-module(mlx_distributed). %% Advanced distributed training primitives and communication patterns -export([ %% Communication primitives all_reduce/2, all_reduce/3, all_gather/2, all_gather/3, reduce_scatter/3, reduce_scatter/4, broadcast/3, broadcast/4, %% Advanced communication patterns ring_all_reduce/2, ring_all_reduce/3, tree_all_reduce/2, tree_all_reduce/3, butterfly_all_reduce/2, butterfly_all_reduce/3, %% Topology-aware communication hierarchical_all_reduce/3, hierarchical_all_reduce/4, torus_all_reduce/3, torus_all_reduce/4, %% Gradient compression compressed_all_reduce/3, compressed_all_reduce/4, quantized_all_reduce/3, quantized_all_reduce/4, sparse_all_reduce/2, sparse_all_reduce/3, %% Communication scheduling overlapped_communication/3, overlapped_communication/4, pipelined_communication/3, pipelined_communication/4, batched_communication/2, batched_communication/3, %% Fault tolerance fault_tolerant_all_reduce/3, fault_tolerant_all_reduce/4, checkpoint_communication/2, recover_communication/2, %% Performance optimization adaptive_communication/2, adaptive_communication/3, communication_profiling/2, optimize_communication_plan/2, %% Heterogeneous training heterogeneous_all_reduce/3, heterogeneous_all_reduce/4, device_aware_communication/3, device_aware_communication/4, %% Communication backends init_nccl_backend/1, init_gloo_backend/1, init_mpi_backend/1, create_communication_group/2, destroy_communication_group/1, %% Distributed optimizers distributed_sgd/3, distributed_adam/3, distributed_adamw/3, local_sgd/4, federated_averaging/3, %% Model parallelism pipeline_parallel/3, pipeline_parallel/4, tensor_parallel/3, tensor_parallel/4, expert_parallel/3, expert_parallel/4, %% Data parallelism enhancements dynamic_data_parallel/2, dynamic_data_parallel/3, gradient_compression_ddp/3, zero_redundancy_optimizer/3 ]). -record(comm_group, { id, ranks, backend, topology, compression_config = #{}, fault_tolerance_config = #{} }). -record(comm_stats, { total_bytes = 0, total_time = 0.0, operation_counts = #{}, bandwidth_history = [], latency_history = [] }). %% Communication primitives all_reduce(Tensor, ReduceOp) -> all_reduce(Tensor, ReduceOp, #{}). all_reduce(Tensor, ReduceOp, Options) -> % All-reduce operation with automatic algorithm selection CommGroup = maps:get(group, Options, default_group()), Algorithm = maps:get(algorithm, Options, auto), % Select optimal algorithm based on tensor size and network topology SelectedAlgorithm = case Algorithm of auto -> select_optimal_algorithm(Tensor, ReduceOp, CommGroup); _ -> Algorithm end, % Execute all-reduce case SelectedAlgorithm of ring -> ring_all_reduce(Tensor, ReduceOp, Options); tree -> tree_all_reduce(Tensor, ReduceOp, Options); butterfly -> butterfly_all_reduce(Tensor, ReduceOp, Options); hierarchical -> hierarchical_all_reduce(Tensor, ReduceOp, CommGroup, Options); nccl -> nccl_all_reduce(Tensor, ReduceOp, Options); _ -> {error, {unsupported_algorithm, SelectedAlgorithm}} end. all_gather(Tensor, Options) -> all_gather(Tensor, default_group(), Options). all_gather(Tensor, CommGroup, Options) -> % All-gather operation Algorithm = maps:get(algorithm, Options, ring), case Algorithm of ring -> ring_all_gather(Tensor, CommGroup, Options); tree -> tree_all_gather(Tensor, CommGroup, Options); nccl -> nccl_all_gather(Tensor, CommGroup, Options) end. reduce_scatter(Tensor, ReduceOp, CommGroup) -> reduce_scatter(Tensor, ReduceOp, CommGroup, #{}). reduce_scatter(Tensor, ReduceOp, CommGroup, Options) -> % Reduce-scatter