TPU Pod Optical Interconnect System

┌─────────────────────────────────────────────────┐
│              TPU v4 Chip                        │
├─────────────────────────────────────────────────┤
│  ┌─────────────┐  ┌─────────────┐              │
│  │   MXU 0     │  │   MXU 1     │  Matrix      │
│  │  128×128    │  │  128×128    │  Multiply    │
│  │  Systolic   │  │  Systolic   │  Units       │
│  └─────────────┘  └─────────────┘              │
│         │                 │                     │
│  ┌──────┴─────────────────┴──────┐             │
│  │     Vector Units (VPU)        │             │
│  │  • FP32/BF16/INT8 operations  │             │
│  │  • 16K elements/cycle         │             │
│  └───────────────────────────────┘             │
│         │                                       │
│  ┌──────┴─────────────────────────┐            │
│  │   High Bandwidth Memory (HBM)  │            │
│  │   • 32 GB HBM2e                │            │
│  │   • 1.2 TB/s bandwidth         │            │
│  └────────────────────────────────┘            │
│         │                                       │
│  ┌──────┴─────────────────────────┐            │
│  │   Interconnect Controllers     │            │
│  │   • 6× Optical Links           │ ◄─────────┐│
│  │   • Router logic               │         I │
│  │   • DMA engines                │         C │
│  └────────────────────────────────┘         I │
└─────────────────────────────────────────────────┘

Model size: 175B parameters (GPT-3 scale)
4096 TPUs, sharded across all chips
Per-chip: 175B / 4096 = 42.7M parameters
 
All-reduce requirements per iteration:
- Forward pass: Receive activations
- Backward pass: Send gradients
- Parameter sync: All-reduce (~171 MB per chip)
 
Target: 500 iterations/second
Required BW: 171 MB × 500 = 85 GB/s bidirectional
 
Actual: 6 links × 15 GB/s = 90 GB/s ✓

Source → [Header|Payload] → Router (store, forward) → Destination
 
Latency = Serialization + Propagation + Queueing + Switching
        = (Packet_size/BW) + (Distance/c) + (Queue_depth × Packet_time) + Switch_latency
 
Overhead:
- Headers: 5-10% of bandwidth
- Buffering: SRAM, power hungry
- Arbitration: Complex, non-deterministic

Source → Optical Switch (passive) → Destination
 
Latency = Serialization + Propagation + Circuit_setup (one-time)
        = (Message_size/BW) + (Distance/c) + Setup_latency
 
Advantages:
- No packet overhead (100% efficiency)
- No buffering needed
- Deterministic latency
- Lower power

      Input Fibers          Mirrors (actuated)        Output Fibers
         │                       ╱                         │
   ──────┼──────────────────────●──────────────────────────┼──────
         │                     ╱ ╲                         │
   ──────┼────────────────────●───●────────────────────────┼──────
         │                   ╱     ╲                       │
   ──────┼──────────────────●───────●──────────────────────┼──────

           Ring Resonators (electrically tuned)
    In ────●───●───●───●──── Out 1
           │   │   │   │
           ●───●───●───●──── Out 2

# Pseudo-code for circuit configuration
 
# Static configuration (set at Pod initialization)
def configure_static_topology(pod_size):
    """Set up 3D torus"""
    for chip_id in range(pod_size):
        x, y, z = chip_id_to_coords(chip_id)
        
        neighbors = {
            '+X': coords_to_chip_id((x+1) % X_DIM, y, z),
            '-X': coords_to_chip_id((x-1) % X_DIM, y, z),
            '+Y': coords_to_chip_id(x, (y+1) % Y_DIM, z),
            '-Y': coords_to_chip_id(x, (y-1) % Y_DIM, z),
            '+Z': coords_to_chip_id(x, y, (z+1) % Z_DIM),
            '-Z': coords_to_chip_id(x, y, (z-1) % Z_DIM),
        }
        
        configure_optical_circuits(chip_id, neighbors)
 
# Dynamic reconfiguration (for fault tolerance)
def reconfigure_around_failure(failed_chip):
    """Reroute around failed chip"""
    affected_neighbors = get_neighbors(failed_chip)
    
    for neighbor in affected_neighbors:
        # Find alternate path (e.g., skip failed chip)
        new_route = find_alternate_path(neighbor, failed_chip)
        reconfigure_optical_switch(neighbor, new_route)

           Z-axis
            │
            │
         (0,0,1)───(1,0,1)
           ╱│      ╱│
          ╱ │     ╱ │
      (0,1,1)───(1,1,1)
         │  │    │  │
         │(0,0,0)┼(1,0,0)
         │ ╱     │╱
         │╱      │
      (0,1,0)───(1,1,0)──── Y-axis
        ╱
       ╱
    X-axis
 
Wrap-around connections (torus):
- (X_DIM-1, y, z) ↔ (0, y, z)
- (x, Y_DIM-1, z) ↔ (x, 0, z)
- (x, y, Z_DIM-1) ↔ (x, y, 0)

Bisection: Minimum link capacity if Pod is cut in half
 
For 16×16×16 torus, cut along one dimension:
Cut through X=8 plane: 16×16 = 256 links
Bandwidth per link: ~150 Gbps
Total bisection BW: 256 × 150 Gbps = 38.4 Tbps
 
Compare to Fat-tree (2:1 oversubscription):
Would need 256 × 75 Gbps = 19.2 Tbps
Torus: 2× better bisection bandwidth

def route_packet(source, dest):
    """
    Simple dimension-ordered routing for 3D torus
    Route along X, then Y, then Z
    """
    current = source
    path = [current]
    
    # Route along X dimension
    while current.x != dest.x:
        if (dest.x - current.x) % X_DIM < X_DIM / 2:
            current.x = (current.x + 1) % X_DIM  # +X direction
        else:
            current.x = (current.x - 1 + X_DIM) % X_DIM  # -X direction
        path.append(current)
    
    # Route along Y dimension
    while current.y != dest.y:
        if (dest.y - current.y) % Y_DIM < Y_DIM / 2:
            current.y = (current.y + 1) % Y_DIM
        else:
            current.y = (current.y - 1 + Y_DIM) % Y_DIM
        path.append(current)
    
    # Route along Z dimension
    while current.z != dest.z:
        if (dest.z - current.z) % Z_DIM < Z_DIM / 2:
            current.z = (current.z + 1) % Z_DIM
        else:
            current.z = (current.z - 1 + Z_DIM) % Z_DIM
        path.append(current)
    
    return path

def adaptive_route(source, dest, link_utilization):
    """
    Choose dimension order based on current link utilization
    """
    dims_to_route = []
    if source.x != dest.x:
        dims_to_route.append('X')
    if source.y != dest.y:
        dims_to_route.append('Y')
    if source.z != dest.z:
        dims_to_route.append('Z')
    
    # Sort dimensions by current link utilization (least busy first)
    dims_to_route.sort(key=lambda d: link_utilization[d])
    
    # Route in order of least congestion
    for dim in dims_to_route:
        route_along_dimension(dim)

Form factor: QSFP-DD
Lanes: 8 × 25 Gbps (PAM4) = 200 Gbps
Wavelength: 850 nm (multi-mode) or 1310 nm (single-mode)
Reach: 100m (MM) or 10 km (SM)
Power: 5-8W per module

Symbol Encoding:
  3 ─┐         ┌──  (11)
  2 ─┤   ┌─────┘    (10)
  1 ─┤   │          (01)
  0 ─└───┘          (00)
 
2 bits per symbol
→ 2× spectral efficiency
→ 50 Gbps per lane at 25 GHz bandwidth

Wavelengths: 1270 nm, 1290 nm, 1310 nm, 1330 nm, ...
Spacing: 20 nm
Channels: Typically 4-8
 
Example:
  4 wavelengths × 100 Gbps = 400 Gbps per fiber

Wavelengths: C-band (1530-1565 nm)
Spacing: 0.8 nm (100 GHz grid) or 0.4 nm (50 GHz)
Channels: 40-80+
 
Example:
  40 wavelengths × 100 Gbps = 4 Tbps per fiber

RS(528, 514):
  514 data symbols
  14 parity symbols
  Overhead: 14/514 = 2.7%
  
Can correct: 7 symbol errors
Pre-FEC BER: ~1×10^-4
Post-FEC BER: <1×10^-15

Overhead: ~5%
Pre-FEC BER: ~2×10^-4
Post-FEC BER: <1×10^-15

┌─────────────────────────────────────┐
│  Application Layer (XLA, JAX)      │
├─────────────────────────────────────┤
│  Collective Ops (NCCL-like)        │  ← All-reduce, All-gather
├─────────────────────────────────────┤
│  Transport Layer (Custom)           │  ← Message fragmentation, reassembly
├─────────────────────────────────────┤
│  Link Layer (Google proprietary)   │  ← Flow control, error detection
├─────────────────────────────────────┤
│  Physical Layer (Optical)           │  ← Transceivers, FEC
└─────────────────────────────────────┘

┌──────┬──────┬───────────┬──────────────────┬─────┬─────┐
│ SOF  │ Dest │  Source   │     Payload      │ CRC │ EOF │
│ 8b   │ 16b  │   16b     │   N bytes        │ 32b │ 8b  │
└──────┴──────┴───────────┴──────────────────┴─────┴─────┘
 
SOF: Start of Frame
Dest: Destination chip ID (16 bits → 65536 chips addressable)
Source: Source chip ID
Payload: Data (typically 4 KB - 1 MB)
CRC: Cyclic Redundancy Check
EOF: End of Frame

class FlowControl:
    def __init__(self, link_id, buffer_size):
        self.link_id = link_id
        self.credits = buffer_size  # In units of max packet size
        self.remote_credits = buffer_size
    
    def can_send(self, packet_size):
        """Check if we have credits to send"""
        required_credits = (packet_size + MAX_PACKET - 1) // MAX_PACKET
        return self.remote_credits >= required_credits
    
    def send_packet(self, packet):
        """Send packet and decrement credits"""
        if self.can_send(len(packet)):
            transmit(packet)
            self.remote_credits -= 1
            return True
        return False
    
    def receive_credit_return(self):
        """Remote side consumed a packet, credit returned"""
        self.remote_credits += 1
    
    def receive_packet(self, packet):
        """Receive packet and send credit back"""
        process(packet)
        self.credits += 1
        send_credit_return(self.link_id)

def reliable_send(dest, data):
    """
    Reliable send with retransmission
    """
    seq_num = get_next_sequence_number(dest)
    max_retries = 3
    timeout = 100_000  # cycles
    
    for attempt in range(max_retries):
        packet = create_packet(dest, data, seq_num)
        send_packet(packet)
        
        # Wait for ACK
        start_time = get_cycle_count()
        while get_cycle_count() - start_time < timeout:
            if check_ack_received(dest, seq_num):
                return SUCCESS
        
        # Timeout, retry
        log_warning(f"Timeout on link to {dest}, retry {attempt+1}")
    
    # Exhausted retries, escalate error
    return FAILURE

def naive_all_reduce(local_gradient):
    """
    Terrible: O(N) communication, O(N) latency
    """
    if rank == 0:
        # Master collects from all workers
        total = local_gradient
        for worker in range(1, num_workers):
            total += receive_from(worker)
        
        # Master broadcasts result
        result = total / num_workers
        for worker in range(1, num_workers):
            send_to(worker, result)
    else:
        send_to(0, local_gradient)
        result = receive_from(0)
    
    return result

def ring_all_reduce(local_data, num_chips):
    """
    Ring all-reduce: O(N) latency, optimal bandwidth
    
    Phase 1: Reduce-scatter
    Phase 2: All-gather
    """
    chunk_size = len(local_data) // num_chips
    chunks = split_into_chunks(local_data, chunk_size)
    
