diff --git a/mostlyai/qa/_accuracy.py b/mostlyai/qa/_accuracy.py
index b96a3b2..9445da4 100644
--- a/mostlyai/qa/_accuracy.py
+++ b/mostlyai/qa/_accuracy.py
@@ -12,6 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
+import datetime
 import functools
 import hashlib
 import logging
@@ -1034,7 +1035,7 @@ def binning_data(
 def bin_data(
     df: pd.DataFrame,
     bins: int | dict[str, list],
-    non_categorical_label_style: Literal["bounded", "unbounded"] = "unbounded",
+    non_categorical_label_style: Literal["bounded", "unbounded", "lower"] = "unbounded",
 ) -> tuple[pd.DataFrame, dict[str, list]]:
     """
     Splits data into bins.
@@ -1048,41 +1049,32 @@ def bin_data(
 
     # Note, that we create a new pd.DataFrame to avoid fragmentation warning messages that can occur if we try to
     # replace hundreds of columns of a large dataset
-    cols = {}
-
-    bins_dct = {}
-    num_cols = [c for c in df.columns if pd.api.types.is_numeric_dtype(df[c])]
-    dat_cols = [c for c in df.columns if pd.api.types.is_datetime64_any_dtype(df[c])]
-    cat_cols = [c for c in df.columns if c not in num_cols + dat_cols]
+    cols, bins_dct = {}, {}
     if isinstance(bins, int):
-        for col in num_cols:
-            cols[col], bins_dct[col] = bin_numeric(df[col], bins, label_style=non_categorical_label_style)
-        for col in dat_cols:
-            cols[col], bins_dct[col] = bin_datetime(df[col], bins, label_style=non_categorical_label_style)
-        for col in cat_cols:
-            cols[col], bins_dct[col] = bin_categorical(df[col], bins)
-    else:  # bins is a dict
-        for col in num_cols:
-            if col in bins:
-                cols[col], _ = bin_numeric(df[col], bins[col], label_style=non_categorical_label_style)
+        for col in df.columns:
+            if pd.api.types.is_numeric_dtype(df[col]):
+                cols[col], bins_dct[col] = bin_numeric(df[col], bins, label_style=non_categorical_label_style)
+            elif pd.api.types.is_datetime64_any_dtype(df[col]):
+                cols[col], bins_dct[col] = bin_datetime(df[col], bins, label_style=non_categorical_label_style)
             else:
-                _LOG.warning(f"'{col}' is missing in bins")
-        for col in dat_cols:
-            if col in bins:
-                cols[col], _ = bin_datetime(df[col], bins[col], label_style=non_categorical_label_style)
-            else:
-                _LOG.warning(f"'{col}' is missing in bins")
-        for col in cat_cols:
+                cols[col], bins_dct[col] = bin_categorical(df[col], bins)
+    else:  # bins is a dict
+        for col in df.columns:
             if col in bins:
-                cols[col], _ = bin_categorical(df[col], bins[col])
+                if isinstance(bins[col][0], (int, float, np.integer, np.floating)):
+                    cols[col], _ = bin_numeric(df[col], bins[col], label_style=non_categorical_label_style)
+                elif isinstance(bins[col][0], (datetime.date, datetime.datetime, np.datetime64)):
+                    cols[col], _ = bin_datetime(df[col], bins[col], label_style=non_categorical_label_style)
+                else:
+                    cols[col], _ = bin_categorical(df[col], bins[col])
             else:
-                _LOG.warning(f"'{col}' is missing in bins")
+                cols[col] = df[col]
         bins_dct = bins
     return pd.DataFrame(cols), bins_dct
 
 
 def bin_numeric(
-    col: pd.Series, bins: int | list[str], label_style: Literal["bounded", "unbounded"] = "unbounded"
+    col: pd.Series, bins: int | list[str], label_style: Literal["bounded", "unbounded", "lower"] = "unbounded"
 ) -> tuple[pd.Categorical, list]:
     def _clip(col, bins):
         if isinstance(bins, list):
@@ -1131,7 +1123,7 @@ def _adjust_breaks(breaks):
 
