In [82]: c = np.einsum('...ij,...j->...i', a, b)
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [82], in <cell line: 1>()
----> 1 c = np.einsum('...ij,...j->...i', a, b)

File <__array_function__ internals>:5, in einsum(*args,**kwargs)

File ~\anaconda3\lib\site-packages\numpy\core\einsumfunc.py:1359, in einsum(out, optimize, *operands,**kwargs)
   1357     if specified_out:
   1358         kwargs['out'] = out
-> 1359     return c_einsum(*operands,**kwargs)
   1361 # Check the kwargs to avoid a more cryptic error later, without having to
   1362 # repeat default values here
   1363 valid_einsum_kwargs = ['dtype', 'order', 'casting']

ValueError: operands could not be broadcast together with remapped shapes 
[original->remapped]: (10,10,3,3)->(10,10,3,3) (5,3)->(5,newaxis,3)

所以它试图使用broadcasting来匹配尺寸。
让我们做a(10，10，1，3，3)形状。这样，(10，10，1)部分用b的(5，)广播：

In [83]: c = np.einsum('...ij,...j->...i', a[:,:,None], b)
In [84]: c.shape
Out[84]: (10, 10, 5, 3)

最终通过以下助手函数绕过了这个问题

def batch_matvec(A, b):
    product = np.einsum('...ij, ...kj->...ki', A, b.reshape(-1, b.shape[-1]))
    return product.reshape((*A.shape[:-2], *b.shape[:-1], -1))