chunk_every(state.batch_size)
      |> Task.async_stream(
        fn batch -> process_batch(batch, state) end,
        max_concurrency: System.schedulers_online(),
        timeout: 30_000
      )
      |> Enum.flat_map(fn
        {:ok, results} -> results
        {:exit, _reason} -> [] # Handle gracefully
      end)
    
    {:noreply, processed_batches, state}
  end
  
  defp process_batch(inputs, state) do
    Enum.map(inputs, fn input ->
      case DSPEx.Predict.forward(build_program(state), input) do
        {:ok, output} -> 
          %{input: input, output: output, status: :success, timestamp: DateTime.utc_now()}
        
        {:error, reason} ->
          %{input: input, error: reason, status: :error, timestamp: DateTime.utc_now()}
      end
    end)
  end
  
  defp build_program(state) do
    %DSPEx.Predict{
      signature: state.signature,
      client: state.client,
      adapter: state.adapter
    }
  end
  
  # Consumer for results
  def handle_demand(demand, state) do
    # Implement adaptive demand based on current load
    actual_demand = min(demand, state.buffer_size)
    {:noreply, [], state}
  end
end

# lib/dspex/predict/adaptive_predict.ex
defmodule DSPEx.Predict.AdaptivePredict do
  @moduledoc """
  Adaptive prediction engine with dynamic optimization.
  
  Learns from execution patterns to optimize model selection,
  parameter tuning, and adapter selection automatically.
  """
  
  use GenServer
  
  defstruct [
    :program,
    :adaptation_state,
    :performance_history,
    :optimization_strategy,
    :learning_rate
  ]
  
  @type adaptation_state :: %{
    model_performance: %{atom() => float()},
    adapter_performance: %{module() => float()},
    parameter_optimization: %{atom() => term()},
    success_rate: float(),
    avg_latency: float(),
    error_patterns: [term()]
  }
  
  def start_link(program, opts \\ []) do
    GenServer.start_link(__MODULE__, {program, opts}, name: __MODULE__)
  end
  
  def adaptive_forward(inputs, opts \\ []) do
    GenServer.call(__MODULE__, {:adaptive_forward, inputs, opts})
  end
  
  def init({program, opts}) do
    state = %__MODULE__{
      program: program,
      adaptation_state: initial_adaptation_state(),
      performance_history: :queue.new(),
      optimization_strategy: Keyword.get(opts, :strategy, :balanced),
      learning_rate: Keyword.get(opts, :learning_rate, 0.1)
    }
    
    {:ok, state}
  end
  
  def handle_call({:adaptive_forward, inputs, opts}, _from, state) do
    start_time = System.monotonic_time()
    
    # Optimize execution parameters based on learning
    optimized_opts = optimize_execution_options(opts, state.adaptation_state)
    optimized_program = optimize_program_config(state.program, state.adaptation_state)
    
    # Execute with optimized configuration
    result = DSPEx.Program.forward(optimized_program, inputs, optimized_opts)
    
    # Record performance metrics
    execution_time = System.monotonic_time() - start_time
    performance_record = build_performance_record(result, execution_time, optimized_opts)
    
    # Update adaptation state
    new_adaptation_state = update_adaptation_state(
      state.adaptation_state, 
      performance_record,
      state.learning_rate
    )
    
    new_state = %{state | 
      adaptation_state: new_adaptation_state,
      performance_history: :queue.in(performance_record, state.performance_history)
    }
    
    {:reply, result, new_state}
  end
  
  # Optimize execution options based on learned patterns
  defp optimize_execution_options(opts, adaptation_state) do
    base_opts = opts
    
    # Dynamic temperature optimization
    optimal_temp = Map.get(adaptation_state.parameter_optimization, :temperature, 0.7)
    
    # Model selection based on performance
    best_model = select_best_model(adaptation_state.model_performance)
    
    # Timeout optimization based on historical latency
    optimal_timeout = calculate_optimal_timeout(adaptation_state.avg_latency)
    
    base_opts
    |> Keyword.put(:temperature, optimal_temp)
    |> Keyword.put(:model, best_model)
    |> Keyword.put(:timeout, optimal_timeout)
  end
  
  # Optimize program configuration based on learning
  defp optimize_program_config(program, adaptation_state) do
    # Select best adapter based on performance
    best_adapter = select_best_adapter(adaptation_state.adapter_performance)
    
    %{program | adapter: best_adapter}
  end
  
  defp select_best_model(model_performance) do
    case Enum.max_by(model_performance, fn {_model, score} -> score end, fn -> nil end) do
      {best_model, _score} -> best_model
      nil -> :openai  # Default fallback
    end
  end
  
  defp select_best_adapter(adapter_performance) do
    case Enum.max_by(adapter_performance, fn {_adapter, score} -> score end, fn -> nil end) do
      {best_adapter, _score} -> best_adapter
      nil -> DSPEx.Adapters.JSONAdapter  # Default fallback
    end
  end
  
  defp calculate_optimal_timeout(avg_latency) do
    # Set timeout to 3x average latency with minimum bounds
    max(round(avg_latency * 3), 5_000)
  end
  
  defp update_adaptation_state(state, performance_record, learning_rate) do
    # Update model performance with exponential moving average
    model = performance_record.model
    success_score = if performance_record.success, do: 1.0, else: 0.0
    latency_score = 1.0 / max(performance_record.latency_ms, 1)
    combined_score = success_score * 0.7 + latency_score * 0.3
    
    current_model_score = Map.get(state.model_performance, model, 0.5)
    new_model_score = current_model_score * (1 - learning_rate) + combined_score * learning_rate
    
    # Update adapter performance similarly
    adapter = performance_record.adapter
    current_adapter_score = Map.get(state.adapter_performance, adapter, 0.5)
    new_adapter_score = current_adapter_score * (1 - learning_rate) + combined_score * learning_rate
    
    %{state |
      model_performance: Map.put(state.model_performance, model, new_model_score),
      adapter_performance: Map.put(state.adapter_performance, adapter, new_adapter_score),
      success_rate: state.success_rate * (1 - learning_rate) + success_score * learning_rate,
      avg_latency: state.avg_latency * (1 - learning_rate) + performance_record.latency_ms * learning_rate
    }
  end
end

# lib/dspex/predict/patterns/chain_of_thought_v2.ex
defmodule DSPEx.Predict.Patterns.ChainOfThoughtV2 do
  @moduledoc """
  Enhanced Chain of Thought with dynamic reasoning depth.
  
