diff --git a/examples/src/fibonacci/fib2/air.rs b/examples/src/fibonacci/fib2/air.rs
index 150d8a777..2689a48f8 100644
--- a/examples/src/fibonacci/fib2/air.rs
+++ b/examples/src/fibonacci/fib2/air.rs
@@ -95,7 +95,7 @@ impl air::LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/fibonacci/fib8/air.rs b/examples/src/fibonacci/fib8/air.rs
index a9573634b..765f3980d 100644
--- a/examples/src/fibonacci/fib8/air.rs
+++ b/examples/src/fibonacci/fib8/air.rs
@@ -103,7 +103,7 @@ impl air::LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/fibonacci/fib_small/air.rs b/examples/src/fibonacci/fib_small/air.rs
index c567394ed..e32330a9b 100644
--- a/examples/src/fibonacci/fib_small/air.rs
+++ b/examples/src/fibonacci/fib_small/air.rs
@@ -95,7 +95,7 @@ impl air::LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/fibonacci/mulfib2/air.rs b/examples/src/fibonacci/mulfib2/air.rs
index ba9427443..323ed623f 100644
--- a/examples/src/fibonacci/mulfib2/air.rs
+++ b/examples/src/fibonacci/mulfib2/air.rs
@@ -97,7 +97,7 @@ impl air::LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/fibonacci/mulfib8/air.rs b/examples/src/fibonacci/mulfib8/air.rs
index f7b04b0ae..2c63fe907 100644
--- a/examples/src/fibonacci/mulfib8/air.rs
+++ b/examples/src/fibonacci/mulfib8/air.rs
@@ -118,7 +118,7 @@ impl air::LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/lamport/aggregate/air.rs b/examples/src/lamport/aggregate/air.rs
index 58331527e..71cefe6ac 100644
--- a/examples/src/lamport/aggregate/air.rs
+++ b/examples/src/lamport/aggregate/air.rs
@@ -316,7 +316,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/lamport/threshold/air.rs b/examples/src/lamport/threshold/air.rs
index afac4f8c3..be93d0295 100644
--- a/examples/src/lamport/threshold/air.rs
+++ b/examples/src/lamport/threshold/air.rs
@@ -392,7 +392,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/merkle/air.rs b/examples/src/merkle/air.rs
index e605f7ffe..138bddf03 100644
--- a/examples/src/merkle/air.rs
+++ b/examples/src/merkle/air.rs
@@ -162,7 +162,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/rescue/air.rs b/examples/src/rescue/air.rs
index 06a994c64..42c8e772f 100644
--- a/examples/src/rescue/air.rs
+++ b/examples/src/rescue/air.rs
@@ -167,7 +167,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/rescue_raps/air.rs b/examples/src/rescue_raps/air.rs
index a2f2e5312..e51f6f42f 100644
--- a/examples/src/rescue_raps/air.rs
+++ b/examples/src/rescue_raps/air.rs
@@ -297,7 +297,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/vdf/exempt/air.rs b/examples/src/vdf/exempt/air.rs
index 2152d632f..b02258b20 100644
--- a/examples/src/vdf/exempt/air.rs
+++ b/examples/src/vdf/exempt/air.rs
@@ -109,7 +109,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/examples/src/vdf/regular/air.rs b/examples/src/vdf/regular/air.rs
index 6e1e2fc32..1a7ed8827 100644
--- a/examples/src/vdf/regular/air.rs
+++ b/examples/src/vdf/regular/air.rs
@@ -100,7 +100,7 @@ impl LogUpGkrEvaluator for PlainLogUpGkrEval<BaseElement> {
         unimplemented!()
     }
 
-    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E]) -> Vec<E>
+    fn build_query<E>(&self, _frame: &EvaluationFrame<E>, _periodic_values: &[E], _query: &mut [E])
     where
         E: FieldElement<BaseField = Self::BaseField>,
     {
diff --git a/prover/src/logup_gkr/prover.rs b/prover/src/logup_gkr/prover.rs
index e6dde54f3..f95597825 100644
--- a/prover/src/logup_gkr/prover.rs
+++ b/prover/src/logup_gkr/prover.rs
@@ -73,11 +73,11 @@ pub fn prove_gkr<E: FieldElement>(
         prove_intermediate_layers(&mut circuit, public_coin)?;
 
     // build the MLEs of the relevant main trace columns
-    let main_trace_mls =
+    let mut main_trace_mls =
         build_mls_from_main_trace_segment(evaluator.get_oracles(), main_trace.main_segment())?;
 
     let final_layer_proof =
-        prove_input_layer(evaluator, logup_randomness, main_trace_mls, gkr_claim, public_coin)?;
+        prove_input_layer(evaluator, logup_randomness, &mut main_trace_mls, gkr_claim, public_coin)?;
 
     // include the circuit output as part of the final proof
     let CircuitLayerPolys { numerators, denominators } = circuit.output_layer().clone();
@@ -97,12 +97,12 @@ fn prove_input_layer<
 >(
     evaluator: &impl LogUpGkrEvaluator<BaseField = E::BaseField>,
     log_up_randomness: Vec<E>,
-    mut mls: Vec<MultiLinearPoly<E>>,
-    gkr_claim: GkrClaim<E>,
+    multi_linear_ext_polys: &mut[MultiLinearPoly<E>],
+    claim: GkrClaim<E>,
     transcript: &mut C,
 ) -> Result<FinalLayerProof<E>, GkrProverError> {
     // parse the [GkrClaim] resulting from the previous GKR layer
-    let GkrClaim { evaluation_point, claimed_evaluation } = gkr_claim;
+    let GkrClaim { evaluation_point, claimed_evaluation } = claim;
 
     transcript.reseed(H::hash_elements(&[claimed_evaluation.0, claimed_evaluation.1]));
     let r_batch = transcript.draw().map_err(|_| GkrProverError::FailedToGenerateChallenge)?;
@@ -114,11 +114,11 @@ fn prove_input_layer<
         claim,
         r_batch,
         log_up_randomness,
-        &mut mls,
+        multi_linear_ext_polys,
         transcript,
     )?;
 
-    Ok(FinalLayerProof { proof })
+    Ok(FinalLayerProof::new(proof))
 }
 
 // TODO: Make the multi-linears over the base field and define an operation of folding with a challenge
@@ -172,10 +172,10 @@ fn prove_intermediate_layers<
 
     // generate the challenge and reduce [p0, p1, q0, q1] to [pr, qr]
     let r = transcript.draw().map_err(|_| GkrProverError::FailedToGenerateChallenge)?;
-    let mut claim = circuit.evaluate_output_layer(r);
+    let mut claimed_evaluation = circuit.evaluate_output_layer(r);
 
-    let mut proof_layers: Vec<SumCheckProof<E>> = Vec::new();
-    let mut rand = vec![r];
+    let mut layer_proofs: Vec<SumCheckProof<E>> = Vec::new();
+    let mut evaluation_point = vec![r];
 
     // Loop over all inner layers, from output to input.
     //
@@ -186,7 +186,7 @@ fn prove_intermediate_layers<
     // reduced in terms of the input layer separately in `prove_final_circuit_layer`.
     for inner_layer in circuit.layers().iter().skip(1).rev().skip(1) {
         // construct the Lagrange kernel evaluated at the previous GKR round randomness
-        let mut poly_x = EqFunction::ml_at(rand.into());
+        let mut eq_mle = EqFunction::ml_at(evaluation_point.into());
 
         // construct the vector of multi-linear polynomials
         // TODO: avoid unnecessary allocation
@@ -197,12 +197,12 @@ fn prove_intermediate_layers<
 