 
 def bin_datetime(
-    col: pd.Series, bins: int | list[str], label_style: Literal["bounded", "unbounded"] = "unbounded"
+    col: pd.Series, bins: int | list[str], label_style: Literal["bounded", "unbounded", "lower"] = "unbounded"
 ) -> tuple[pd.Categorical, list]:
     def _clip(col, bins):
         if isinstance(bins, list):
@@ -1184,7 +1176,7 @@ def bin_non_categorical(
     clip_and_breaks: Callable,
     create_labels: Callable,
     adjust_breaks: Callable,
-    label_style: Literal["bounded", "unbounded"] = "unbounded",
+    label_style: Literal["bounded", "unbounded", "lower"] = "unbounded",
 ) -> tuple[pd.Categorical, list]:
     col = col.fillna(np.nan).infer_objects(copy=False)
 
@@ -1203,7 +1195,9 @@ def bin_non_categorical(
         )
         labels = [str(b) for b in breaks[:-1]]
 
-    if label_style == "unbounded":
+    if label_style == "lower":
+        new_labels_map = {label: f"{label}" for label in labels}
+    elif label_style == "unbounded":
         new_labels_map = {label: f"⪰ {label}" for label in labels}
     else:  # label_style == "bounded"
         new_labels_map = {label: f"⪰ {label} ≺ {next_label}" for label, next_label in zip(labels, labels[1:] + ["∞"])}
diff --git a/mostlyai/qa/_sampling.py b/mostlyai/qa/_sampling.py
index 995224e..2e9871e 100644
--- a/mostlyai/qa/_sampling.py
+++ b/mostlyai/qa/_sampling.py
@@ -25,6 +25,7 @@
 #  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 #  See the License for the specific language governing permissions and
 #  limitations under the License.
+import datetime
 import logging
 import random
 import time
@@ -229,7 +230,7 @@ def pull_data_for_embeddings(
     ctx_primary_key: str | None = None,
     tgt_context_key: str | None = None,
     max_sample_size: int | None = None,
-    tgt_num_dat_bins: dict[str, list] | None = None,
+    bins: dict[str, list] | None = None,
 ) -> list[str]:
     _LOG.info("pulling data for embeddings")
     t0 = time.time()
@@ -264,12 +265,19 @@ def pull_data_for_embeddings(
     df_tgt = df_tgt.rename(columns={tgt_context_key: key})
     tgt_context_key = key
 
-    # bin numeric and datetime columns; partly also to prevent
-    # embedding distortion by adding extra precision to values
-    prefixes = string.ascii_lowercase + string.ascii_uppercase
-    tgt_num_dat_bins = tgt_num_dat_bins or {}
-    for i, col in enumerate(tgt_num_dat_bins.keys()):
-        df_tgt[col] = bin_num_dat(values=df_tgt[col], bins=tgt_num_dat_bins[col], prefix=prefixes[i % len(prefixes)])
+    # bin columns; also to prevent distortion of embeddings by adding extra precision or unknown values
+    bins = bins or {}
+    df_tgt.columns = [TGT_COLUMN_PREFIX + c if c != key else c for c in df_tgt.columns]
+    df_tgt, _ = bin_data(df_tgt, bins=bins, non_categorical_label_style="lower")
+    # add some prefix to make numeric and date values unique in the embedding space
+    for col in df_tgt.columns:
+        if col in bins:
+            if isinstance(
+                bins[col][0], (int, float, np.integer, np.floating, datetime.date, datetime.datetime, np.datetime64)
+            ):
+                prefixes = string.ascii_lowercase + string.ascii_uppercase
+                prefix = prefixes[xxhash.xxh32_intdigest(col) % len(prefixes)]
+                df_tgt[col] = prefix + df_tgt[col].astype(str)
 