operation Algorithm = maps:get(algorithm, Options, ring), case Algorithm of ring -> ring_reduce_scatter(Tensor, ReduceOp, CommGroup, Options); tree -> tree_reduce_scatter(Tensor, ReduceOp, CommGroup, Options); nccl -> nccl_reduce_scatter(Tensor, ReduceOp, CommGroup, Options) end. broadcast(Tensor, Root, CommGroup) -> broadcast(Tensor, Root, CommGroup, #{}). broadcast(Tensor, Root, CommGroup, Options) -> % Broadcast operation Algorithm = maps:get(algorithm, Options, tree), case Algorithm of tree -> tree_broadcast(Tensor, Root, CommGroup, Options); linear -> linear_broadcast(Tensor, Root, CommGroup, Options); nccl -> nccl_broadcast(Tensor, Root, CommGroup, Options) end. %% Advanced communication patterns ring_all_reduce(Tensor, ReduceOp) -> ring_all_reduce(Tensor, ReduceOp, #{}). ring_all_reduce(Tensor, ReduceOp, Options) -> % Ring-based all-reduce implementation CommGroup = maps:get(group, Options, default_group()), Ranks = get_group_ranks(CommGroup), MyRank = get_my_rank(), NumRanks = length(Ranks), case NumRanks of 1 -> {ok, Tensor}; _ -> % Chunk tensor for ring algorithm {ok, Chunks} = chunk_tensor_for_ring(Tensor, NumRanks), % Reduce-scatter phase {ok, ReducedChunks} = ring_reduce_scatter_phase(Chunks, ReduceOp, Ranks, MyRank), % All-gather phase {ok, GatheredChunks} = ring_all_gather_phase(ReducedChunks, Ranks, MyRank), % Reconstruct tensor mlx:concatenate(GatheredChunks, 0) end. tree_all_reduce(Tensor, ReduceOp) -> tree_all_reduce(Tensor, ReduceOp, #{}). tree_all_reduce(Tensor, ReduceOp, Options) -> % Tree-based all-reduce implementation CommGroup = maps:get(group, Options, default_group()), TreeTopology = maps:get(tree_topology, Options, binary_tree), % Build communication tree CommTree = build_communication_tree(CommGroup, TreeTopology), % Execute tree all-reduce execute_tree_all_reduce(Tensor, ReduceOp, CommTree). butterfly_all_reduce(Tensor, ReduceOp) -> butterfly_all_reduce(Tensor, ReduceOp, #{}). butterfly_all_reduce(Tensor, ReduceOp, Options) -> % Butterfly-based all-reduce implementation CommGroup = maps:get(group, Options, default_group()), Ranks = get_group_ranks(CommGroup), NumRanks = length(Ranks), % Check if number of ranks is power of 2 case is_power_of_two(NumRanks) of false -> {error, butterfly_requires_power_of_two_ranks}; true -> MyRank = get_my_rank(), LogRanks = round(math:log2(NumRanks)), % Execute butterfly phases execute_butterfly_phases(Tensor, ReduceOp, MyRank, LogRanks) end. %% Topology-aware communication hierarchical_all_reduce(Tensor, ReduceOp, CommGroup) -> hierarchical_all_reduce(Tensor, ReduceOp, CommGroup, #{}). hierarchical_all_reduce(Tensor, ReduceOp, CommGroup, Options) -> % Hierarchical all-reduce for multi-node, multi-GPU setups NodeGroups = get_node_groups(CommGroup), % Intra-node all-reduce {ok, NodeReducedTensor} = intra_node_all_reduce(Tensor, ReduceOp, Options), % Inter-node all-reduce {ok, GlobalReducedTensor} = inter_node_all_reduce(NodeReducedTensor, ReduceOp, NodeGroups, Options), % Intra-node broadcast intra_node_broadcast(GlobalReducedTensor, Options). torus_all_reduce(Tensor, ReduceOp, TorusTopology) -> torus_all_reduce(Tensor, ReduceOp, TorusTopology, #{}). torus_all_reduce(Tensor, ReduceOp, TorusTopology, Options) -> % Torus topology all-reduce for large-scale systems #{dimensions := Dimensions, coordinates := MyCoords} = TorusTopology, % Perform all-reduce along each dimension lists:foldl(fun(Dim, CurrentTensor) -> {ok, ReducedTensor} = torus_reduce_along_dimension(CurrentTensor, ReduceOp, Dim, TorusTopology), ReducedTensor end, Tensor, lists:seq(0, length(Dimensions) - 1)). %% Gradient compression compressed_all_reduce(Tensor, ReduceOp, CompressionConfig) -> compressed_all_reduce(Tensor, ReduceOp, CompressionConfig, #{}). compressed_all_reduce(Tensor, ReduceOp, CompressionConfig, Options) -> % All-reduce with gradient compression CompressionType = maps:get(type, CompressionConfig, topk), CompressionRatio = maps:get(ratio, CompressionConfig, 0.01), % Compress tensor {ok, CompressedTensor, CompressionMeta} = compress_tensor(Tensor, CompressionType, CompressionRatio), % Perform all-reduce on compressed tensor {ok, ReducedCompressed} = all_reduce(CompressedTensor, ReduceOp, Options), % Decompress result decompress_tensor(ReducedCompressed, CompressionMeta). quantized_all_reduce(Tensor, ReduceOp, QuantizationConfig) -> quantized_all_reduce(Tensor, ReduceOp, QuantizationConfig, #{}). quantized_all_reduce(Tensor, ReduceOp, QuantizationConfig, Options) -> % All-reduce with quantization QuantBits = maps:get(bits, QuantizationConfig, 8), ScaleType = maps:get(scale_type, QuantizationConfig, layer_wise), % Quantize tensor {ok, QuantizedTensor, QuantMeta} = quantize_for_communication(Tensor, QuantBits, ScaleType), % Perform all-reduce on quantized tensor {ok, ReducedQuantized} = all_reduce(QuantizedTensor, ReduceOp, Options), % Dequantize result dequantize_from_communication(ReducedQuantized, QuantMeta). sparse_all_reduce(SparseTensor, ReduceOp) -> sparse_all_reduce(SparseTensor, ReduceOp, #{}). sparse_all_reduce(SparseTensor, ReduceOp, Options) -> % All-reduce for sparse tensors SparsityThreshold = maps:get(sparsity_threshold, Options, 0.01), % Extract indices and values {ok, Indices, Values} = extract_sparse_components(SparseTensor, SparsityThreshold), % All-gather indices from all ranks {ok, AllIndices} = all_gather(Indices, Options), % All-gather values from all ranks {ok, AllValues} = all_gather(Values, Options), % Merge sparse tensors merge_sparse_tensors(AllIndices, AllValues, ReduceOp). %% Communication scheduling overlapped_communication(ComputeFun, CommunicationOps, Tensor) -> overlapped_communication(ComputeFun, CommunicationOps, Tensor, #{}). overlapped_communication(ComputeFun, CommunicationOps, Tensor, Options) -> % Overlap computation with communication OverlapStrategy = maps:get(strategy, Options, automatic), case OverlapStrategy of automatic -> % Automatically determine optimal overlap auto_overlap_communication(ComputeFun, CommunicationOps, Tensor); manual -> % Manual overlap control manual_overlap_communication(ComputeFun, CommunicationOps, Tensor, Options) end. pipelined_communication(TensorList, CommunicationOp, PipelineStages) -> pipelined_communication(TensorList, CommunicationOp, PipelineStages, #{}). pipelined_communication(TensorList, CommunicationOp, PipelineStages, Options) -> % Pipelined communication for better bandwidth utilization ChunkSize = length(TensorList) div PipelineStages, % Create pipeline stages PipelineChunks = create_pipeline_chunks(TensorList, ChunkSize), % Execute pipelined communication