  Automatically adjusts reasoning depth based on problem complexity
  and provides structured reasoning with confidence scoring.
  """
  
  use DSPEx.Program
  
  defstruct [
    :base_signature,
    :reasoning_depth,
    :confidence_threshold,
    :adaptive_depth,
    :reasoning_strategy
  ]
  
  @type reasoning_strategy :: :step_by_step | :tree_search | :analogical | :causal
  
  def new(signature, opts \\ []) do
    %__MODULE__{
      base_signature: signature,
      reasoning_depth: Keyword.get(opts, :depth, :adaptive),
      confidence_threshold: Keyword.get(opts, :confidence_threshold, 0.8),
      adaptive_depth: Keyword.get(opts, :adaptive_depth, true),
      reasoning_strategy: Keyword.get(opts, :strategy, :step_by_step)
    }
  end
  
  @impl DSPEx.Program
  def forward(program, inputs, opts \\ []) do
    # Analyze problem complexity to determine reasoning approach
    complexity = analyze_problem_complexity(inputs, program.base_signature)
    
    # Select optimal reasoning strategy
    strategy = select_reasoning_strategy(complexity, program.reasoning_strategy)
    
    # Generate structured reasoning
    case strategy do
      :step_by_step -> step_by_step_reasoning(program, inputs, opts)
      :tree_search -> tree_search_reasoning(program, inputs, opts)
      :analogical -> analogical_reasoning(program, inputs, opts)
      :causal -> causal_reasoning(program, inputs, opts)
    end
  end
  
  defp step_by_step_reasoning(program, inputs, opts) do
    # Create dynamic CoT signature with structured reasoning
    cot_signature = create_structured_cot_signature(program.base_signature)
    
    # Execute with reasoning structure
    predict_program = %DSPEx.Predict{
      signature: cot_signature,
      client: Keyword.get(opts, :client, :openai),
      adapter: Keyword.get(opts, :adapter, DSPEx.Adapters.JSONAdapter)
    }
    
    case DSPEx.Program.forward(predict_program, inputs, opts) do
      {:ok, outputs} ->
        # Validate reasoning quality and adjust if needed
        case validate_reasoning_quality(outputs) do
          {:ok, validated_outputs} -> {:ok, validated_outputs}
          {:error, :low_confidence} when program.adaptive_depth ->
            # Retry with deeper reasoning
            retry_with_deeper_reasoning(program, inputs, opts)
          error -> error
        end
      
      error -> error
    end
  end
  
  defp create_structured_cot_signature(base_signature) do
    # Create a signature with structured reasoning fields
    input_fields = base_signature.input_fields()
    output_fields = base_signature.output_fields()
    
    # Add structured reasoning fields
    reasoning_fields = [
      :problem_analysis,
      :step_by_step_reasoning, 
      :confidence_assessment,
      :alternative_approaches
    ] ++ output_fields
    
    # Create dynamic signature
    signature_string = build_signature_string(input_fields, reasoning_fields)
    create_dynamic_signature(signature_string, base_signature.instructions())
  end
  
  defp validate_reasoning_quality(outputs) do
    # Extract confidence if available
    confidence = Map.get(outputs, :confidence_assessment, "medium")
    
    # Parse confidence level
    confidence_score = case String.downcase(confidence) do
      "high" -> 0.9
      "medium" -> 0.7
      "low" -> 0.3
      _ -> 0.5
    end
    
    if confidence_score >= 0.8 do
      {:ok, outputs}
    else
      {:error, :low_confidence}
    end
  end
  
  defp retry_with_deeper_reasoning(program, inputs, opts) do
    # Add instruction for deeper analysis
    deeper_opts = Keyword.update(opts, :custom_instructions, 
      "Please provide more detailed reasoning and analysis.",
      &("#{&1}\n\nPlease provide more detailed reasoning and analysis.")
    )
    
    step_by_step_reasoning(program, inputs, deeper_opts)
  end
end

# lib/dspex/predict/patterns/react_v2.ex  
defmodule DSPEx.Predict.Patterns.ReActV2 do
  @moduledoc """
  Enhanced ReAct with parallel tool execution and intelligent planning.
  
  Supports concurrent tool calls, dynamic tool registration,
  and adaptive planning based on execution history.
  """
  
  use DSPEx.Program
  use GenServer
  
  defstruct [
    :base_signature,
    :tools,
    :max_iterations,
    :parallel_execution,
    :planning_strategy,
    :trajectory_manager
  ]
  
  def start_link(signature, tools, opts \\ []) do
    GenServer.start_link(__MODULE__, {signature, tools, opts})
  end
  
  def init({signature, tools, opts}) do
    state = %__MODULE__{
      base_signature: signature,
      tools: normalize_tools(tools),
      max_iterations: Keyword.get(opts, :max_iterations, 10),
      parallel_execution: Keyword.get(opts, :parallel_execution, true),
      planning_strategy: Keyword.get(opts, :planning_strategy, :adaptive),
      trajectory_manager: start_trajectory_manager()
    }
    
    {:ok, state}
  end
  
  @impl DSPEx.Program
  def forward(program, inputs, opts \\ []) do
    GenServer.call(program, {:execute, inputs, opts}, 60_000)
  end
  
  def handle_call({:execute, inputs, opts}, _from, state) do
    # Initialize execution context
    context = %{
      inputs: inputs,
      trajectory: [],
      completed: false,
      iteration: 0,
      parallel_tasks: %{}
    }
    