     # split into chunks while keeping groups together and process in parallel
     n_jobs = min(16, max(1, cpu_count() - 1))
@@ -303,15 +311,6 @@ def sequence_to_string(sequence: pd.DataFrame) -> str:
     return strings
 
 
-def bin_num_dat(values: pd.Series, bins: list, prefix: str) -> pd.Series:
-    bins = sorted(set(bins))
-    binned = pd.cut(values, bins=bins, labels=bins[:-1], include_lowest=True).astype(str)
-    binned[values <= min(bins)] = str(bins[0])
-    binned[values >= max(bins)] = str(bins[-1])
-    binned[values.isna()] = "NA"
-    return prefix + binned
-
-
 def calculate_embeddings(
     strings: list[str],
     progress: ProgressCallbackWrapper | None = None,
diff --git a/mostlyai/qa/reporting.py b/mostlyai/qa/reporting.py
index 164abcb..4fba2a4 100644
--- a/mostlyai/qa/reporting.py
+++ b/mostlyai/qa/reporting.py
@@ -12,7 +12,6 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import datetime
 import logging
 import warnings
 from pathlib import Path
@@ -289,12 +288,6 @@ def report(
         embedder = load_embedder()
         _LOG.info("load tgt bins")
         bins = statistics.load_bins()
-        tgt_num_dat_bins = {
-            c.replace(TGT_COLUMN_PREFIX, ""): bins[c]
-            for c in bins.keys()
-            if c.replace(TGT_COLUMN_PREFIX, "") in trn_tgt_data.columns
-            and isinstance(bins[c][0], (int, float, datetime.date, datetime.datetime))
-        }
 
         _LOG.info("calculate embeddings for synthetic")
         syn_embeds = calculate_embeddings(
@@ -304,7 +297,7 @@ def report(
                 ctx_primary_key=ctx_primary_key,
                 tgt_context_key=tgt_context_key,
                 max_sample_size=max_sample_size_embeddings_final,
-                tgt_num_dat_bins=tgt_num_dat_bins,
+                bins=bins,
             ),
             progress=progress,
             progress_from=25,
@@ -319,7 +312,7 @@ def report(
                 ctx_primary_key=ctx_primary_key,
                 tgt_context_key=tgt_context_key,
                 max_sample_size=max_sample_size_embeddings_final,
-                tgt_num_dat_bins=tgt_num_dat_bins,
+                bins=bins,
             ),
             progress=progress,
             progress_from=45,
@@ -335,7 +328,7 @@ def report(
                     ctx_primary_key=ctx_primary_key,
                     tgt_context_key=tgt_context_key,
                     max_sample_size=max_sample_size_embeddings_final,
-                    tgt_num_dat_bins=tgt_num_dat_bins,
+                    bins=bins,
                 ),
                 progress=progress,
                 progress_from=65,
diff --git a/mostlyai/qa/reporting_from_statistics.py b/mostlyai/qa/reporting_from_statistics.py
index 418a06b..b379fa3 100644
--- a/mostlyai/qa/reporting_from_statistics.py
+++ b/mostlyai/qa/reporting_from_statistics.py
@@ -12,7 +12,6 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 
-import datetime
 import logging
 from pathlib import Path
 
@@ -28,7 +27,6 @@
 )
 from mostlyai.qa._sampling import pull_data_for_embeddings, calculate_embeddings, pull_data_for_coherence
 from mostlyai.qa._common import (
-    TGT_COLUMN_PREFIX,
     ProgressCallback,
     PrerequisiteNotMetError,
     check_min_sample_size,
@@ -169,12 +167,6 @@ def report_from_statistics(
         embedder = load_embedder()
         _LOG.info("load bins")
         bins = statistics.load_bins()
-        tgt_num_dat_bins = {
-            c.replace(TGT_COLUMN_PREFIX, ""): bins[c]
-            for c in bins.keys()
-            if c.replace(TGT_COLUMN_PREFIX, "") in syn_tgt_data.columns
-            and isinstance(bins[c][0], (int, float, datetime.date, datetime.datetime))
-        }
 
