diff --git a/.github/workflows/rust.yml b/.github/workflows/rust.yml
index 68706eab7..7e5301c40 100644
--- a/.github/workflows/rust.yml
+++ b/.github/workflows/rust.yml
@@ -236,6 +236,8 @@ jobs:
         with:
           crate: cargo-nextest
           locked: true
+      - name: public outputs and tolerance > 0
+        run: cargo nextest run --release --verbose tests::mock_tolerance_public_outputs_ --test-threads 32
       - name: public outputs + batch size == 10
         run: cargo nextest run --release --verbose tests::mock_large_batch_public_outputs_ --test-threads 32
       - name: kzg inputs
diff --git a/src/circuit/ops/layouts.rs b/src/circuit/ops/layouts.rs
index 55014fd8f..f37691542 100644
--- a/src/circuit/ops/layouts.rs
+++ b/src/circuit/ops/layouts.rs
@@ -2953,8 +2953,17 @@ pub fn range_check_percent<F: PrimeField + TensorType + PartialOrd>(
         return enforce_equality(config, region, values);
     }
 
+    let mut values = [values[0].clone(), values[1].clone()];
+
+    values[0] = region.assign(&config.inputs[0], &values[0])?;
+    values[1] = region.assign(&config.inputs[1], &values[1])?;
+    let total_assigned_0 = values[0].len();
+    let total_assigned_1 = values[1].len();
+    let total_assigned = std::cmp::max(total_assigned_0, total_assigned_1);
+    region.increment(total_assigned);
+
     // Calculate the difference between the expected output and actual output
-    let diff = pairwise(config, region, values, BaseOp::Sub)?;
+    let diff = pairwise(config, region, &values, BaseOp::Sub)?;
 
     // Calculate the reciprocal of the expected output tensor, scaling by double the scaling factor
     let recip = nonlinearity(
diff --git a/src/circuit/ops/lookup.rs b/src/circuit/ops/lookup.rs
index 0e891cf7f..3ba39da8b 100644
--- a/src/circuit/ops/lookup.rs
+++ b/src/circuit/ops/lookup.rs
@@ -243,10 +243,10 @@ impl<F: PrimeField + TensorType + PartialOrd> Op<F> for LookupOp {
             LookupOp::Max { scale, a } => format!("MAX(scale={}, a={})", scale, a),
             LookupOp::Min { scale, a } => format!("MIN(scale={}, a={})", scale, a),
             LookupOp::Sign => "SIGN".into(),
-            LookupOp::GreaterThan { .. } => "GREATER_THAN".into(),
-            LookupOp::GreaterThanEqual { .. } => "GREATER_THAN_EQUAL".into(),
-            LookupOp::LessThan { .. } => "LESS_THAN".into(),
-            LookupOp::LessThanEqual { .. } => "LESS_THAN_EQUAL".into(),
+            LookupOp::GreaterThan { a } => format!("GREATER_THAN(a={})", a),
+            LookupOp::GreaterThanEqual { a } => format!("GREATER_THAN_EQUAL(a={})", a),
+            LookupOp::LessThan { a } => format!("LESS_THAN(a={})", a),
+            LookupOp::LessThanEqual { a } => format!("LESS_THAN_EQUAL(a={})", a),
             LookupOp::Recip {
                 input_scale,
                 output_scale,
diff --git a/src/graph/mod.rs b/src/graph/mod.rs
index 48b22bede..842865b1e 100644
--- a/src/graph/mod.rs
+++ b/src/graph/mod.rs
@@ -1248,7 +1248,7 @@ impl GraphCircuit {
             }
         }
 
-        let mut model_results = self.model().forward(inputs)?;
+        let mut model_results = self.model().forward(inputs, &self.settings().run_args)?;
 
         if visibility.output.requires_processing() {
             let module_outlets = visibility.output.overwrites_inputs();
diff --git a/src/graph/model.rs b/src/graph/model.rs
index 964717a89..46e707230 100644
--- a/src/graph/model.rs
+++ b/src/graph/model.rs
@@ -556,12 +556,16 @@ impl Model {
     /// * `reader` - A reader for an Onnx file.
     /// * `model_inputs` - A vector of [Tensor]s to use as inputs to the model.
     /// * `run_args` - [RunArgs]
-    pub fn forward(&self, model_inputs: &[Tensor<Fp>]) -> Result<ForwardResult, Box<dyn Error>> {
+    pub fn forward(
+        &self,
+        model_inputs: &[Tensor<Fp>],
+        run_args: &RunArgs,
+    ) -> Result<ForwardResult, Box<dyn Error>> {
         let valtensor_inputs: Vec<ValTensor<Fp>> = model_inputs
             .iter()
             .map(|x| x.map(|elem| ValType::Value(Value::known(elem))).into())
             .collect();
-        let res = self.dummy_layout(&RunArgs::default(), &valtensor_inputs)?;
+        let res = self.dummy_layout(&run_args, &valtensor_inputs)?;
         Ok(res.into())
     }
 
@@ -1371,27 +1375,26 @@ impl Model {
                 ValType::Constant(Fp::ONE)
             };
 
-            let comparator = outputs
+            let output_scales = self.graph.get_output_scales()?;
+            let res = outputs
                 .iter()
-                .map(|x| {
-                    let mut v: ValTensor<Fp> =
-                        vec![default_value.clone(); x.dims().iter().product::<usize>()].into();
-                    v.reshape(x.dims())?;
-                    Ok(v)
-                })
-                .collect::<Result<Vec<_>, Box<dyn Error>>>()?;
+                .enumerate()
+                .map(|(i, output)| {
+                    let mut tolerance = run_args.tolerance;
+                    tolerance.scale = scale_to_multiplier(output_scales[i]).into();
+
+                    let mut comparator: ValTensor<Fp> =
+                        vec![default_value.clone(); output.dims().iter().product::<usize>()].into();
+                    comparator.reshape(output.dims())?;
 
-            let _ = outputs
-                .iter()
-                .zip(comparator)
-                .map(|(o, c)| {
                     dummy_config.layout(
                         &mut region,
-                        &[o.clone(), c],
-                        Box::new(HybridOp::RangeCheck(run_args.tolerance)),
+                        &[output.clone(), comparator],
+                        Box::new(HybridOp::RangeCheck(tolerance)),
                     )
                 })
-                .collect::<Result<Vec<_>, _>>()?;
+                .collect::<Result<Vec<_>, _>>();
+            res?;
         } else if !self.visibility.output.is_private() {
             for output in &outputs {
                 region.increment_total_constants(output.num_constants());
diff --git a/src/pfsys/mod.rs b/src/pfsys/mod.rs
index f62142bbb..7f3152129 100644
--- a/src/pfsys/mod.rs
+++ b/src/pfsys/mod.rs
@@ -728,12 +728,13 @@ where
     let f =
         File::open(path.clone()).map_err(|_| format!("failed to load vk at {}", path.display()))?;
     let mut reader = BufReader::with_capacity(*EZKL_BUF_CAPACITY, f);
-    VerifyingKey::<Scheme::Curve>::read::<_, C>(
+    let vk = VerifyingKey::<Scheme::Curve>::read::<_, C>(
         &mut reader,
         serde_format_from_str(&EZKL_KEY_FORMAT),
         params,
-    )
-    .map_err(Box::<dyn Error>::from)
+    )?;
+    info!("done loading verification key ✅");
+    Ok(vk)
 }
 
 /// Loads a [ProvingKey] at `path`.
@@ -750,12 +751,13 @@ where
     let f =
         File::open(path.clone()).map_err(|_| format!("failed to load pk at {}", path.display()))?;
     let mut reader = BufReader::with_capacity(*EZKL_BUF_CAPACITY, f);
-    ProvingKey::<Scheme::Curve>::read::<_, C>(
+    let pk = ProvingKey::<Scheme::Curve>::read::<_, C>(
         &mut reader,
         serde_format_from_str(&EZKL_KEY_FORMAT),
         params,
-    )
-    .map_err(Box::<dyn Error>::from)
+    )?;
+    info!("done loading proving key ✅");
+    Ok(pk)
 }
 
 /// Saves a [ProvingKey] to `path`.
@@ -772,6 +774,7 @@ where
     let mut writer = BufWriter::with_capacity(*EZKL_BUF_CAPACITY, f);
     pk.write(&mut writer, serde_format_from_str(&EZKL_KEY_FORMAT))?;
     writer.flush()?;
+    info!("done saving proving key ✅");
     Ok(())
 }
 
