Project: 049_ProtComposer_Compositional_Protein_Structure_Gener | Function: InvariantCrossAttention.forward (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Core SE(3)-equivariant cross attention mechanism that enables message passing between 3D ellipsoid layouts and protein residue frames. Implements the novel Invariant Cross Attention (ICA) that transforms ellipsoid positions and covariances into residue local coordinate frames for equivariant conditioning.

**KEY TERMS:** {
  "relpos": "relative positions between ellipsoids and residues",
  "covar": "ellipsoid covariance matrices",
  "attn": "attention weights for cross-attention",
  "gamma": "learnable gating parameter"
}

**CONTEXT CODE:** # SPDX-FileCopyrightText: Copyright (c) 2025 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: LicenseRef-NvidiaProprietary
#
# NVIDIA CORPORATION, its affiliates and licensors retain all intellectual
# property and proprietary rights in and to this material, related
# documentation and any modifications thereto. Any use, reproduction,
# disclosure or distribution of this material and related documentation
# without an express license agreement from NVIDIA CORPORATION or
# its affiliates is strictly prohibited.

import torch.nn as nn

import torch
import math

def positional_encoding(x, channels, max_period=10000, min_period=None):
    min_period = min_period or max_period / 10000 # second one recommended
    freqs = torch.exp(-torch.linspace(math.log(min_period), math.log(max_period), channels // 2, device=x.device))
    emb = freqs * x.unsqueeze(-1) # [..., C]
    return torch.cat([torch.sin(emb), torch.cos(emb)], -1) # [..., 2C]



class InvariantCrossAttention(nn.Module):
    def __init__(self, cfg):
        super().__init__()
        self.cfg = cfg
        pos_emb_dim = 64
        self.linear_pos = nn.Linear(3 * pos_emb_dim, cfg.c_s)
        self.linear_kv = nn.Linear(cfg.c_s, 2 * cfg.c_s)
        self.linear_covar = nn.Linear(9, cfg.c_s)
        
        self.linear_q = nn.Linear(cfg.c_s, cfg.c_s)
        self.linear_out = nn.Linear(cfg.c_s, cfg.c_s)
        self.gamma = nn.Parameter(torch.zeros(1))
        self.beta = nn.Parameter(torch.ones(1))
        self.beta.requires_grad_(False)
        self.inf = 1e10

    def forward(self, s, r, x, y, c, mask):
        '''
        s: frame features
        r: frames
        x: point positions
        y: point features
        c: blob covariance
        mask: point mask
        '''
        raise NotImplementedError("Function implementation has been masked for testing")

Complete the function implementation replacing "raise NotImplementedError".