    # Execute ReAct loop with enhanced planning
    result = execute_react_loop(context, state, opts)
    
    {:reply, result, state}
  end
  
  defp execute_react_loop(context, state, opts) do
    cond do
      context.completed -> 
        extract_final_answer(context, state)
      
      context.iteration >= state.max_iterations ->
        {:error, :max_iterations_exceeded}
      
      true ->
        # Plan next actions with intelligent strategy
        case plan_next_actions(context, state, opts) do
          {:ok, actions} ->
            # Execute actions (potentially in parallel)
            case execute_actions(actions, context, state, opts) do
              {:ok, new_context} ->
                execute_react_loop(new_context, state, opts)
              
              error -> error
            end
          
          error -> error
        end
    end
  end
  
  defp plan_next_actions(context, state, opts) do
    # Use adaptive planning based on trajectory and available tools
    planning_signature = create_planning_signature(state.base_signature, state.tools)
    
    planner = %DSPEx.Predict{
      signature: planning_signature,
      client: Keyword.get(opts, :client, :openai),
      adapter: DSPEx.Adapters.JSONAdapter
    }
    
    planning_inputs = %{
      original_inputs: context.inputs,
      trajectory: format_trajectory(context.trajectory),
      available_tools: format_tools(state.tools),
      iteration: context.iteration
    }
    
    case DSPEx.Program.forward(planner, planning_inputs, opts) do
      {:ok, plan} -> 
        parse_planned_actions(plan, state.tools)
      
      error -> error
    end
  end
  
  defp execute_actions(actions, context, state, opts) do
    if state.parallel_execution and length(actions) > 1 do
      execute_actions_parallel(actions, context, state, opts)
    else
      execute_actions_sequential(actions, context, state, opts)
    end
  end
  
  defp execute_actions_parallel(actions, context, state, opts) do
    # Execute multiple tool calls concurrently
    tasks = 
      Enum.map(actions, fn action ->
        Task.async(fn -> execute_single_action(action, state.tools) end)
      end)
    
    # Wait for all tasks with timeout
    timeout = Keyword.get(opts, :tool_timeout, 10_000)
    results = Task.await_many(tasks, timeout)
    
    # Update trajectory with results
    new_trajectory = context.trajectory ++ Enum.zip(actions, results)
    new_context = %{context | 
      trajectory: new_trajectory,
      iteration: context.iteration + 1,
      completed: check_completion_criteria(new_trajectory, state.base_signature)
    }
    
    {:ok, new_context}
  end
  
  defp execute_single_action(action, tools) do
    tool_name = action.tool_name
    tool_args = action.tool_args
    
    case Map.get(tools, tool_name) do
      nil -> 
        {:error, "Tool #{tool_name} not found"}
      
      tool ->
        try do
          result = apply(tool.function, [tool_args])
          {:ok, result}
        rescue
          error -> {:error, "Tool execution failed: #{inspect(error)}"}
        end
    end
  end
end

# lib/dspex/predict/tools/tool_registry.ex
defmodule DSPEx.Predict.Tools.ToolRegistry do
  @moduledoc """
  Dynamic tool registry with capability detection and optimization.
  
  Automatically discovers tool capabilities, optimizes tool selection,
  and provides intelligent tool composition for complex tasks.
  """
  
  use GenServer
  
  defstruct [
    :tools,
    :capabilities,
    :performance_metrics,
    :composition_patterns
  ]
  
  def start_link(opts \\ []) do
    GenServer.start_link(__MODULE__, opts, name: __MODULE__)
  end
  
  def register_tool(tool_spec) do
    GenServer.call(__MODULE__, {:register_tool, tool_spec})
  end
  
  def discover_tools(capabilities) do
    GenServer.call(__MODULE__, {:discover_tools, capabilities})
  end
  
  def compose_tools(task_description) do
    GenServer.call(__MODULE__, {:compose_tools, task_description})
  end
  
  def init(opts) do
    state = %__MODULE__{
      tools: %{},
      capabilities: %{},
      performance_metrics: %{},
      composition_patterns: []
    }
    
    # Register built-in tools
    state = register_builtin_tools(state)
    
    {:ok, state}
  end
  
  def handle_call({:register_tool, tool_spec}, _from, state) do
    # Analyze tool capabilities
    capabilities = analyze_tool_capabilities(tool_spec)
    
    new_state = %{state |
      tools: Map.put(state.tools, tool_spec.name, tool_spec),
      capabilities: Map.put(state.capabilities, tool_spec.name, capabilities)
    }
    
    {:reply, :ok, new_state}
  end
  
  def handle_call({:discover_tools, required_capabilities}, _from, state) do
    # Find tools that match required capabilities
    matching_tools = 
      state.capabilities
      |> Enum.filter(fn {_tool, caps} ->
        capabilities_match?(caps, required_capabilities)
      end)
      |> Enum.map(fn {tool_name, _caps} -> Map.get(state.tools, tool_name) end)
    
    {:reply, {:ok, matching_tools}, state}
  end
  
  def handle_call({:compose_tools, task_description}, _from, state) do
    # Use LLM to analyze task and recommend tool composition
    composition = analyze_task_and_compose_tools(task_description, state.tools)
    
    {:reply, {:ok, composition}, state}
  end
  
  defp analyze_tool_capabilities(tool_spec) do
    %{
      input_types: infer_input_types(tool_spec),
      output_types: infer_output_types(tool_spec),
      side_effects: analyze_side_effects(tool_spec),
      complexity: estimate_complexity(tool_spec),
      domains: extract_domains(tool_spec),
      dependencies: extract_dependencies(tool_spec)
    }
  end
  
  defp capabilities_match?(tool_caps, required_caps) do
    # Check if tool capabilities satisfy requirements
    required_caps
    |> Enum.all?(fn {capability, requirement} ->
      case Map.get(tool_caps, capability) do
        nil -> false
        tool_value -> satisfies_requirement?(tool_value, requirement)
      end
    end)
  end
  
  defp analyze_task_and_compose_tools(task_description, available_tools) do
    # Use LLM to break down task and recommend tool sequence
    analysis_signature = create_task_analysis_signature()
    
    analyzer = %DSPEx.Predict{
      signature: analysis_signature,
      client: :openai,
      adapter: DSPEx.Adapters.JSONAdapter
    }
    
    inputs = %{
      task_description: task_description,
      available_tools: format_tools_for_analysis(available_tools)
    }
    
    case DSPEx.Program.forward(analyzer, inputs) do
      {:ok, analysis} -> parse_tool_composition(analysis, available_tools)
      error -> error
    end
  end
end

# lib/dspex/predict/tools/function_calling.ex
defmodule DSPEx.Predict.Tools.FunctionCalling do
  @moduledoc """
  Advanced function calling with type safety and automatic validation.
  
