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src/mlx_distributed.erl

-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}.