    # Phase 1: Reduce-scatter
    for step in range(num_chips - 1):
        send_chunk_idx = (rank - step) % num_chips
        recv_chunk_idx = (rank - step - 1) % num_chips
        
        # Send to next neighbor, receive from previous
        send_to_neighbor((rank + 1) % num_chips, chunks[send_chunk_idx])
        received = receive_from_neighbor((rank - 1 + num_chips) % num_chips)
        
        # Accumulate
        chunks[recv_chunk_idx] += received
    
    # Phase 2: All-gather
    for step in range(num_chips - 1):
        send_chunk_idx = (rank - step + 1) % num_chips
        recv_chunk_idx = (rank - step) % num_chips
        
        send_to_neighbor((rank + 1) % num_chips, chunks[send_chunk_idx])
        chunks[recv_chunk_idx] = receive_from_neighbor((rank - 1 + num_chips) % num_chips)
    
    return concatenate(chunks)

def torus_3d_all_reduce(local_data, coords):
    """
    All-reduce on 3D torus: O(log N) latency, better than ring
    
    Reduce-scatter along each dimension, then all-gather in reverse
    """
    x, y, z = coords
    X_DIM, Y_DIM, Z_DIM = get_torus_dimensions()
    
    # Phase 1: Reduce-scatter along X dimension
    data_x = reduce_scatter_dimension(local_data, dimension='X', 
                                       my_coord=x, dim_size=X_DIM)
    
    # Phase 2: Reduce-scatter along Y dimension
    data_xy = reduce_scatter_dimension(data_x, dimension='Y',
                                        my_coord=y, dim_size=Y_DIM)
    
    # Phase 3: Reduce-scatter along Z dimension
    data_xyz = reduce_scatter_dimension(data_xy, dimension='Z',
                                         my_coord=z, dim_size=Z_DIM)
    
    # Now each chip has unique portion of reduced data
    
    # Phase 4: All-gather along Z dimension
    data_xy_gathered = all_gather_dimension(data_xyz, dimension='Z',
                                             my_coord=z, dim_size=Z_DIM)
    
    # Phase 5: All-gather along Y dimension
    data_x_gathered = all_gather_dimension(data_xy_gathered, dimension='Y',
                                            my_coord=y, dim_size=Y_DIM)
    
    # Phase 6: All-gather along X dimension
    final_data = all_gather_dimension(data_x_gathered, dimension='X',
                                       my_coord=x, dim_size=X_DIM)
    
    return final_data
 
def reduce_scatter_dimension(data, dimension, my_coord, dim_size):
    """
    Reduce-scatter along one dimension of torus
    Similar to ring all-reduce, but only in one dimension
    """
    chunk_size = len(data) // dim_size
    chunks = split_into_chunks(data, chunk_size)
    
    for step in range(dim_size - 1):
        send_chunk = chunks[(my_coord - step) % dim_size]
        recv_chunk_idx = (my_coord - step - 1) % dim_size
        
        send_in_dimension(dimension, +1, send_chunk)
        received = receive_in_dimension(dimension, -1)
        
        chunks[recv_chunk_idx] += received
    
    # Return the chunk that belongs to this coordinate
    return chunks[my_coord]
 
def all_gather_dimension(data, dimension, my_coord, dim_size):
    """
    All-gather along one dimension
    Each chip gets complete data from all chips in this dimension
    """
    chunks = [None] * dim_size
    chunks[my_coord] = data
    
    for step in range(dim_size - 1):
        send_chunk_idx = (my_coord - step + 1) % dim_size
        recv_chunk_idx = (my_coord - step) % dim_size
        
        send_in_dimension(dimension, +1, chunks[send_chunk_idx])
        chunks[recv_chunk_idx] = receive_in_dimension(dimension, -1)
    
    return concatenate(chunks)

Latency:
  Reduce-scatter: (X_DIM-1) + (Y_DIM-1) + (Z_DIM-1) steps
  All-gather:     (Z_DIM-1) + (Y_DIM-1) + (X_DIM-1) steps
  Total:          2 × (X_DIM + Y_DIM + Z_DIM - 3) steps
  
For 16×16×16 = 4096 chips:
  Latency: 2 × (16+16+16-3) = 90 steps
  
Compare to ring:
  Ring: 2 × (4096-1) = 8190 steps
  
Speed-up: 8190 / 90 ≈ 91×  (!!!)
 
Bandwidth Utilization:
  All 12,288 links used simultaneously
  Each link carries unique data
  → Near-optimal bandwidth efficiency

def model_all_reduce_time(data_size, num_chips, link_bw, link_latency):
    """
    Model all-reduce time on 3D torus
    """
    X_DIM = Y_DIM = Z_DIM = int(num_chips ** (1/3))
    
    # Data size per chip after scatter
    chunk_size = data_size / num_chips
    
    # Time to send chunk over link
    transfer_time = chunk_size / link_bw
    
    # Number of steps per dimension
    steps_per_dim = X_DIM - 1
    
    # Total time
    num_dimensions = 3
    phases = 2  # Reduce-scatter + All-gather
    
    total_latency = phases * num_dimensions * steps_per_dim * link_latency
    total_transfer = phases * num_dimensions * steps_per_dim * transfer_time
    
    return total_latency + total_transfer
 
# Example: TPU v4 Pod
data_size = 700e9  # 175B parameters × 4 bytes
num_chips = 4096
link_bw = 150e9 / 8  # 150 Gbps = 18.75 GB/s
link_latency = 1e-6  # 1 μs per hop
 
time = model_all_reduce_time(data_size, num_chips, link_bw, link_latency)
print(f"All-reduce time: {time*1000:.2f} ms")
# Output: All-reduce time: ~52 ms
 
# With ring (for comparison):
ring_time = 2 * (num_chips - 1) * (data_size / num_chips / link_bw + link_latency)
print(f"Ring all-reduce time: {ring_time:.2f} s")
# Output: Ring all-reduce time: ~8.2 seconds (!!)

TPU v4 (estimated):
  6 links × 150 Gbps = 900 Gbps total
  Bidirectional: 450 Gbps each direction
  = 56.25 GB/s per direction
 
TPU v5p (estimated):
  6 links × 300 Gbps = 1.8 Tbps total
  = 225 GB/s bidirectional
 
Compare to GPU (H100):
  NVLink: 18 ports × 50 GB/s = 900 GB/s bidirectional

TPU v4 Pod (4,096 chips):
  12,288 links (each chip has 6, shared bidirectionally)
  Total: 12,288 × 150 Gbps = 1.8 Pbps
 
NVIDIA DGX SuperPOD (256 H100s):
  Intra-server: 32 servers × 8 GPUs × 900 GB/s ≈ 230 Tbps
  Inter-server: 256 GPUs × 400 Gbps (IB) = 102 Tbps
  → Bandwidth cliff at server boundary
 
Key: TPU Pod has uniform bandwidth, no cliffs

Nearest neighbor (1 hop):    ~1 μs
4 hops (corner to corner):   ~4 μs
8 hops (maximum diameter):   ~8 μs
 
All-reduce (16×16×16):
  45 hops total (dimension-ordered)
  Latency component: 45 × 1 μs = 45 μs
  Bandwidth component: 2 × 700 GB / 18.75 GB/s = 75 ms
  Total: ~75 ms (dominated by bandwidth)

def bandwidth_utilization(workload):
    """
    Measure effective vs. theoretical bandwidth
    """
    theoretical_bw = num_links * link_bandwidth
    
    if workload == "all_reduce":
        # All links carry unique data
        effective_bw = theoretical_bw * 0.95  # ~95% efficiency
    elif workload == "point_to_point":
        # Many links idle
        effective_bw = theoretical_bw * 0.3  # ~30% efficiency
    elif workload == "all_to_all":
        # Contention on some links
        effective_bw = theoretical_bw * 0.6  # ~60% efficiency
    
    return effective_bw / theoretical_bw

Physical:
  - Optical reach: ~100m (multi-mode fiber)
  - Power density: ~25W interconnect per chip × 4096 = 102 kW
  - Cooling capacity: Liquid cooling required
  