  Provides native Elixir function calling with automatic schema generation,
  parameter validation, and result transformation.
  """
  
  defstruct [
    :function,
    :name,
    :description,
    :parameters,
    :return_type,
    :validation_schema,
    :timeout
  ]
  
  @type t :: %__MODULE__{
    function: function(),
    name: String.t(),
    description: String.t(),
    parameters: map(),
    return_type: term(),
    validation_schema: map(),
    timeout: pos_integer()
  }
  
  def new(function, opts \\ []) when is_function(function) do
    # Introspect function to generate schema
    {name, arity} = Function.info(function, :name) |> elem(1), Function.info(function, :arity) |> elem(1)
    
    %__MODULE__{
      function: function,
      name: Keyword.get(opts, :name, to_string(name)),
      description: Keyword.get(opts, :description, "Function #{name}/#{arity}"),
      parameters: infer_parameters(function, opts),
      return_type: Keyword.get(opts, :return_type, :any),
      validation_schema: generate_validation_schema(function, opts),
      timeout: Keyword.get(opts, :timeout, 5_000)
    }
  end
  
  def call(tool, args) do
    # Validate arguments
    case validate_arguments(args, tool.validation_schema) do
      {:ok, validated_args} ->
        # Execute with timeout
        task = Task.async(fn -> apply_function_safely(tool.function, validated_args) end)
        
        case Task.yield(task, tool.timeout) do
          {:ok, result} -> 
            validate_return_value(result, tool.return_type)
          
          nil ->
            Task.shutdown(task, :brutal_kill)
            {:error, :timeout}
        end
      
      error -> error
    end
  end
  
  defp infer_parameters(function, opts) do
    # Use beam introspection to infer parameter types
    case Keyword.get(opts, :parameters) do
      nil -> 
        # Attempt to infer from function metadata
        infer_from_function_info(function)
      
      explicit_params -> 
        explicit_params
    end
  end
  
  defp generate_validation_schema(function, opts) do
    parameters = infer_parameters(function, opts)
    
    %{
      type: "object",
      properties: build_properties_schema(parameters),
      required: extract_required_parameters(parameters),
      additionalProperties: false
    }
  end
  
  defp validate_arguments(args, schema) do
    # Use ExJsonSchema for validation
    case ExJsonSchema.Validator.validate(schema, args) do
      :ok -> {:ok, args}
      {:error, errors} -> {:error, {:validation_failed, errors}}
    end
  end
  
  defp apply_function_safely(function, args) do
    try do
      # Convert args map to function arguments
      case args do
        args when is_map(args) ->
          # For named parameters, convert to positional
          arg_list = convert_map_to_args(args, function)
          apply(function, arg_list)
        
        args when is_list(args) ->
          apply(function, args)
        
        single_arg ->
          apply(function, [single_arg])
      end
    rescue
      error -> {:error, {:function_error, error}}
    catch
      kind, reason -> {:error, {:function_exception, {kind, reason}}}
    end
  end
  
  defp validate_return_value(result, expected_type) do
    case {result, expected_type} do
      {value, :any} -> {:ok, value}
      {value, type} when is_atom(type) -> validate_basic_type(value, type)
      {value, complex_type} -> validate_complex_type(value, complex_type)
    end
  end
end

# lib/dspex/predict/testing/property_testing.ex
defmodule DSPEx.Predict.Testing.PropertyTesting do
  @moduledoc """
  Property-based testing for prediction systems.
  
  Generates comprehensive test cases and validates prediction
  invariants across different execution modes and configurations.
  """
  
  import PropCheck
  
  def prediction_invariants(program_module) do
    property "prediction consistency across execution modes" do
      forall {inputs, opts} <- {valid_inputs(program_module), valid_options()} do
        program = program_module.new(:test_signature, opts)
        
        # Test consistency between sync and async execution
        {:ok, sync_result} = DSPEx.Program.forward(program, inputs, opts)
        {:ok, async_result} = DSPEx.Program.aforward(program, inputs, opts)
        
        # Results should be deterministic (with same random seed)
        sync_result == async_result
      end
    end
  end
  
  def stream_processing_invariants(program_module) do
    property "stream processing preserves order and completeness" do
      forall input_list <- list(valid_inputs(program_module)) do
        program = program_module.new(:test_signature)
        
        # Process as stream
        {:ok, stream_stage} = DSPEx.Program.stream_forward(program, Stream.from_enumerable(input_list))
        stream_results = collect_stream_results(stream_stage)
        
        # Process individually
        individual_results = Enum.map(input_list, fn inputs ->
          {:ok, result} = DSPEx.Program.forward(program, inputs)
          result
        end)
        
        # Order and completeness should be preserved
        length(stream_results) == length(individual_results) and
        Enum.zip(stream_results, individual_results) |> Enum.all?(fn {a, b} -> a == b end)
      end
    end
  end
end

# lib/dspex/predict/monitoring/prediction_monitor.ex
defmodule DSPEx.Predict.Monitoring.PredictionMonitor do
  @moduledoc """
  Real-time monitoring and alerting for prediction systems.
  
  Tracks performance metrics, error patterns, and resource usage
  with configurable alerting and automatic remediation.
  """
  
  use GenServer
  
  defstruct [
    :metrics_collector,
    :alert_manager,
    :remediation_actions,
    :performance_thresholds,
    :error_patterns
  ]
  
  def start_link(opts \\ []) do
    GenServer.start_link(__MODULE__, opts, name: __MODULE__)
  end
  
  def record_prediction(program, inputs, result, metadata) do
    GenServer.cast(__MODULE__, {:record_prediction, program, inputs, result, metadata})
  end
  
  def get_metrics(time_window \\ :last_hour) do
    GenServer.call(__MODULE__, {:get_metrics, time_window})
  end
  
  def init(opts) do
    state = %__MODULE__{
      metrics_collector: start_metrics_collector(),
      alert_manager: start_alert_manager(opts),
      remediation_actions: configure_remediation_actions(opts),
      performance_thresholds: configure_thresholds(opts),
      error_patterns: %{}
    }
    
    # Start periodic metric aggregation
    schedule_metric_aggregation()
    
    {:ok, state}
  end
  
  def handle_cast({:record_prediction, program, inputs, result, metadata}, state) do
    # Record core metrics
    record_latency_metric(metadata.execution_time)
    record_success_metric(result)
    record_resource_usage(metadata.resource_usage)
    
    # Analyze for patterns
    analyze_error_patterns(result, state.error_patterns)
    check_performance_thresholds(metadata, state.performance_thresholds)
    
    # Update error patterns
    new_error_patterns = update_error_patterns(state.error_patterns, result)
    
    {:noreply, %{state | error_patterns: new_error_patterns}}
  end
  
  def handle_call({:get_metrics, time_window}, _from, state) do
    metrics = aggregate_metrics(time_window, state.metrics_collector)
    {:reply, {:ok, metrics}, state}
  end
  
  def handle_info(:aggregate_metrics, state) do
    # Perform periodic metric aggregation and alerting
    perform_metric_aggregation(state)
    check_alert_conditions(state)
    
    # Schedule next aggregation
    schedule_metric_aggregation()
    
    {:noreply, state}
  end
  
  defp check_performance_thresholds(metadata, thresholds) do
    Enum.each(thresholds, fn {metric, threshold} ->
      current_value = Map.get(metadata, metric)
      
      if current_value && current_value > threshold do
        trigger_alert({:threshold_exceeded, metric, current_value, threshold})
      end
    end)
  end
  
  defp trigger_alert(alert_data) do
    # Send alert through configured channels
    :telemetry.execute([:dspex, :predict, :alert], %{}, %{alert: alert_data})
    
    # Log critical alerts
    case alert_data do
      {:threshold_exceeded, :error_rate, rate, _} when rate > 0.5 ->
        Logger.error("Critical: Prediction error rate exceeded 50%: #{rate}")
      
      {:threshold_exceeded, :latency, latency, _} when latency > 10_000 ->
        Logger.warn("Warning: Prediction latency exceeded 10s: #{latency}ms")
      
      _ ->
        Logger.info("Alert: #{inspect(alert_data)}")
    end
  end
end

# lib/dspex/predict/nx_analytics.ex
defmodule DSPEx.Predict.NxAnalytics do
  @moduledoc """
  Nx-powered prediction analytics for performance optimization and insights.
  
  Provides high-performance numerical analysis of prediction patterns,
  confidence scoring, and parameter optimization using Nx tensor operations.
  """
  
  import Nx.Defn
  
  @doc """
  Analyze prediction confidence using statistical methods.
  
  ## Examples
      
      iex> predictions = [0.9, 0.8, 0.95, 0.7]
      iex> NxAnalytics.analyze_confidence(predictions)
      %{mean_confidence: 0.8375, confidence_std: 0.109, reliability_score: 0.82}
  """
  def analyze_confidence(confidence_scores) when is_list(confidence_scores) do
    tensor = Nx.tensor(confidence_scores)
    analyze_confidence_impl(tensor)
  end
  
  defn analyze_confidence_impl(scores) do
    mean_confidence = Nx.mean(scores)
    confidence_std = Nx.standard_deviation(scores)
    
    # Calculate reliability score based on consistency
    consistency = 1.0 / (1.0 + confidence_std)
    reliability_score = mean_confidence * consistency
    
    %{
      mean_confidence: mean_confidence,
      confidence_std: confidence_std,
      reliability_score: reliability_score,
      min_confidence: Nx.reduce_min(scores),
      max_confidence: Nx.reduce_max(scores)
    }
  end
  
  @doc """
  Optimize prediction parameters using gradient-based methods.
  """
  def optimize_parameters(prediction_history, target_metrics, opts \\ []) do
    # Convert prediction history to tensors
    {inputs_tensor, outputs_tensor, metrics_tensor} = prepare_optimization_data(prediction_history)
    
    # Run optimization
    learning_rate = Keyword.get(opts, :learning_rate, 0.01)
    max_iterations = Keyword.get(opts, :max_iterations, 100)
    
    optimized_params = run_parameter_optimization(
      inputs_tensor, 
      outputs_tensor, 
      metrics_tensor, 
      target_metrics,
      learning_rate,
      max_iterations
    )
    
    {:ok, convert_params_to_map(optimized_params)}
  end
  
  defn run_parameter_optimization(inputs, outputs, metrics, targets, learning_rate, max_iter) do
    # Initialize parameters
    initial_params = initialize_parameters(Nx.shape(inputs))
    
    # Gradient descent optimization
    {optimized_params, _final_loss} = 
      while {{initial_params, 0.0}, {inputs, outputs, targets, learning_rate, 0}} do
        {{params, _loss}, {inp, out, tgt, lr, iter}} ->
          
          # Compute current predictions and loss
          predictions = forward_predict(inp, params)
          current_loss = compute_loss(predictions, tgt)
          
          # Compute gradients
          gradients = grad(params, fn p -> 
            pred = forward_predict(inp, p)
            compute_loss(pred, tgt)
          end)
          
          # Update parameters
          updated_params = update_params(params, gradients, lr)
          
          {{updated_params, current_loss}, {inp, out, tgt, lr, iter + 1}}
      end
    
    optimized_params
  end
  
  defn initialize_parameters(input_shape) do
    # Initialize with small random values
    %{
      temperature: Nx.tensor(0.7),
      top_p: Nx.tensor(0.9),
      frequency_penalty: Nx.tensor(0.0),
      presence_penalty: Nx.tensor(0.0)
    }
  end
  
  defn forward_predict(inputs, params) do
    # Simplified prediction function
    # In practice, this would use the actual model
    base_pred = Nx.dot(inputs, Nx.tensor([[1.0], [0.5], [0.3]]))
    
    # Apply temperature scaling
    scaled_pred = base_pred / params.temperature
    
    # Apply other parameter effects
    adjusted_pred = scaled_pred * (1.0 + params.top_p * 0.1)
    
    adjusted_pred
  end
  
  defn compute_loss(predictions, targets) do
    # Mean squared error
    diff = Nx.subtract(predictions, targets)
    squared_diff = Nx.pow(diff, 2)
    Nx.mean(squared_diff)
  end
  
  defn update_params(params, gradients, learning_rate) do
    %{
      temperature: params.temperature - learning_rate * gradients.temperature,
      top_p: params.top_p - learning_rate * gradients.top_p,
      frequency_penalty: params.frequency_penalty - learning_rate * gradients.frequency_penalty,
      presence_penalty: params.presence_penalty - learning_rate * gradients.presence_penalty
    }
  end
  
  @doc """
  Batch prediction performance analysis using vectorized operations.
  """
  def analyze_batch_performance(predictions, references, opts \\ []) do
    pred_tensor = Nx.tensor(predictions)
    ref_tensor = Nx.tensor(references)
    
    analyze_performance_impl(pred_tensor, ref_tensor, opts)
  end
  
  defn analyze_performance_impl(predictions, references, _opts) do
    # Compute various performance metrics
    