execute_pipelined_communication(PipelineChunks, CommunicationOp, Options). batched_communication(CommunicationOps, MaxBatchSize) -> batched_communication(CommunicationOps, MaxBatchSize, #{}). batched_communication(CommunicationOps, MaxBatchSize, Options) -> % Batch multiple communication operations BatchingStrategy = maps:get(strategy, Options, size_based), % Group operations into batches Batches = create_communication_batches(CommunicationOps, MaxBatchSize, BatchingStrategy), % Execute batched operations lists:map(fun(Batch) -> execute_communication_batch(Batch) end, Batches). %% Fault tolerance fault_tolerant_all_reduce(Tensor, ReduceOp, FaultConfig) -> fault_tolerant_all_reduce(Tensor, ReduceOp, FaultConfig, #{}). fault_tolerant_all_reduce(Tensor, ReduceOp, FaultConfig, Options) -> % Fault-tolerant all-reduce implementation ReplicationFactor = maps:get(replication_factor, FaultConfig, 2), MaxRetries = maps:get(max_retries, FaultConfig, 3), % Execute with fault tolerance execute_with_fault_tolerance(fun() -> all_reduce(Tensor, ReduceOp, Options) end, ReplicationFactor, MaxRetries). checkpoint_communication(CommState, CheckpointPath) -> % Checkpoint communication state for fault recovery CheckpointData = #{ communication_state => CommState, timestamp => erlang:system_time(microsecond), version => "1.0" }, mlx_io:save_model_data(CheckpointData, CheckpointPath). recover_communication(CheckpointPath, RecoveryOptions) -> % Recover communication state from checkpoint case mlx_io:load_model_data(CheckpointPath) of {ok, CheckpointData} -> CommState = maps:get(communication_state, CheckpointData), {ok, CommState}; {error, Reason} -> {error, {recovery_failed, Reason}} end. %% Performance optimization adaptive_communication(Tensor, CommunicationHistory) -> adaptive_communication(Tensor, CommunicationHistory, #{}). adaptive_communication(Tensor, CommunicationHistory, Options) -> % Adaptively choose communication algorithm based on history {ok, TensorSize} = mlx:size(Tensor), NetworkBandwidth = estimate_network_bandwidth(CommunicationHistory), Latency = estimate_network_latency(CommunicationHistory), % Choose optimal algorithm Algorithm = choose_adaptive_algorithm(TensorSize, NetworkBandwidth, Latency), % Execute with chosen algorithm all_reduce(Tensor, sum, maps:put(algorithm, Algorithm, Options)). communication_profiling(CommunicationOp, ProfilingOptions) -> % Profile communication operation EnableDetailedProfiling = maps:get(detailed, ProfilingOptions, false), % Start profiling StartTime = erlang:system_time(microsecond), % Execute operation Result = CommunicationOp(), % End profiling EndTime = erlang:system_time(microsecond), % Collect profiling data ProfilingData = #{ execution_time => EndTime - StartTime, result => Result, detailed_metrics => case EnableDetailedProfiling of true -> collect_detailed_metrics(); false -> #{} end }, {ok, ProfilingData}. optimize_communication_plan(CommunicationOps, NetworkTopology) -> % Optimize communication plan based on network topology % Analyze dependencies between operations Dependencies = analyze_communication_dependencies(CommunicationOps), % Create optimal schedule OptimalSchedule = create_optimal_schedule(Dependencies, NetworkTopology), {ok, OptimalSchedule}. %% Heterogeneous training heterogeneous_all_reduce(Tensor, ReduceOp, DeviceConfig) -> heterogeneous_all_reduce(Tensor, ReduceOp, DeviceConfig, #{}). heterogeneous_all_reduce(Tensor, ReduceOp, DeviceConfig, Options) -> % All-reduce for heterogeneous devices (CPU/GPU/TPU mix) DeviceGroups = group_by_device_type(DeviceConfig), % Perform device-specific optimizations lists:foldl(fun({DeviceType, Devices}, CurrentTensor) -> DeviceOptions = maps:put(device_type, DeviceType, Options), {ok, ReducedTensor} = device_specific_all_reduce(CurrentTensor, ReduceOp, Devices, DeviceOptions), ReducedTensor end, Tensor, DeviceGroups). device_aware_communication(Tensor, CommunicationOp, DeviceTopology) -> device_aware_communication(Tensor, CommunicationOp, DeviceTopology, #{}). device_aware_communication(Tensor, CommunicationOp, DeviceTopology, Options) -> % Communication aware of device capabilities and interconnects OptimalPath = find_optimal_communication_path(DeviceTopology), % Execute communication along optimal path execute_along_path(Tensor, CommunicationOp, OptimalPath, Options). %% Communication backends init_nccl_backend(NCCLConfig) -> % Initialize NCCL backend CommId = mlx_nif:nccl_get_unique_id(), mlx_nif:nccl_init_rank(maps:get(rank, NCCLConfig), maps:get(world_size, NCCLConfig), CommId). init_gloo_backend(GlooConfig) -> % Initialize Gloo backend mlx_nif:gloo_init(GlooConfig). init_mpi_backend(MPIConfig) -> % Initialize MPI backend mlx_nif:mpi_init(MPIConfig). create_communication_group(Ranks, Backend) -> % Create communication group GroupId = make_ref(), Group = #comm_group{ id = GroupId, ranks = Ranks, backend = Backend }, put({comm_group, GroupId}, Group), {ok, GroupId}. destroy_communication_group(GroupId) -> % Destroy communication group erase({comm_group, GroupId}), ok. %% Distributed optimizers distributed_sgd(Gradients, LearningRate, Momentum) -> % Distributed SGD optimizer % All-reduce gradients {ok, ReducedGradients} = all_reduce(Gradients, sum), % Scale by world size WorldSize = get_world_size(), {ok, ScaledGradients} = mlx:divide(ReducedGradients, mlx:array(WorldSize)), % Apply momentum apply_momentum_update(ScaledGradients, LearningRate, Momentum). distributed_adam(Gradients, LearningRate, AdamConfig) -> % Distributed Adam optimizer Beta1 = maps:get(beta1, AdamConfig, 0.9), Beta2 = maps:get(beta2, AdamConfig, 0.999), Epsilon = maps:get(epsilon, AdamConfig, 0.00000001), % All-reduce gradients {ok, ReducedGradients} = all_reduce(Gradients, sum), % Scale by world size WorldSize = get_world_size(), {ok, ScaledGradients} = mlx:divide(ReducedGradients, mlx:array(WorldSize)), % Apply Adam update apply_adam_update(ScaledGradients, LearningRate, Beta1, Beta2, Epsilon). distributed_adamw(Gradients, LearningRate, AdamWConfig) -> % Distributed AdamW optimizer WeightDecay = maps:get(weight_decay, AdamWConfig, 0.01), % First apply weight decay, then distributed Adam {ok, DecayedGradients} = apply_weight_decay(Gradients, WeightDecay), distributed_adam(DecayedGradients, LearningRate, AdamWConfig). local_sgd(Gradients, LearningRate, Momentum, LocalSteps) -> % Local SGD with periodic synchronization CurrentStep = get_local_sgd_step(), case CurrentStep rem LocalSteps of 0 -> % Synchronization step distributed_sgd(Gradients, LearningRate, Momentum); _ -> % Local update apply_momentum_update(Gradients, LearningRate, Momentum) end. federated_averaging(LocalModels, AggregationWeights, FedConfig) -> % Federated averaging algorithm % Weighted average of local models WeightedModels = lists:zipwith(fun(Model, Weight) -> maps:map(fun(_Name, Param) -> {ok, Weighted} = mlx:multiply(Param, mlx:array(Weight)), Weighted end, Model) end, LocalModels, AggregationWeights), % Sum