Architectural:
  - Diameter: 8 hops (manageable)
  - All-reduce time: ~75 ms for 175B parameters
  - Addressing: 16-bit chip ID (65K chips addressable)
 
Scale-out beyond 4096 chips:
  - Option 1: Larger 3D torus (e.g., 32×32×32 = 32K chips)
    - Diameter: 16 hops (still okay)
    - Latency: ~150 ms for all-reduce (acceptable)
  
  - Option 2: Multi-Pod with inter-Pod links
    - 8× 4096-chip Pods = 32K chips
    - High-bandwidth inter-Pod links (1-10 Tbps)
    - Hierarchical all-reduce

Compute (MXUs, VPUs):        ~150W
HBM:                         ~20W
Interconnect:
  - Optical transceivers:    ~12W (6 × 2W)
  - Router logic:            ~5W
  - DMA engines:             ~3W
Total interconnect:          ~20W
-----------------------------------------
Total per chip:              ~190W

Compute:                   ~615 kW
Interconnect:              ~82 kW
Optical switches:          ~10 kW (amortized)
-----------------------------------------
Total:                     ~707 kW
 
Interconnect fraction: 82/707 = 11.6%
(vs. 25-30% for electrical interconnect)

Electrical SerDes (50 Gbps PAM4):
  Power: ~5-8W per lane
  Efficiency: 0.1-0.16 W/Gbps
 
Optical (50 Gbps lane):
  Laser: ~0.5-1W
  Driver: ~0.5W
  Receiver: ~0.5W
  Total: ~1.5-2W per lane
  Efficiency: 0.03-0.04 W/Gbps
 
Advantage: 3-4× better power efficiency

For 4,096 chips × 6 links = 24,576 links:
 
Electrical (150 Gbps per link):
  24,576 × 150 Gbps × 0.15 W/Gbps = 553 kW
  
Optical (150 Gbps per link):
  24,576 × 150 Gbps × 0.04 W/Gbps = 147 kW
 
Savings: 406 kW
  → $350K/year at $0.10/kWh
  → Major OPEX reduction

Cold plate on compute side:
  - Dissipates ~170W per chip
  - Water temperature: 20-25°C inlet, 30-35°C outlet
 
Air cooling for transceivers:
  - Smaller heatsinks
  - Localized airflow
  - ~20W per chip, manageable
 
Benefits:
  - Higher density (more chips per rack)
  - Quieter operation
  - More efficient (PUE ~1.1-1.2 vs. 1.4-1.6 for air)

class LinkMonitor:
    def __init__(self, link_id):
        self.link_id = link_id
        self.error_count = 0
        self.ber_history = []
    
    def monitor(self):
        """Continuous monitoring"""
        while True:
            # Check pre-FEC BER
            pre_fec_ber = measure_pre_fec_ber(self.link_id)
            self.ber_history.append(pre_fec_ber)
            
            # Check CRC errors
            crc_errors = get_crc_error_count(self.link_id)
            self.error_count += crc_errors
            
            # Predictive failure detection
            if pre_fec_ber > 1e-4:
                log_warning(f"Link {self.link_id} BER degrading: {pre_fec_ber}")
                if pre_fec_ber > 5e-4:
                    trigger_link_failover(self.link_id)
            
            # Periodic link test
            if idle_time() > 1000:  # ms
                send_test_pattern(self.link_id)
            
            sleep(10)  # ms

3D torus provides multiple paths:
  From (0,0,0) to (15,15,15):
    - Primary: +X(15), +Y(15), +Z(15)
    - Alternate 1: +Y(15), +X(15), +Z(15)
    - Alternate 2: -X(1), -Y(1), -Z(1)  [wraparound]
 
