diff --git a/Cargo.lock b/Cargo.lock
index d319c82f2..4a202ce51 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1904,7 +1904,7 @@ dependencies = [
 [[package]]
 name = "ff_ext"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "once_cell",
  "p3",
@@ -2716,7 +2716,7 @@ dependencies = [
 [[package]]
 name = "mpcs"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "bincode",
  "clap",
@@ -2740,7 +2740,7 @@ dependencies = [
 [[package]]
 name = "multilinear_extensions"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "either",
  "ff_ext",
@@ -3061,7 +3061,7 @@ dependencies = [
 [[package]]
 name = "p3"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "p3-air",
  "p3-baby-bear",
@@ -3498,7 +3498,7 @@ dependencies = [
 [[package]]
 name = "poseidon"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "ff_ext",
  "p3",
@@ -4482,7 +4482,7 @@ dependencies = [
 [[package]]
 name = "sp1-curves"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "cfg-if",
  "dashu",
@@ -4604,7 +4604,7 @@ checksum = "13c2bddecc57b384dee18652358fb23172facb8a2c51ccc10d74c157bdea3292"
 [[package]]
 name = "sumcheck"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "either",
  "ff_ext",
@@ -4622,7 +4622,7 @@ dependencies = [
 [[package]]
 name = "sumcheck_macro"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "itertools 0.13.0",
  "p3",
@@ -5017,7 +5017,7 @@ dependencies = [
 [[package]]
 name = "transcript"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "ff_ext",
  "itertools 0.13.0",
@@ -5289,7 +5289,7 @@ dependencies = [
 [[package]]
 name = "whir"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "bincode",
  "clap",
@@ -5576,7 +5576,7 @@ dependencies = [
 [[package]]
 name = "witness"
 version = "0.1.0"
-source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.13#89aa6add9f4d16cd2f10ec81f7c11d4507400c9b"
+source = "git+https://github.com/scroll-tech/gkr-backend.git?tag=v1.0.0-alpha.14#08462f562a091792262ddb63eb5b774f9896be77"
 dependencies = [
  "ff_ext",
  "multilinear_extensions",
diff --git a/Cargo.toml b/Cargo.toml
index a0b824a62..8a573fc94 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -23,16 +23,16 @@ repository = "https://github.com/scroll-tech/ceno"
 version = "0.1.0"
 
 [workspace.dependencies]
-ff_ext = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "ff_ext", tag = "v1.0.0-alpha.13" }
-mpcs = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "mpcs", tag = "v1.0.0-alpha.13" }
-multilinear_extensions = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "multilinear_extensions", tag = "v1.0.0-alpha.13" }
-p3 = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "p3", tag = "v1.0.0-alpha.13" }
-poseidon = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "poseidon", tag = "v1.0.0-alpha.13" }
-sp1-curves = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "sp1-curves", tag = "v1.0.0-alpha.13" }
-sumcheck = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "sumcheck", tag = "v1.0.0-alpha.13" }
-transcript = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "transcript", tag = "v1.0.0-alpha.13" }
-whir = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "whir", tag = "v1.0.0-alpha.13" }
-witness = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "witness", tag = "v1.0.0-alpha.13" }
+ff_ext = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "ff_ext", tag = "v1.0.0-alpha.14" }
+mpcs = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "mpcs", tag = "v1.0.0-alpha.14" }
+multilinear_extensions = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "multilinear_extensions", tag = "v1.0.0-alpha.14" }
+p3 = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "p3", tag = "v1.0.0-alpha.14" }
+poseidon = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "poseidon", tag = "v1.0.0-alpha.14" }
+sp1-curves = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "sp1-curves", tag = "v1.0.0-alpha.14" }
+sumcheck = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "sumcheck", tag = "v1.0.0-alpha.14" }
+transcript = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "transcript", tag = "v1.0.0-alpha.14" }
+whir = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "whir", tag = "v1.0.0-alpha.14" }
+witness = { git = "https://github.com/scroll-tech/gkr-backend.git", package = "witness", tag = "v1.0.0-alpha.14" }
 
 alloy-primitives = "1.3"
 anyhow = { version = "1.0", default-features = false }
@@ -97,17 +97,17 @@ opt-level = 3
 [profile.release]
 lto = "thin"
 
-# [patch."ssh://git@github.com/scroll-tech/ceno-gpu.git"]
-# ceno_gpu = { path = "../ceno-gpu/cuda_hal", package = "cuda_hal", default-features = false, features=["bb31"] }
-
-# [patch."https://github.com/scroll-tech/gkr-backend"]
-# ff_ext = { path = "../gkr-backend/crates/ff_ext", package = "ff_ext" }
-# mpcs = { path = "../gkr-backend/crates/mpcs", package = "mpcs" }
-# multilinear_extensions = { path = "../gkr-backend/crates/multilinear_extensions", package = "multilinear_extensions" }
-# p3 = { path = "../gkr-backend/crates/p3", package = "p3" }
-# poseidon = { path = "../gkr-backend/crates/poseidon", package = "poseidon" }
-# sp1-curves = { path = "../gkr-backend/crates/curves", package = "sp1-curves" }
-# sumcheck = { path = "../gkr-backend/crates/sumcheck", package = "sumcheck" }
-# transcript = { path = "../gkr-backend/crates/transcript", package = "transcript" }
-# whir = { path = "../gkr-backend/crates/whir", package = "whir" }
-# witness = { path = "../gkr-backend/crates/witness", package = "witness" }
+#[patch."ssh://git@github.com/scroll-tech/ceno-gpu.git"]
+#ceno_gpu = { path = "../ceno-gpu/cuda_hal", package = "cuda_hal", default-features = false, features = ["bb31"] }
+#
+#[patch."https://github.com/scroll-tech/gkr-backend"]
+#ff_ext = { path = "../gkr-backend/crates/ff_ext", package = "ff_ext" }
+#mpcs = { path = "../gkr-backend/crates/mpcs", package = "mpcs" }
+#multilinear_extensions = { path = "../gkr-backend/crates/multilinear_extensions", package = "multilinear_extensions" }
+#p3 = { path = "../gkr-backend/crates/p3", package = "p3" }
+#poseidon = { path = "../gkr-backend/crates/poseidon", package = "poseidon" }
+#sp1-curves = { path = "../gkr-backend/crates/curves", package = "sp1-curves" }
+#sumcheck = { path = "../gkr-backend/crates/sumcheck", package = "sumcheck" }
+#transcript = { path = "../gkr-backend/crates/transcript", package = "transcript" }
+#whir = { path = "../gkr-backend/crates/whir", package = "whir" }
+#witness = { path = "../gkr-backend/crates/witness", package = "witness" }
diff --git a/gkr_iop/src/gkr/layer.rs b/gkr_iop/src/gkr/layer.rs
index 64eb747be..9f23a40ba 100644
--- a/gkr_iop/src/gkr/layer.rs
+++ b/gkr_iop/src/gkr/layer.rs
@@ -6,6 +6,7 @@ use multilinear_extensions::{
     Expression, Instance, StructuralWitIn, ToExpr,
     mle::{Point, PointAndEval},
     monomial::Term,
+    utils::Node,
 };
 use p3::field::FieldAlgebra;
 use rayon::iter::{IntoParallelIterator, IntoParallelRefIterator};
@@ -48,6 +49,8 @@ pub enum LayerType {
     Linear,
 }
 
+pub type DagInfo<E> = (Vec<Node>, Vec<Expression<E>>, u32, usize, usize);
+
 #[derive(Clone, Debug, Serialize, Deserialize)]
 #[serde(bound(
     serialize = "E::BaseField: Serialize",
@@ -103,6 +106,10 @@ pub struct Layer<E: ExtensionField> {
     pub main_sumcheck_expression_monomial_terms: Option<Vec<Term<Expression<E>, Expression<E>>>>,
     pub main_sumcheck_expression: Option<Expression<E>>,
 
+    // flatten computation dag
+    // (dag, coeffs, final_out_index, max_dag_depth, max_degree)
+    pub main_sumcheck_expression_dag: Option<DagInfo<E>>,
+
     // rotation sumcheck expression, only optionally valid for zerocheck
     // store in 2 forms: expression & monomial
     pub rotation_sumcheck_expression_monomial_terms:
@@ -175,6 +182,7 @@ impl<E: ExtensionField> Layer<E> {
                     expr_names,
                     main_sumcheck_expression_monomial_terms: None,
                     main_sumcheck_expression: None,
+                    main_sumcheck_expression_dag: None,
                     rotation_sumcheck_expression_monomial_terms: None,
                     rotation_sumcheck_expression: None,
                 };
diff --git a/gkr_iop/src/gkr/layer/gpu/mod.rs b/gkr_iop/src/gkr/layer/gpu/mod.rs
index 5840111e7..ee0eb05c4 100644
--- a/gkr_iop/src/gkr/layer/gpu/mod.rs
+++ b/gkr_iop/src/gkr/layer/gpu/mod.rs
@@ -18,6 +18,7 @@ use multilinear_extensions::{
     Expression,
     mle::{MultilinearExtension, Point},
     monomial::Term,
+    utils::eval_by_expr_constant,
 };
 use rayon::{
     iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator},
@@ -232,8 +233,26 @@ impl<E: ExtensionField, PCS: PolynomialCommitmentScheme<E>> ZerocheckLayerProver
             layer.n_fixed,
             layer.n_instance,
         );
+
+        // process dag
+        // (dag, coeffs, final_out_index, max_dag_depth, max_degree)
+        let (dag, dag_coeffs, final_out_index, max_dag_depth, max_degree) =
+            layer.main_sumcheck_expression_dag.as_ref().unwrap();
+
+        let pub_io_eval_scalar = pub_io_evals.iter().map(|v| Either::Right(*v)).collect_vec();
+        // format: pub_io ++ challenge ++ constant
+        let dag_coeffs = dag_coeffs
+            .iter()
+            .map(|c| eval_by_expr_constant(&pub_io_eval_scalar, &main_sumcheck_challenges, c))
+            .map(|either_v| match either_v {
+                Either::Left(base_field_val) => E::from(base_field_val),
+                Either::Right(ext_field_val) => ext_field_val,
+            })
+            .collect_vec();
+
+        // process monomial terms
         // Calculate max_num_var and max_degree from the extracted relationships
-        let (term_coefficients, mle_indices_per_term, mle_size_info) =
+        let (monomial_coefficients, mle_indices_per_term, mle_size_info) =
             extract_mle_relationships_from_monomial_terms(
                 &layer
                     .main_sumcheck_expression_monomial_terms
@@ -243,18 +262,18 @@ impl<E: ExtensionField, PCS: PolynomialCommitmentScheme<E>> ZerocheckLayerProver
                 &pub_io_evals.iter().map(|v| Either::Right(*v)).collect_vec(),
                 &main_sumcheck_challenges,
             );
+
         let max_num_var = max_num_variables;
-        let max_degree = mle_indices_per_term
-            .iter()
-            .map(|indices| indices.len())
-            .max()
-            .unwrap_or(0);
+
+        // Convert types for GPU function Call
+        let monomial_coefficients: Vec<BB31Ext> =
+            unsafe { std::mem::transmute(monomial_coefficients) };
 
         // Convert types for GPU function Call
         let basic_tr: &mut BasicTranscript<BB31Ext> =
             unsafe { &mut *(transcript as *mut _ as *mut BasicTranscript<BB31Ext>) };
-        let term_coefficients_gl64: Vec<BB31Ext> =
-            unsafe { std::mem::transmute(term_coefficients) };
+        let dag_coeffs: Vec<BB31Ext> = unsafe { std::mem::transmute(dag_coeffs) };
+
         let all_witins_gpu_gl64: Vec<&MultilinearExtensionGpu<BB31Ext>> =
             unsafe { std::mem::transmute(all_witins_gpu) };
         let all_witins_gpu_type_gl64 = all_witins_gpu_gl64.iter().map(|mle| &mle.mle).collect_vec();
@@ -264,13 +283,18 @@ impl<E: ExtensionField, PCS: PolynomialCommitmentScheme<E>> ZerocheckLayerProver
                 &cuda_hal,
                 all_witins_gpu_type_gl64,
                 &mle_size_info,
-                &term_coefficients_gl64,
+                &monomial_coefficients,
                 &mle_indices_per_term,
                 max_num_var,
-                max_degree,
+                *max_degree,
+                dag,
+                *max_dag_depth,
+                &dag_coeffs,
+                *final_out_index,
                 basic_tr,
             )
             .unwrap();
+
         let evals_gpu = evals_gpu.into_iter().flatten().collect_vec();
         let row_challenges = challenges_gpu.iter().map(|c| c.elements).collect_vec();
 
@@ -389,6 +413,10 @@ pub(crate) fn prove_rotation_gpu<E: ExtensionField, PCS: PolynomialCommitmentSch
             &mle_indices_per_term,
             max_num_var,
             max_degree,
+            &[],
+            0,
+            &[],
+            0,
             basic_tr,
         )
         .unwrap();
diff --git a/gkr_iop/src/gkr/layer/zerocheck_layer.rs b/gkr_iop/src/gkr/layer/zerocheck_layer.rs
index 18bf4485a..9703e9c8e 100644
--- a/gkr_iop/src/gkr/layer/zerocheck_layer.rs
+++ b/gkr_iop/src/gkr/layer/zerocheck_layer.rs
@@ -5,7 +5,10 @@ use multilinear_extensions::{
     macros::{entered_span, exit_span},
     mle::{IntoMLE, Point},
     monomialize_expr_to_wit_terms,
-    utils::{eval_by_expr, eval_by_expr_with_instance, expr_convert_to_witins},
+    utils::{
+        build_factored_dag_commutative, dag_stats, eval_by_expr, eval_by_expr_with_instance,
+        expr_convert_to_witins,
+    },
     virtual_poly::VPAuxInfo,
 };
 use p3::field::{FieldAlgebra, dot_product};
@@ -165,18 +168,44 @@ impl<E: ExtensionField> ZerocheckLayer<E> for Layer<E> {
             self.n_fixed as WitnessId,
             self.n_instance,
         );
-        tracing::debug!("main sumcheck degree: {}", zero_expr.degree());
+        let zero_expr_degree = zero_expr.degree();
         self.main_sumcheck_expression = Some(zero_expr);
         self.main_sumcheck_expression_monomial_terms = self
             .main_sumcheck_expression
             .as_ref()
             .map(|expr| expr.get_monomial_terms());
-        tracing::debug!(
-            "main sumcheck monomial terms count: {}",
+
+        {
+            if let Some(terms) = self.main_sumcheck_expression_monomial_terms.as_ref() {
+                let num_mul: usize = terms.iter().map(|term| term.product.len()).sum();
+                let num_add = terms.iter().len() - 1;
+
+                tracing::debug!(
+                    "layer name {} monomial num_add: {num_add} num_mul: {num_mul}",
+                    self.name,
+                );
+            }
+        }
+
+        self.main_sumcheck_expression_dag = {
             self.main_sumcheck_expression_monomial_terms
                 .as_ref()
-                .map_or(0, |terms| terms.len()),
-        );
+                .map(|terms| {
+                    // selector are structural witin, which is used to be the largest id.
+                    let (dag, coeffs, Some(final_out_index), max_dag_depth) = build_factored_dag_commutative(terms, false) else { panic!() };
+                    let max_degree = zero_expr_degree;
+
+                    let (num_add, num_mul) = dag_stats(&dag);
+                    tracing::debug!(
+                        "layer name {} dag got num_add {num_add} num_mul {num_mul} max_degree {max_degree} \
+                        max_dag_depth {max_dag_depth} num_scalar {} final_out_index {final_out_index}",
+                        self.name,
+                        coeffs.len(),
+                    );
+                    (dag, coeffs, final_out_index, max_dag_depth as usize, zero_expr_degree)
+                })
+        };
+
         exit_span!(span);
     }