    # Mean Absolute Error
    mae = Nx.mean(Nx.abs(Nx.subtract(predictions, references)))
    
    # Root Mean Squared Error
    mse = Nx.mean(Nx.pow(Nx.subtract(predictions, references), 2))
    rmse = Nx.sqrt(mse)
    
    # Correlation coefficient
    correlation = compute_correlation_coeff(predictions, references)
    
    # R-squared
    r_squared = Nx.pow(correlation, 2)
    
    %{
      mae: mae,
      mse: mse,
      rmse: rmse,
      correlation: correlation,
      r_squared: r_squared,
      prediction_mean: Nx.mean(predictions),
      reference_mean: Nx.mean(references)
    }
  end
  
  defn compute_correlation_coeff(x, y) do
    mean_x = Nx.mean(x)
    mean_y = Nx.mean(y)
    
    numerator = Nx.sum(Nx.multiply(
      Nx.subtract(x, mean_x),
      Nx.subtract(y, mean_y)
    ))
    
    denominator = Nx.sqrt(
      Nx.multiply(
        Nx.sum(Nx.pow(Nx.subtract(x, mean_x), 2)),
        Nx.sum(Nx.pow(Nx.subtract(y, mean_y), 2))
      )
    )
    
    Nx.divide(numerator, denominator)
  end
  
  @doc """
  Real-time prediction quality monitoring using moving averages.
  """
  def monitor_prediction_quality(quality_stream, window_size \\ 50) do
    quality_stream
    |> Stream.chunk_every(window_size, 1, :discard)
    |> Stream.map(fn window ->
      tensor = Nx.tensor(window)
      
      %{
        window_mean: Nx.to_number(Nx.mean(tensor)),
        window_std: Nx.to_number(Nx.standard_deviation(tensor)),
        trend: calculate_trend(tensor),
        anomaly_score: detect_anomalies(tensor)
      }
    end)
  end
  
  defn calculate_trend(window) do
    # Simple linear trend calculation
    n = Nx.size(window)
    indices = Nx.iota({n})
    
    # Linear regression slope
    mean_x = Nx.mean(indices)
    mean_y = Nx.mean(window)
    
    numerator = Nx.sum(
      Nx.multiply(
        Nx.subtract(indices, mean_x),
        Nx.subtract(window, mean_y)
      )
    )
    
    denominator = Nx.sum(Nx.pow(Nx.subtract(indices, mean_x), 2))
    
    Nx.divide(numerator, denominator)
  end
  
  defn detect_anomalies(window) do
    mean = Nx.mean(window)
    std = Nx.standard_deviation(window)
    
    # Count values outside 2 standard deviations
    lower_bound = mean - 2 * std
    upper_bound = mean + 2 * std
    
    outliers = Nx.logical_or(
      Nx.less(window, lower_bound),
      Nx.greater(window, upper_bound)
    )
    
    anomaly_rate = Nx.mean(outliers)
    anomaly_rate
  end
  
  # Helper functions
  
  defp prepare_optimization_data(prediction_history) do
    inputs = Enum.map(prediction_history, & &1.inputs) |> convert_to_tensor()
    outputs = Enum.map(prediction_history, & &1.outputs) |> convert_to_tensor()
    metrics = Enum.map(prediction_history, & &1.metrics) |> convert_to_tensor()
    
    {inputs, outputs, metrics}
  end
  
  defp convert_to_tensor(data) when is_list(data) do
    # Convert list of maps/data to tensor format
    case List.first(data) do
      map when is_map(map) ->
        # Convert map values to tensor
        values = Enum.map(data, fn item -> Map.values(item) end)
        Nx.tensor(values)
      
      list when is_list(list) ->
        Nx.tensor(data)
      
      number when is_number(number) ->
        Nx.tensor(data)
      
      _ ->
        # Fallback for complex data
        Nx.tensor([0.0])
    end
  end
  
  defp convert_params_to_map(nx_params) do
    %{
      temperature: Nx.to_number(nx_params.temperature),
      top_p: Nx.to_number(nx_params.top_p),
      frequency_penalty: Nx.to_number(nx_params.frequency_penalty),
      presence_penalty: Nx.to_number(nx_params.presence_penalty)
    }
  end
end

# lib/dspex/predict/nx_adaptive_engine.ex
defmodule DSPEx.Predict.NxAdaptiveEngine do
  @moduledoc """
  Nx-powered adaptive prediction engine with numerical optimization.
  
  Uses Nx for high-performance parameter optimization, pattern recognition,
  and predictive analytics to improve prediction quality over time.
  """
  
  use GenServer
  
  defstruct [
    :performance_history,
    :parameter_optimizer,
    :pattern_detector,
    :confidence_tracker,
    :nx_backend
  ]
  
  def start_link(opts \\ []) do
    GenServer.start_link(__MODULE__, opts, name: __MODULE__)
  end
  
  def adaptive_predict(inputs, base_program, opts \\ []) do
    GenServer.call(__MODULE__, {:adaptive_predict, inputs, base_program, opts}, 30_000)
  end
  
  def update_performance(prediction_result, actual_outcome) do
    GenServer.cast(__MODULE__, {:update_performance, prediction_result, actual_outcome})
  end
  
  def get_optimization_insights do
    GenServer.call(__MODULE__, :get_optimization_insights)
  end
  
  def init(opts) do
    # Configure Nx backend
    nx_backend = configure_nx_backend(opts)
    Nx.default_backend(nx_backend)
    
    state = %__MODULE__{
      performance_history: [],
      parameter_optimizer: initialize_optimizer(opts),
      pattern_detector: initialize_pattern_detector(opts),
      confidence_tracker: initialize_confidence_tracker(opts),
      nx_backend: nx_backend
    }
    
    {:ok, state}
  end
  
  def handle_call({:adaptive_predict, inputs, base_program, opts}, _from, state) do
    # Analyze input patterns
    input_patterns = analyze_input_patterns(inputs, state.pattern_detector)
    
    # Optimize parameters based on historical performance
    optimized_params = optimize_prediction_parameters(
      base_program, 
      input_patterns, 
      state.parameter_optimizer
    )
    
    # Create optimized program
    optimized_program = apply_parameter_optimizations(base_program, optimized_params)
    
    # Execute prediction with confidence tracking
    result = execute_with_confidence_tracking(
      optimized_program, 
      inputs, 
      opts, 
      state.confidence_tracker
    )
    
    # Update state with prediction record
    prediction_record = %{
      inputs: inputs,
      base_program: base_program,
      optimized_params: optimized_params,
      result: result,
      timestamp: DateTime.utc_now(),
      confidence: extract_confidence(result)
    }
    
    new_state = %{state | 
      performance_history: [prediction_record | state.performance_history] |> Enum.take(1000)
    }
    
    {:reply, result, new_state}
  end
  
  def handle_call(:get_optimization_insights, _from, state) do
    insights = generate_optimization_insights(state)
    {:reply, insights, state}
  end
  
  def handle_cast({:update_performance, prediction_result, actual_outcome}, state) do
    # Update performance tracking with actual outcomes
    updated_history = update_performance_history(
      state.performance_history, 
      prediction_result, 
      actual_outcome
    )
    
    # Retrain parameter optimizer if enough new data
    updated_optimizer = maybe_retrain_optimizer(
      state.parameter_optimizer, 
      updated_history
    )
    
    new_state = %{state |
      performance_history: updated_history,
      parameter_optimizer: updated_optimizer
    }
    
    {:noreply, new_state}
  end
  
  # Core optimization functions
  
  defp analyze_input_patterns(inputs, pattern_detector) do
    # Convert inputs to tensor format for pattern analysis
    input_tensor = convert_inputs_to_tensor(inputs)
    
    # Use Nx to identify patterns
    case Nx.rank(input_tensor) do
      0 -> %{type: :scalar, complexity: :simple}
      1 -> analyze_vector_patterns(input_tensor)
      2 -> analyze_matrix_patterns(input_tensor)
      _ -> %{type: :high_dimensional, complexity: :complex}
    end
  end
  
  defp analyze_vector_patterns(vector_tensor) do
    # Analyze statistical properties
    mean = Nx.mean(vector_tensor)
    std = Nx.standard_deviation(vector_tensor)
    
    # Detect patterns
    complexity = cond do
      Nx.to_number(std) < 0.1 -> :simple
      Nx.to_number(std) < 0.5 -> :moderate
      true -> :complex
    end
    
    %{
      type: :vector,
      complexity: complexity,
      mean: Nx.to_number(mean),
      std: Nx.to_number(std),
      size: Nx.size(vector_tensor)
    }
  end
  
  defp analyze_matrix_patterns(matrix_tensor) do
    # More complex pattern analysis for matrices
    {rows, cols} = Nx.shape(matrix_tensor)
    
    # Compute matrix properties
    frobenius_norm = Nx.LinAlg.norm(matrix_tensor)
    
    %{
      type: :matrix,
      complexity: :complex,
      shape: {rows, cols},
      norm: Nx.to_number(frobenius_norm)
    }
  end
  
  defp optimize_prediction_parameters(base_program, input_patterns, optimizer) do
    # Use historical data to optimize parameters
    case Map.get(optimizer, :optimization_method, :gradient_free) do
      :gradient_free ->
        optimize_with_grid_search(base_program, input_patterns, optimizer)
      
      :gradient_based ->
        optimize_with_gradients(base_program, input_patterns, optimizer)
      
      :evolutionary ->
        optimize_with_evolution(base_program, input_patterns, optimizer)
    end
  end
  
  defp optimize_with_grid_search(base_program, input_patterns, optimizer) do
    # Define parameter search space
    temp_range = Nx.linspace(0.1, 1.5, n: 10)
    top_p_range = Nx.linspace(0.5, 1.0, n: 5)
    
    # Evaluate all combinations
    best_params = 
      for temp <- Nx.to_flat_list(temp_range),
          top_p <- Nx.to_flat_list(top_p_range) do
        params = %{temperature: temp, top_p: top_p}
        score = evaluate_parameter_combination(params, input_patterns, optimizer)
        {params, score}
      end
      |> Enum.max_by(fn {_params, score} -> score end)
      |> elem(0)
    
    best_params
  end
  
  defp evaluate_parameter_combination(params, input_patterns, optimizer) do
    # Score parameter combination based on historical performance
    historical_scores = Map.get(optimizer, :historical_scores, [])
    
    case historical_scores do
      [] -> 0.5  # Default score
      scores -> 
        # Use Nx to compute similarity to successful parameter combinations
        param_vector = Nx.tensor([params.temperature, params.top_p])
        
        similarities = 
          Enum.map(scores, fn {historical_params, score} ->
            historical_vector = Nx.tensor([
              historical_params.temperature, 
              historical_params.top_p
            ])
            
            similarity = compute_vector_similarity(param_vector, historical_vector)
            similarity * score
          end)
        
        case similarities do
          [] -> 0.5
          _ -> Enum.sum(similarities) / length(similarities)
        end
    end
  end
  
  defp compute_vector_similarity(vec_a, vec_b) do
    # Cosine similarity using Nx
    dot_product = Nx.dot(vec_a, vec_b)
    norm_a = Nx.LinAlg.norm(vec_a)
    norm_b = Nx.LinAlg.norm(vec_b)
    
    similarity = dot_product / (norm_a * norm_b)
    Nx.to_number(similarity)
  end
  
  defp apply_parameter_optimizations(base_program, optimized_params) do
    # Apply optimized parameters to the program
    # This would depend on the specific program structure
    case base_program do
      %DSPEx.Predict{} = program ->
        # Apply parameters to predict program
        Map.merge(program, optimized_params)
      
      _ ->
        # Generic parameter application
        Map.merge(base_program, optimized_params)
    end
  end
  
  defp execute_with_confidence_tracking(program, inputs, opts, confidence_tracker) do
    # Execute prediction while tracking confidence metrics
    start_time = System.monotonic_time()
    
    result = DSPEx.Program.forward(program, inputs, opts)
    
    execution_time = System.monotonic_time() - start_time
    
    # Analyze confidence
    confidence = case result do
      {:ok, outputs} ->
        analyze_output_confidence(outputs, confidence_tracker)
      
      {:error, _} ->
        %{confidence: 0.0, reliability: :low}
    end
    
    # Add metadata to result
    enhanced_result = case result do
      {:ok, outputs} ->
        {:ok, Map.put(outputs, :_metadata, %{
          confidence: confidence,
          execution_time: execution_time,
          optimization_applied: true
        })}
      
      error -> error
    end
    
    enhanced_result
  end
  
  defp analyze_output_confidence(outputs, confidence_tracker) do
    # Use Nx to analyze output patterns for confidence estimation
    numerical_outputs = extract_numerical_values(outputs)
    
    case numerical_outputs do
      [] ->
        %{confidence: 0.5, reliability: :medium}
      
      values ->
        tensor = Nx.tensor(values)
        