On link failure:
  → Use alternate path
  → Slightly longer latency, but training continues

def checkpoint_and_recover(failed_chip_id):
    """
    Recovery strategy for chip failure
    """
    # Option 1: Checkpoint-restart
    if training_supports_checkpointing():
        save_checkpoint()
        blacklist_chip(failed_chip_id)
        relaunch_on_healthy_chips()
    
    # Option 2: Spare chips
    if spare_chips_available():
        spare = allocate_spare_chip()
        reconfigure_optical_switch(failed_chip_id, spare)
        restore_state_to_spare(spare)
    
    # Option 3: Degraded mode
    else:
        continue_training_with_fewer_chips()

Dynamic circuit reconfiguration allows:
  1. Isolate failed chips
  2. Reconfigure topology (e.g., 16×16×16 → 16×16×15)
  3. Continue training with slightly degraded performance
 
Reconfiguration time: 1-10 seconds (MEMS) or <1 second (silicon photonics)
  → Acceptable compared to hours of training time

Component MTBFs:
  TPU chip: ~1,000,000 hours
  Optical transceiver: ~500,000 hours
  Fiber/connector: ~10,000,000 hours
 
Pod-level MTBF (4,096 chips):
  Chip failures: 4,096 / 1,000,000 hours = 1 failure every 10 days
  Optical failures: 24,576 / 500,000 hours = 1 failure every 21 days
  
Expected: ~1 failure per week
 
With fault tolerance:
  → Training continues (slight performance degradation)
  → Repair during scheduled maintenance

Target: 99.9% availability (8.76 hours downtime/year)
 
With redundancy and fast failover:
  Achieved: >99.95% (4.38 hours/year)

┌─────────────────────────────────────────┐
│  User Code (Python)                     │
│  • TensorFlow, JAX, PyTorch (via XLA)   │
└─────────────────────────────────────────┘
              ↓
┌─────────────────────────────────────────┐
│  XLA (Accelerated Linear Algebra)       │
│  • Compiler and optimizer               │
│  • Collective ops lowering              │
└─────────────────────────────────────────┘
              ↓
┌─────────────────────────────────────────┐
│  Collective Communication Library       │
│  • All-reduce, all-gather, reduce-scatter│
│  • Topology-aware optimization          │
└─────────────────────────────────────────┘
              ↓
┌─────────────────────────────────────────┐
│  ICI (Inter-Chip Interconnect) Driver   │
│  • Link management                      │
│  • DMA operations                       │
│  • Error handling                       │
└─────────────────────────────────────────┘
              ↓
┌─────────────────────────────────────────┐
│  Optical Interconnect Hardware          │
└─────────────────────────────────────────┘

import jax
import jax.numpy as jnp
from jax.experimental import maps
 
# Define mesh for 4096 TPUs arranged as 16×16×16
mesh_shape = (16, 16, 16)
mesh = maps.Mesh(jax.devices(), ('x', 'y', 'z'))
 
# Partition data across mesh
@maps.xmap(
    in_axes=(['x', 'y', 'z'], ...),
    out_axes=['x', 'y', 'z'],
    axis_resources={'x': 'x', 'y': 'y', 'z': 'z'}
)
def distributed_matmul(A, B):
    """
    Matrix multiply distributed across 3D mesh
    Collective ops automatically inserted by XLA
    """
    return jnp.dot(A, B)
 
# XLA compiler will:
# 1. Partition A and B across mesh
# 2. Insert all-reduce after local matmuls
# 3. Use topology-aware all-reduce (3D torus algorithm)
# 4. Generate efficient ICI operations

import jax
from jax import lax
 
def data_parallel_training_step(params, batch):
    """
    One step of data-parallel training
    """
    # Each TPU computes gradients on local batch
    local_gradients = compute_gradients(params, batch)
    
    # All-reduce to average gradients across all TPUs
    # JAX automatically uses topology-aware all-reduce
    averaged_gradients = lax.psum(local_gradients, axis_name='batch')
    