weighted models aggregate_models(WeightedModels). %% Model parallelism pipeline_parallel(Model, InputData, PipelineConfig) -> pipeline_parallel(Model, InputData, PipelineConfig, #{}). pipeline_parallel(Model, InputData, PipelineConfig, Options) -> % Pipeline parallelism implementation Stages = maps:get(stages, PipelineConfig), MicroBatchSize = maps:get(micro_batch_size, PipelineConfig), % Split model into pipeline stages PipelineStages = split_model_into_stages(Model, Stages), % Execute pipeline execute_pipeline(PipelineStages, InputData, MicroBatchSize, Options). tensor_parallel(Model, InputData, TensorParallelConfig) -> tensor_parallel(Model, InputData, TensorParallelConfig, #{}). tensor_parallel(Model, InputData, TensorParallelConfig, Options) -> % Tensor parallelism implementation ParallelDimension = maps:get(parallel_dim, TensorParallelConfig), TensorParallelSize = maps:get(tp_size, TensorParallelConfig), % Partition tensors PartitionedModel = partition_model_tensors(Model, ParallelDimension, TensorParallelSize), % Execute with tensor parallelism execute_tensor_parallel(PartitionedModel, InputData, Options). expert_parallel(Model, InputData, ExpertConfig) -> expert_parallel(Model, InputData, ExpertConfig, #{}). expert_parallel(Model, InputData, ExpertConfig, Options) -> % Expert parallelism (Mixture of Experts) NumExperts = maps:get(num_experts, ExpertConfig), ExpertCapacity = maps:get(expert_capacity, ExpertConfig), % Route inputs to experts {ok, RoutingDecisions} = route_to_experts(InputData, NumExperts), % Execute expert computation execute_expert_parallel(Model, InputData, RoutingDecisions, ExpertCapacity, Options). %% Data parallelism enhancements dynamic_data_parallel(Model, DataLoader) -> dynamic_data_parallel(Model, DataLoader, #{}). dynamic_data_parallel(Model, DataLoader, Options) -> % Dynamic data parallelism with load balancing LoadBalancingStrategy = maps:get(load_balancing, Options, round_robin), % Monitor worker performance WorkerStats = monitor_worker_performance(), % Dynamically adjust data distribution AdjustedDataLoader = adjust_data_distribution(DataLoader, WorkerStats, LoadBalancingStrategy), {ok, AdjustedDataLoader}. gradient_compression_ddp(Model, CompressionConfig, DDPConfig) -> % Data parallel with gradient compression CompressionRatio = maps:get(compression_ratio, CompressionConfig, 0.01), CompressionType = maps:get(compression_type, CompressionConfig, topk), % Wrap model with compression CompressedModel = wrap_model_with_compression(Model, CompressionType, CompressionRatio), {ok, CompressedModel}. zero_redundancy_optimizer(Optimizer, OptimizerConfig, ZeROConfig) -> % ZeRO (Zero Redundancy Optimizer) implementation Stage = maps:get(stage, ZeROConfig, 1), case Stage of 1 -> zero_stage1(Optimizer, OptimizerConfig); 2 -> zero_stage2(Optimizer, OptimizerConfig); 3 -> zero_stage3(Optimizer, OptimizerConfig) end. %% Helper functions default_group() -> case get(default_comm_group) of undefined -> {ok, GroupId} = create_communication_group(get_all_ranks(), nccl), put(default_comm_group, GroupId), GroupId; GroupId -> GroupId end. get_group_ranks(GroupId) -> case get({comm_group, GroupId}) of undefined -> [0]; % Fallback for single rank Group -> Group#comm_group.ranks end. get_my_rank() -> case get(my_rank) of undefined -> 0; Rank -> Rank end. get_world_size() -> length(get_all_ranks()). get_all_ranks() -> case get(all_ranks) of undefined -> [0]; Ranks -> Ranks end. select_optimal_algorithm(Tensor, ReduceOp, CommGroup) -> % Select optimal algorithm based on tensor size and topology {ok, TensorSize} = mlx:size(Tensor), NumRanks = length(get_group_ranks(CommGroup)), case {TensorSize, NumRanks} of {Size, _} when Size < 1024 -> tree; {_, Ranks} when Ranks < 8 -> ring; {Size, Ranks} when Size > 1024*1024, Ranks >= 8 -> hierarchical; _ -> ring end. chunk_tensor_for_ring(Tensor, NumChunks) -> % Chunk tensor for ring algorithm mlx:split(Tensor, NumChunks, 0). ring_reduce_scatter_phase(Chunks, ReduceOp, Ranks, MyRank) -> % Ring reduce-scatter phase implementation {ok, Chunks}. % Simplified ring_all_gather_phase(Chunks, Ranks, MyRank) -> % Ring all-gather phase implementation {ok, Chunks}. % Simplified build_communication_tree(CommGroup, TreeTopology) -> % Build communication tree #{root => 0, children => []}. % Simplified execute_tree_all_reduce(Tensor, ReduceOp, CommTree) -> % Execute tree all-reduce {ok, Tensor}. % Simplified is_power_of_two(N) -> (N > 0) andalso ((N band (N - 1)) =:= 0). execute_butterfly_phases(Tensor, ReduceOp, MyRank, LogRanks) -> % Execute butterfly all-reduce phases {ok, Tensor}. % Simplified get_node_groups(CommGroup) -> % Get node groups for hierarchical communication []. % Simplified intra_node_all_reduce(Tensor, ReduceOp, Options) -> % Intra-node all-reduce {ok, Tensor}. % Simplified inter_node_all_reduce(Tensor, ReduceOp, NodeGroups, Options) -> % Inter-node all-reduce {ok, Tensor}. % Simplified intra_node_broadcast(Tensor, Options) -> % Intra-node broadcast {ok, Tensor}. % Simplified torus_reduce_along_dimension(Tensor, ReduceOp, Dim, TorusTopology) -> % Torus reduce along dimension {ok, Tensor}. % Simplified compress_tensor(Tensor, CompressionType, CompressionRatio) -> % Compress tensor for communication {ok, Tensor, #{}}. % Simplified decompress_tensor(CompressedTensor, CompressionMeta) -> % Decompress tensor {ok, CompressedTensor}. % Simplified quantize_for_communication(Tensor, QuantBits, ScaleType) -> % Quantize tensor for communication {ok, Tensor, #{}}. % Simplified dequantize_from_communication(QuantizedTensor, QuantMeta) -> % Dequantize tensor {ok, QuantizedTensor}. % Simplified extract_sparse_components(SparseTensor, SparsityThreshold) -> % Extract sparse tensor components {ok, [], []}. % Simplified merge_sparse_tensors(AllIndices, AllValues, ReduceOp) -> % Merge sparse tensors {ok, []}. % Simplified auto_overlap_communication(ComputeFun, CommunicationOps, Tensor) -> % Automatic overlap optimization {ok, ComputeFun(Tensor)}. % Simplified manual_overlap_communication(ComputeFun, CommunicationOps, Tensor, Options) -> % Manual overlap control {ok, ComputeFun(Tensor)}. % Simplified create_pipeline_chunks(TensorList, ChunkSize) -> % Create pipeline chunks []. % Simplified execute_pipelined_communication(PipelineChunks, CommunicationOp, Options) -> % Execute pipelined communication {ok, []}. % Simplified create_communication_batches(CommunicationOps, MaxBatchSize, BatchingStrategy) -> % Create communication batches []. % Simplified execute_communication_batch(Batch) -> % Execute communication batch ok. % Simplified execute_with_fault_tolerance(Operation, ReplicationFactor, MaxRetries) -> % Execute with fault tolerance Operation(). % Simplified estimate_network_bandwidth(CommunicationHistory) -> % Estimate network bandwidth 1000000. % Simplified estimate_network_latency(CommunicationHistory) -> % Estimate network latency 0.001. % Simplified choose_adaptive_algorithm(TensorSize, NetworkBandwidth, Latency) -> % Choose adaptive algorithm ring. % Simplified collect_detailed_metrics() -> % Collect detailed profiling metrics #{}. % Simplified analyze_communication_dependencies(CommunicationOps) -> % Analyze dependencies #{}. % Simplified create_optimal_schedule(Dependencies, NetworkTopology) -> % Create optimal schedule []. % Simplified group_by_device_type(DeviceConfig) -> % Group devices by type []. % Simplified device_specific_all_reduce(Tensor, ReduceOp, Devices, DeviceOptions) -> % Device-specific all-reduce {ok, Tensor}. % Simplified find_optimal_communication_path(DeviceTopology) -> % Find optimal communication path []. % Simplified execute_along_path(Tensor, CommunicationOp, OptimalPath, Options) -> % Execute along path {ok, Tensor}. % Simplified apply_momentum_update(Gradients, LearningRate, Momentum) -> % Apply momentum update {ok, Gradients}. % Simplified apply_adam_update(Gradients, LearningRate, Beta1, Beta2, Epsilon) -> % Apply Adam update {ok, Gradients}. % Simplified apply_weight_decay(Gradients, WeightDecay) -> % Apply weight decay {ok, Gradients}. % Simplified get_local_sgd_step() -> case get(local_sgd_step) of undefined -> 0; Step -> Step end. aggregate_models(WeightedModels) -> % Aggregate weighted models {}. % Simplified split_model_into_stages(Model, Stages) -> % Split model into pipeline stages []. % Simplified execute_pipeline(PipelineStages, InputData, MicroBatchSize, Options) -> % Execute pipeline {ok, []}. % Simplified partition_model_tensors(Model, ParallelDimension, TensorParallelSize) -> % Partition model tensors Model. % Simplified execute_tensor_parallel(PartitionedModel, InputData, Options) -> % Execute tensor parallel {ok, []}. % Simplified route_to_experts(InputData, NumExperts) -> % Route inputs to experts {ok, []}. % Simplified execute_expert_parallel(Model, InputData, RoutingDecisions, ExpertCapacity, Options) -> % Execute expert parallel {ok, []}. % Simplified monitor_worker_performance() -> % Monitor worker performance #{}. % Simplified adjust_data_distribution(DataLoader, WorkerStats, LoadBalancingStrategy) -> % Adjust data distribution DataLoader. % Simplified wrap_model_with_compression(Model, CompressionType, CompressionRatio) -> % Wrap model with compression Model. % Simplified zero_stage1(Optimizer, OptimizerConfig) -> % ZeRO Stage 1 {ok, Optimizer}. % Simplified zero_stage2(Optimizer, OptimizerConfig) -> % ZeRO Stage 2 {ok, Optimizer}. % Simplified zero_stage3(Optimizer, OptimizerConfig) -> % ZeRO Stage 3 {ok, Optimizer}. % Simplified % Additional NCCL/backend implementations would be stubs calling actual NIF functions nccl_all_reduce(Tensor, ReduceOp, Options) -> {ok, Tensor}. nccl_all_gather(Tensor, CommGroup, Options) -> {ok, [Tensor]}. nccl_reduce_scatter(Tensor, ReduceOp, CommGroup, Options) -> {ok, Tensor}. nccl_broadcast(Tensor, Root, CommGroup, Options) -> {ok, Tensor}. ring_all_gather(Tensor, CommGroup, Options) -> {ok, [Tensor]}. tree_all_gather(Tensor, CommGroup, Options) -> {ok, [Tensor]}. ring_reduce_scatter(Tensor, ReduceOp, CommGroup, Options) -> {ok, Tensor}. tree_reduce_scatter(Tensor, ReduceOp, CommGroup, Options) -> {ok, Tensor}. tree_broadcast(Tensor, Root, CommGroup, Options) -> {ok, Tensor}. linear_broadcast(Tensor, Root, CommGroup, Options) -> {ok, Tensor}.