        # Statistical analysis
        mean = Nx.mean(tensor)
        std = Nx.standard_deviation(tensor)
        
        # Confidence based on consistency
        consistency = 1.0 / (1.0 + Nx.to_number(std))
        confidence = min(consistency, 1.0)
        
        reliability = cond do
          confidence >= 0.8 -> :high
          confidence >= 0.6 -> :medium
          true -> :low
        end
        
        %{
          confidence: confidence,
          reliability: reliability,
          mean: Nx.to_number(mean),
          std: Nx.to_number(std)
        }
    end
  end
  
  # Helper functions
  
  defp configure_nx_backend(opts) do
    case Keyword.get(opts, :nx_backend, :auto) do
      :auto -> {Nx.BinaryBackend, []}
      backend -> backend
    end
  end
  
  defp initialize_optimizer(opts) do
    %{
      optimization_method: Keyword.get(opts, :optimization_method, :gradient_free),
      historical_scores: [],
      parameter_bounds: %{
        temperature: {0.1, 2.0},
        top_p: {0.1, 1.0},
        frequency_penalty: {-2.0, 2.0},
        presence_penalty: {-2.0, 2.0}
      }
    }
  end
  
  defp initialize_pattern_detector(_opts) do
    %{
      pattern_history: [],
      complexity_threshold: 0.5
    }
  end
  
  defp initialize_confidence_tracker(_opts) do
    %{
      confidence_history: [],
      reliability_threshold: 0.7
    }
  end
  
  defp convert_inputs_to_tensor(inputs) when is_map(inputs) do
    # Extract numerical values from input map
    numerical_values = extract_numerical_values(inputs)
    
    case numerical_values do
      [] -> Nx.tensor([0.0])
      values -> Nx.tensor(values)
    end
  end
  
  defp extract_numerical_values(data) when is_map(data) do
    data
    |> Map.values()
    |> Enum.flat_map(&extract_numerical_values/1)
  end
  
  defp extract_numerical_values(data) when is_list(data) do
    Enum.flat_map(data, &extract_numerical_values/1)
  end
  
  defp extract_numerical_values(data) when is_number(data), do: [data]
  defp extract_numerical_values(_), do: []
  
  defp extract_confidence(result) do
    case result do
      {:ok, outputs} ->
        Map.get(outputs, :_metadata, %{}) |> Map.get(:confidence, %{confidence: 0.5})
      
      _ -> %{confidence: 0.0}
    end
  end
  
  defp generate_optimization_insights(state) do
    case state.performance_history do
      [] ->
        %{status: :insufficient_data}
      
      history ->
        # Use Nx to analyze performance trends
        confidences = Enum.map(history, fn record -> 
          record.confidence.confidence || 0.5 
        end)
        
        confidence_tensor = Nx.tensor(confidences)
        
        %{
          mean_confidence: Nx.to_number(Nx.mean(confidence_tensor)),
          confidence_trend: calculate_trend_nx(confidence_tensor),
          total_predictions: length(history),
          optimization_effectiveness: calculate_optimization_effectiveness(history)
        }
    end
  end
  
  defp calculate_trend_nx(values) do
    n = Nx.size(values)
    indices = Nx.iota({n})
    
    # Linear regression for trend
    mean_x = Nx.mean(indices)
    mean_y = Nx.mean(values)
    
    numerator = Nx.sum(
      Nx.multiply(
        Nx.subtract(indices, mean_x),
        Nx.subtract(values, mean_y)
      )
    )
    
    denominator = Nx.sum(Nx.pow(Nx.subtract(indices, mean_x), 2))
    
    slope = Nx.divide(numerator, denominator)
    Nx.to_number(slope)
  end
  
  defp calculate_optimization_effectiveness(history) do
    # Compare optimized vs baseline performance
    # This is a simplified calculation
    optimized_results = Enum.filter(history, fn record -> 
      record.optimized_params != %{}
    end)
    
    case optimized_results do
      [] -> :unknown
      results -> 
        avg_confidence = 
          results
          |> Enum.map(fn r -> r.confidence.confidence || 0.5 end)
          |> Enum.sum()
          |> Kernel./(length(results))
        
        cond do
          avg_confidence >= 0.8 -> :high
          avg_confidence >= 0.6 -> :medium
          true -> :low
        end
    end
  end
end

# config/config.exs - Nx Configuration for Prediction
config :dspex, :predict,
  # Nx backend configuration
  nx_backend: {Nx.BinaryBackend, []},
  
  # Adaptive prediction settings
  adaptive_prediction: %{
    enabled: true,
    optimization_method: :gradient_free,  # :gradient_free, :gradient_based, :evolutionary
    parameter_bounds: %{
      temperature: {0.1, 2.0},
      top_p: {0.1, 1.0},
      max_tokens: {10, 4000}
    },
    confidence_tracking: true,
    pattern_analysis: true
  },
  
  # Nx performance settings
  batch_processing: %{
    default_batch_size: 16,
    max_memory_mb: 500,
    optimization_frequency: 100  # Optimize every N predictions
  },
  
  # Analytics configuration
  analytics: %{
    enable_performance_tracking: true,
    history_size: 1000,
    confidence_threshold: 0.7,
    trend_analysis_window: 50
  }

# config/prod.exs - Production settings
config :dspex, :predict,
  nx_backend: {Nx.BinaryBackend, []},
  adaptive_prediction: %{
    enabled: true,
    optimization_method: :gradient_based,  # More sophisticated for production
    confidence_tracking: true
  },
  batch_processing: %{
    default_batch_size: 32,
    max_memory_mb: 2000
  }

# config/test.exs - Testing configuration
config :dspex, :predict,
  nx_backend: {Nx.BinaryBackend, []},
  adaptive_prediction: %{enabled: false},  # Disable for deterministic tests
  analytics: %{enable_performance_tracking: false}

# mix.exs - Add Nx dependency
defp deps do
  [
    # ... existing dependencies ...
    {:nx, "~> 0.6"},              # Numerical computing for prediction analytics
    {:ex_llm, "~> 0.8.1"},        # LLM client integration
    {:foundation, path: "../foundation"},  # DSPEx foundation
    # ... other dependencies ...
  ]
end