         _LOG.info("calculate embeddings for synthetic")
         syn_embeds = calculate_embeddings(
@@ -184,7 +176,7 @@ def report_from_statistics(
                 ctx_primary_key=ctx_primary_key,
                 tgt_context_key=tgt_context_key,
                 max_sample_size=max_sample_size_embeddings,
-                tgt_num_dat_bins=tgt_num_dat_bins,
+                bins=bins,
             ),
             progress=progress,
             progress_from=40,
diff --git a/tests/end_to_end/test_report.py b/tests/end_to_end/test_report.py
index b44668b..2b46ee5 100644
--- a/tests/end_to_end/test_report.py
+++ b/tests/end_to_end/test_report.py
@@ -176,17 +176,6 @@ def test_report_flat_rare(tmp_path):
     assert metrics.accuracy.univariate == 0.0
     assert metrics.distances.ims_training == metrics.distances.ims_holdout == 0.0
 
-    # test case where rare values are not protected, and we leak trn into synthetic
-    syn_tgt_data = pd.DataFrame({"x": trn_tgt_data["x"].sample(100, replace=True)})
-    _, metrics = qa.report(
-        syn_tgt_data=syn_tgt_data,
-        trn_tgt_data=trn_tgt_data,
-        hol_tgt_data=hol_tgt_data,
-        statistics_path=statistics_path,
-    )
-    assert metrics.distances.ims_training > metrics.distances.ims_holdout
-    assert metrics.distances.dcr_training < metrics.distances.dcr_holdout
-
 
 def test_report_flat_early_exit(tmp_path):
     # test early exit for dfs with <100 rows
diff --git a/tests/unit/test_accuracy.py b/tests/unit/test_accuracy.py
index a9b84ec..c291703 100644
--- a/tests/unit/test_accuracy.py
+++ b/tests/unit/test_accuracy.py
@@ -615,12 +615,11 @@ def test_trim_labels():
 
 
 def test_calculate_correlations(cols):
-    trn, hol, syn = cols
-    trn, bins = bin_data(trn, 3)
-    syn, _ = bin_data(syn, bins)
-    # prefix some columns with "tgt::"
-    columns = [f"tgt::{c}" if c != "cat" else c for idx, c in enumerate(trn.columns)]
-    trn.columns, syn.columns = columns, columns
+    trn, _, syn = cols
+    trn, bins = bin_data(trn[["num", "dt"]], 3)
+    syn, _ = bin_data(syn[["num", "dt"]], bins)
+    trn = trn.add_prefix("tgt::")
+    syn = syn.add_prefix("tgt::")
     corr_trn = calculate_correlations(trn)
     exp_corr_trn = pd.DataFrame(
         [
diff --git a/tests/unit/test_sampling.py b/tests/unit/test_sampling.py
index 222d76f..4f3f007 100644
--- a/tests/unit/test_sampling.py
+++ b/tests/unit/test_sampling.py
@@ -33,7 +33,7 @@ def test_pull_data_for_embeddings_large_int(tmp_path):
         {"cc": list(np.random.randint(100, 200, size=1000)) + [1800218404984585216] + [pd.NA]}, dtype="Int64"
     )
     bins = {"cc": [100, 200]}
-    pull_data_for_embeddings(df_tgt=df, tgt_num_dat_bins=bins)
+    pull_data_for_embeddings(df_tgt=df, bins=bins)
 
 
 def test_pull_data_for_embeddings_dates(tmp_path):
@@ -48,4 +48,4 @@ def test_pull_data_for_embeddings_dates(tmp_path):
         "y": [datetime(2020, 2, 1), datetime(2024, 1, 1)],
         "z": [datetime(2020, 2, 1), datetime(2024, 1, 1)],
     }
-    pull_data_for_embeddings(df_tgt=df, tgt_num_dat_bins=bins)
+    pull_data_for_embeddings(df_tgt=df, bins=bins)