         // run the sumcheck protocol
         let proof = sum_check_prove_num_rounds_degree_3(
-            claim,
+            claimed_evaluation,
             &mut left_numerators,
             &mut right_numerators,
             &mut left_denominators,
             &mut right_denominators,
-            &mut poly_x,
+            &mut eq_mle,
             transcript,
         )?;
 
@@ -211,7 +211,7 @@ fn prove_intermediate_layers<
         let r_layer = transcript.draw().map_err(|_| GkrProverError::FailedToGenerateChallenge)?;
 
         // reduce the claim
-        claim = {
+        claimed_evaluation = {
             let left_numerators_opening = proof.openings_claim.openings[0];
             let right_numerators_opening = proof.openings_claim.openings[1];
             let left_denominators_opening = proof.openings_claim.openings[2];
@@ -229,16 +229,16 @@ fn prove_intermediate_layers<
         // collect the randomness used for the current layer
         let mut ext = vec![r_layer];
         ext.extend_from_slice(&proof.openings_claim.eval_point);
-        rand = ext;
+        evaluation_point = ext;
 
-        proof_layers.push(proof);
+        layer_proofs.push(proof);
     }
 
     Ok((
-        BeforeFinalLayerProof { proof: proof_layers },
+        BeforeFinalLayerProof { proof: layer_proofs },
         GkrClaim {
-            evaluation_point: rand,
-            claimed_evaluation: claim,
+            evaluation_point,
+            claimed_evaluation,
         },
     ))
 }
diff --git a/sumcheck/src/lib.rs b/sumcheck/src/lib.rs
index f30db974c..5beac9bb9 100644
--- a/sumcheck/src/lib.rs
+++ b/sumcheck/src/lib.rs
@@ -124,8 +124,12 @@ where
 
 /// A proof for the input circuit layer i.e., the final layer in the GKR protocol.
 #[derive(Debug, Clone)]
-pub struct FinalLayerProof<E: FieldElement> {
-    pub proof: SumCheckProof<E>,
+pub struct FinalLayerProof<E: FieldElement>(SumCheckProof<E>);
+
+impl<E: FieldElement> FinalLayerProof<E> {
+    pub fn new(proof: SumCheckProof<E>) -> Self {
+        Self(proof)
+    }
 }
 
 impl<E> Serializable for FinalLayerProof<E>
@@ -133,8 +137,7 @@ where
     E: FieldElement,
 {
     fn write_into<W: ByteWriter>(&self, target: &mut W) {
-        let Self { proof } = self;
-        proof.write_into(target);
+        self.0.write_into(target);
     }
 }
 
@@ -143,9 +146,7 @@ where
     E: FieldElement,
 {
     fn read_from<R: ByteReader>(source: &mut R) -> Result<Self, DeserializationError> {
-        Ok(Self {
-            proof: Deserializable::read_from(source)?,
-        })
+        Ok(Self(Deserializable::read_from(source)?))
     }
 }
 
@@ -170,7 +171,7 @@ pub struct GkrCircuitProof<E: FieldElement> {
 
 impl<E: FieldElement> GkrCircuitProof<E> {
     pub fn get_final_opening_claim(&self) -> FinalOpeningClaim<E> {
-        self.final_layer_proof.proof.openings_claim.clone()
+        self.final_layer_proof.0.openings_claim.clone()
     }
 }
 
@@ -181,7 +182,7 @@ where
     fn write_into<W: ByteWriter>(&self, target: &mut W) {
         self.circuit_outputs.write_into(target);
         self.before_final_layer_proofs.write_into(target);
-        self.final_layer_proof.proof.write_into(target);
+        self.final_layer_proof.0.write_into(target);
     }
 }
 