@@ -789,6 +792,7 @@ where
     let mut writer = BufWriter::with_capacity(*EZKL_BUF_CAPACITY, f);
     vk.write(&mut writer, serde_format_from_str(&EZKL_KEY_FORMAT))?;
     writer.flush()?;
+    info!("done saving verification key ✅");
     Ok(())
 }
 
diff --git a/src/tensor/val.rs b/src/tensor/val.rs
index 890cb75c7..6aa1595c0 100644
--- a/src/tensor/val.rs
+++ b/src/tensor/val.rs
@@ -672,7 +672,7 @@ impl<F: PrimeField + TensorType + PartialOrd> ValTensor<F> {
                 }
                 Ok(indices)
             }
-            ValTensor::Instance { .. } => Err(TensorError::WrongMethod),
+            ValTensor::Instance { .. } => Ok(vec![]),
         }
     }
 
@@ -690,7 +690,7 @@ impl<F: PrimeField + TensorType + PartialOrd> ValTensor<F> {
                 }
                 Ok(indices)
             }
-            ValTensor::Instance { .. } => Err(TensorError::WrongMethod),
+            ValTensor::Instance { .. } => Ok(vec![]),
         }
     }
 
@@ -709,7 +709,11 @@ impl<F: PrimeField + TensorType + PartialOrd> ValTensor<F> {
                 *d = v.dims().to_vec();
             }
             ValTensor::Instance { .. } => {
-                return Err(TensorError::WrongMethod);
+                if indices.is_empty() {
+                    return Ok(());
+                } else {
+                    return Err(TensorError::WrongMethod);
+                }
             }
         }
         Ok(())
diff --git a/tests/integration_tests.rs b/tests/integration_tests.rs
index 3ac43301b..ba4a098d6 100644
--- a/tests/integration_tests.rs
+++ b/tests/integration_tests.rs
@@ -477,6 +477,7 @@ mod native_tests {
             use crate::native_tests::kzg_fuzz;
             use crate::native_tests::render_circuit;
             use crate::native_tests::model_serialization_different_binaries;
+            use rand::Rng;
             use tempdir::TempDir;
 
             #[test]
@@ -496,7 +497,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "fixed", "public", 1, "accuracy", None);
+                mock(path, test.to_string(), "public", "fixed", "public", 1, "accuracy", None, 0.0);
                 test_dir.close().unwrap();
             }
         });
@@ -569,7 +570,18 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "private", "public", 1, "resources", None);
+                mock(path, test.to_string(), "private", "private", "public", 1, "resources", None, 0.0);
+                test_dir.close().unwrap();
+            }
+
+            #(#[test_case(TESTS[N])])*
+            fn mock_tolerance_public_outputs_(test: &str) {
+                crate::native_tests::init_binary();
+                let test_dir = TempDir::new(test).unwrap();
+                let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
+                // gen random number between 0.0 and 1.0
+                let tolerance = rand::thread_rng().gen_range(0.0..1.0) * 100.0;
+                mock(path, test.to_string(), "private", "private", "public", 1, "resources", None, tolerance);
                 test_dir.close().unwrap();
             }
 