    # Update parameters
    new_params = params - learning_rate * averaged_gradients
    
    return new_params
 
# XLA lowers 'psum' to:
# 1. 3D torus all-reduce
# 2. Direct ICI DMA operations
# 3. Optimal scheduling to overlap compute and communication

# Pseudo-code for XLA's collective lowering
 
def lower_allreduce_to_ici(all_reduce_op, mesh_topology):
    """
    XLA compiler optimization for all-reduce
    """
    if mesh_topology.type == '3D_TORUS':
        # Use dimension-ordered all-reduce
        schedule = [
            ('reduce_scatter', 'X'),
            ('reduce_scatter', 'Y'),
            ('reduce_scatter', 'Z'),
            ('all_gather', 'Z'),
            ('all_gather', 'Y'),
            ('all_gather', 'X'),
        ]
        
        for phase, dimension in schedule:
            if phase == 'reduce_scatter':
                emit_reduce_scatter_ici(dimension)
            else:
                emit_all_gather_ici(dimension)
    
    elif mesh_topology.type == 'RING':
        emit_ring_allreduce_ici()
    
    else:
        # Fallback to general algorithm
        emit_tree_allreduce()
 
def emit_reduce_scatter_ici(dimension):
    """
    Emit ICI operations for reduce-scatter along one dimension
    """
    neighbor_plus = get_neighbor(dimension, +1)
    neighbor_minus = get_neighbor(dimension, -1)
    
    for step in range(dimension_size - 1):
        # DMA send to +neighbor
        emit_ici_dma_send(neighbor_plus, chunk_offset, chunk_size)
        
        # DMA receive from -neighbor
        emit_ici_dma_recv(neighbor_minus, recv_buffer, chunk_size)
        
        # Local reduction
        emit_vector_add(local_buffer, recv_buffer)

Current: Pluggable optical modules
  Chip ← (electrical) → Package ← (electrical) → Module ← (optical) → Fiber
  Bottleneck: Electrical chip-to-module link
 
Future: Co-packaged optics
  Chip ← (short electrical) → Optical transceiver (on package) ← (optical) → Fiber
  Advantages:
    - 10× bandwidth (no electrical reach limit)
    - 5× lower power
    - Smaller form factor

Goal: Integrate photonic waveguides directly on silicon
 
Technologies:
  - Silicon-on-insulator (SOI) waveguides
  - Germanium photodetectors (monolithic with Si)
  - III-V laser integration (heterogeneous or bonded)
  - Microring modulators (compact, low power)
 
Benefits:
  - 100× higher I/O density
  - <1 pJ/bit energy efficiency
  - Wavelength-division multiplexing (100+ wavelengths)

Concept: Use wavelength as routing dimension
 
Traditional:
  All transceivers on same wavelength
  Optical switches route by port
 
Wavelength-routed:
  Each transceiver on unique wavelength
  Wavelength determines destination
  No switching needed (passive routing)
 
Example:
  Chip A (λ1, λ2, λ3) → Fiber → Chip B receives λ1
                                Chip C receives λ2
                                Chip D receives λ3
 
Advantages:
  - Ultra-low latency (no switching)
  - High bandwidth (100+ wavelengths × 100 Gbps)
  - Reconfigurable via wavelength tuning

Trend: Move computation closer to data
 
Options:
  1. Processing-in-Memory (PIM)
     - Compute inside HBM stacks
     - Reduce data movement
  
  2. In-Network Reduction
     - Perform reduce operations in optical switches
     - Reduces all-reduce latency
  
  3. Disaggregated Memory
     - Memory pools connected via optical fabric
     - Flexible capacity allocation

Insight: Not everything needs optical
 
Design:
  - Short-reach (<1m): Electrical (lower latency, lower cost)
  - Medium-reach (1-10m): Optical (copper becomes impractical)
  - Long-reach (>10m): Optical (required)
 
Example:
  Within server: Electrical (NVLink-like)
  Rack-to-rack: Optical (TPU Pod-like)
  
Optimizes for cost, power, and performance