diff --git a/ibis/backends/polars/compiler.py b/ibis/backends/polars/compiler.py
index eb4d9cb53232..2f369a65c223 100644
--- a/ibis/backends/polars/compiler.py
+++ b/ibis/backends/polars/compiler.py
@@ -1287,16 +1287,18 @@ def execute_count_distinct_star(op, **kw):
     # Convert polars series into a list
     #   -> map the function element by element
     #   -> convert back to a polars series
-    InputType.PYTHON: lambda func, dtype, args: pl.Series(
-        map(func, *(arg.to_list() for arg in args)),
+    InputType.PYTHON: lambda func, dtype, fields, args: pl.Series(
+        map(func, *(arg.to_list() for arg in map(args.struct.field, fields))),
         dtype=PolarsType.from_ibis(dtype),
     ),
     # Convert polars series into a pyarrow array
     #  -> invoke the function on the pyarrow array
     #  -> cast the result to match the ibis dtype
     #  -> convert back to a polars series
-    InputType.PYARROW: lambda func, dtype, args: pl.from_arrow(
-        func(*(arg.to_arrow() for arg in args)).cast(dtype.to_pyarrow()),
+    InputType.PYARROW: lambda func, dtype, fields, args: pl.from_arrow(
+        func(*(arg.to_arrow() for arg in map(args.struct.field, fields))).cast(
+            dtype.to_pyarrow()
+        ),
     ),
 }
 
@@ -1306,9 +1308,12 @@ def execute_scalar_udf(op, **kw):
     input_type = op.__input_type__
     if input_type in _UDF_INVOKERS:
         dtype = op.dtype
-        return pl.map_batches(
-            exprs=[translate(arg, **kw) for arg in op.args],
-            function=partial(_UDF_INVOKERS[input_type], op.__func__, dtype),
+        argnames = op.argnames
+        args = pl.struct(
+            **dict(zip(argnames, (translate(arg, **kw) for arg in op.args)))
+        )
+        return args.map_batches(
+            function=partial(_UDF_INVOKERS[input_type], op.__func__, dtype, argnames),
             return_dtype=PolarsType.from_ibis(dtype),
         )
     elif input_type == InputType.BUILTIN: