[Fix Big Tensor] Fix backward accuracy diff of paddle.linalg.slogdet

paddle/phi/kernels/impl/slogdeterminant_grad_kernel_impl.h

@@ -82,8 +82,54 @@ void SlogDeterminantGradKernel(const Context& dev_ctx,
   inverse_A.Resize(x.dims());
   dev_ctx.template Alloc<T>(&inverse_A);
 
-  phi::funcs::MatrixInverseFunctor<Context, T> mat_inv;
-  mat_inv(dev_ctx, x, &inverse_A);
+  const auto& mat_dims = x.dims();
+  const int rank = mat_dims.size();
+  int n = mat_dims[rank - 1];
+  int64_t total_batch_size = rank > 2 ? x.numel() / (n * n) : 1;
+
+  // Divide the batch into chunks because of cublasMatInv limitation
+  if (total_batch_size <= 65536) {
+    phi::funcs::MatrixInverseFunctor<Context, T> mat_inv;
+    mat_inv(dev_ctx, x, &inverse_A);
+  } else {
+    constexpr int64_t max_batch_size = 65536;
+    int64_t processed = 0;
+
+    VLOG(3) << "Large batch size detected (" << total_batch_size
+            << "), processing in chunks of " << max_batch_size;
+
+    while (processed < total_batch_size) {
+      int64_t current_batch =
+          std::min(max_batch_size, total_batch_size - processed);
+
+      // Extract current batch data
+      DenseTensor x_batch;
+      x_batch.ShareDataWith(x);
+      x_batch.Resize({total_batch_size, n, n});
+      x_batch = x_batch.Slice(processed, processed + current_batch);
+      x_batch.Resize({current_batch, n, n});
+
+      DenseTensor inverse_batch;
+      inverse_batch.Resize({current_batch, n, n});
+      dev_ctx.template Alloc<T>(&inverse_batch);
+
+      // Compute the inverse matrix for the current batch
+      phi::funcs::MatrixInverseFunctor<Context, T> mat_inv;
+      mat_inv(dev_ctx, x_batch, &inverse_batch);
+
+      // Copy the result to the output tensor
+      DenseTensor output_slice;
+      output_slice.ShareDataWith(inverse_A);
+      output_slice.Resize({total_batch_size, n, n});
+      output_slice = output_slice.Slice(processed, processed + current_batch);
+      output_slice.Resize({current_batch, n, n});
+
+      phi::Copy(
+          dev_ctx, inverse_batch, dev_ctx.GetPlace(), false, &output_slice);
+
+      processed += current_batch;
+    }
+  }
 
   VLOG(3) << "inverse(A) dims: " << inverse_A.dims();