diff --git a/sumcheck/src/verifier/mod.rs b/sumcheck/src/verifier/mod.rs
index d1cfae3a4..5cc338bb7 100644
--- a/sumcheck/src/verifier/mod.rs
+++ b/sumcheck/src/verifier/mod.rs
@@ -64,8 +64,6 @@ pub fn verify_sum_check_input_layer<E: FieldElement, H: ElementHasher<BaseField
     claim: (E, E),
     transcript: &mut impl RandomCoin<Hasher = H, BaseField = E::BaseField>,
 ) -> Result<FinalOpeningClaim<E>, SumCheckVerifierError> {
-    let FinalLayerProof { proof } = proof;
-
     // generate challenge to batch sum-checks
     transcript.reseed(H::hash_elements(&[claim.0, claim.1]));
     let r_batch: E = transcript
@@ -77,17 +75,17 @@ pub fn verify_sum_check_input_layer<E: FieldElement, H: ElementHasher<BaseField
 
     // verify the sum-check proof
     let SumCheckRoundClaim { eval_point, claim } =
-        verify_rounds(reduced_claim, &proof.round_proofs, transcript)?;
+        verify_rounds(reduced_claim, &proof.0.round_proofs, transcript)?;
 
     // execute the final evaluation check
-    if proof.openings_claim.eval_point != eval_point {
+    if proof.0.openings_claim.eval_point != eval_point {
         return Err(SumCheckVerifierError::WrongOpeningPoint);
     }
 
     let mut numerators = vec![E::ZERO; evaluator.get_num_fractions()];
     let mut denominators = vec![E::ZERO; evaluator.get_num_fractions()];
     evaluator.evaluate_query(
-        &proof.openings_claim.openings,
+        &proof.0.openings_claim.openings,
         &log_up_randomness,
         &mut numerators,
         &mut denominators,
@@ -99,14 +97,14 @@ pub fn verify_sum_check_input_layer<E: FieldElement, H: ElementHasher<BaseField
     let eq_mu = EqFunction::new(evaluation_point_mu.into()).evaluations();
     let eq_nu = EqFunction::new(evaluation_point_nu.into());
 
-    let eq_nu_eval = eq_nu.evaluate(&proof.openings_claim.eval_point);
+    let eq_nu_eval = eq_nu.evaluate(&proof.0.openings_claim.eval_point);
     let expected_evaluation =
         evaluate_composition_poly(&eq_mu, &numerators, &denominators, eq_nu_eval, r_batch);
 
     if expected_evaluation != claim {
         Err(SumCheckVerifierError::FinalEvaluationCheckFailed)
     } else {
-        Ok(proof.openings_claim.clone())
+        Ok(proof.0.openings_claim.clone())
     }
 }
 
diff --git a/verifier/src/logup_gkr/mod.rs b/verifier/src/logup_gkr/mod.rs
index b98ae603b..dcc1529ed 100644
--- a/verifier/src/logup_gkr/mod.rs
+++ b/verifier/src/logup_gkr/mod.rs
@@ -55,11 +55,11 @@ pub fn verify_logup_gkr<
 
     // verify all GKR layers but for the last one
     let num_layers = before_final_layer_proofs.proof.len();
-    let mut rand = vec![r];
+    let mut evaluation_point = vec![r];
     for i in 0..num_layers {
         let FinalOpeningClaim { eval_point, openings } = verify_sum_check_intermediate_layers(
             &before_final_layer_proofs.proof[i],
-            &rand,
+            &evaluation_point,
             reduced_claim,
             transcript,
         )?;
@@ -78,7 +78,7 @@ pub fn verify_logup_gkr<
         let rand_sumcheck = eval_point;
         let mut ext = vec![r_layer];
         ext.extend_from_slice(&rand_sumcheck);
-        rand = ext;
+        evaluation_point = ext;
     }
 
     // verify the proof of the final GKR layer and pass final opening claim for verification
@@ -87,7 +87,7 @@ pub fn verify_logup_gkr<
         evaluator,
         final_layer_proof,
         log_up_randomness,
-        &rand,
+        &evaluation_point,
         reduced_claim,
         transcript,
     )