@@ -580,7 +592,7 @@ mod native_tests {
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
                 let large_batch_dir = &format!("large_batches_{}", test);
                 crate::native_tests::mk_data_batches_(path, test, &large_batch_dir, 10);
-                mock(path, large_batch_dir.to_string(), "private", "private", "public", 10, "resources", None);
+                mock(path, large_batch_dir.to_string(), "private", "private", "public", 10, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -589,7 +601,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "private", "private", 1, "resources", None);
+                mock(path, test.to_string(), "public", "private", "private", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -598,7 +610,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "fixed", "private", "private", 1, "resources", None);
+                mock(path, test.to_string(), "fixed", "private", "private", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -607,7 +619,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "private", "fixed", 1, "resources", None);
+                mock(path, test.to_string(), "private", "private", "fixed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -616,7 +628,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "fixed", "private", 1, "resources", None);
+                mock(path, test.to_string(), "private", "fixed", "private", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -625,7 +637,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "hashed", "private", "public", 1, "resources", None);
+                mock(path, test.to_string(), "hashed", "private", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -634,7 +646,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "kzgcommit", "private", "public", 1, "resources", None);
+                mock(path, test.to_string(), "kzgcommit", "private", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -644,7 +656,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "hashed", "public", 1, "resources", None);
+                mock(path, test.to_string(), "private", "hashed", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -654,7 +666,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "kzgcommit", "public", 1, "resources", None);
+                mock(path, test.to_string(), "private", "kzgcommit", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -663,7 +675,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "private", "hashed", 1, "resources", None);
+                mock(path, test.to_string(), "public", "private", "hashed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -673,7 +685,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "private", "kzgcommit", 1, "resources", None);
+                mock(path, test.to_string(), "public", "private", "kzgcommit", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -682,7 +694,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "fixed", "hashed", 1, "resources", None);
+                mock(path, test.to_string(), "public", "fixed", "hashed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -692,7 +704,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "public", "kzgcommit", "hashed", 1, "resources", None);
+                mock(path, test.to_string(), "public", "kzgcommit", "hashed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -702,7 +714,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "kzgcommit", "kzgcommit", "kzgcommit", 1, "resources", None);
+                mock(path, test.to_string(), "kzgcommit", "kzgcommit", "kzgcommit", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -712,7 +724,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "hashed", "private", "hashed", 1, "resources", None);
+                mock(path, test.to_string(), "hashed", "private", "hashed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -722,7 +734,7 @@ mod native_tests {
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
                 // needs an extra row for the large model
-                mock(path, test.to_string(),"hashed", "hashed", "public", 1, "resources", None);
+                mock(path, test.to_string(),"hashed", "hashed", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -732,7 +744,7 @@ mod native_tests {
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
                 // needs an extra row for the large model
-                mock(path, test.to_string(),"hashed", "hashed", "hashed", 1, "resources", None);
+                mock(path, test.to_string(),"hashed", "hashed", "hashed", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
 
@@ -876,7 +888,7 @@ mod native_tests {
                 crate::native_tests::init_binary();
                 let test_dir = TempDir::new(test).unwrap();
                 let path = test_dir.path().to_str().unwrap(); crate::native_tests::mv_test_(path, test);
-                mock(path, test.to_string(), "private", "fixed", "public", 1, "resources", None);
+                mock(path, test.to_string(), "private", "fixed", "public", 1, "resources", None, 0.0);
                 test_dir.close().unwrap();
             }
         });
@@ -1273,6 +1285,7 @@ mod native_tests {
         batch_size: usize,
         cal_target: &str,
         scales_to_use: Option<Vec<u32>>,
+        tolerance: f32,
     ) {
         gen_circuit_settings_and_witness(
             test_dir,
@@ -1285,6 +1298,7 @@ mod native_tests {
             scales_to_use,
             2,
             false,
+            tolerance,
         );
 
         let status = Command::new(format!("{}/release/ezkl", *CARGO_TARGET_DIR))
@@ -1312,6 +1326,7 @@ mod native_tests {
         scales_to_use: Option<Vec<u32>>,
         num_inner_columns: usize,
         div_rebasing: bool,
+        tolerance: f32,
     ) {
         let mut args = vec![
             "gen-settings".to_string(),
@@ -1326,6 +1341,7 @@ mod native_tests {
             format!("--param-visibility={}", param_visibility),
             format!("--output-visibility={}", output_visibility),
             format!("--num-inner-cols={}", num_inner_columns),
+            format!("--tolerance={}", tolerance),
         ];
 
         if div_rebasing {
@@ -1425,6 +1441,7 @@ mod native_tests {
             None,
             2,
             div_rebasing,
+            0.0,
         );
 
         println!(
@@ -1684,6 +1701,7 @@ mod native_tests {
             scales_to_use,
             num_inner_columns,
             false,
+            0.0,
         );
 
         let settings_path = format!("{}/{}/settings.json", test_dir, example_name);
@@ -1785,6 +1803,7 @@ mod native_tests {
             None,
             2,
             false,
+            0.0,
         );
 
         let status = Command::new(format!("{}/release/ezkl", *CARGO_TARGET_DIR))
@@ -2061,6 +2080,7 @@ mod native_tests {
             Some(vec![4]),
             1,
             false,
+            0.0,
         );
 
         let model_path = format!("{}/{}/network.compiled", test_dir, example_name);