diff --git a/crates/prover/src/core/backend/simd/column.rs b/crates/prover/src/core/backend/simd/column.rs
index db98d2669..64869405a 100644
--- a/crates/prover/src/core/backend/simd/column.rs
+++ b/crates/prover/src/core/backend/simd/column.rs
@@ -66,6 +66,12 @@ impl BaseColumn {
             .map(BaseColumnMutSlice)
             .collect_vec()
     }
+
+    pub fn into_secure_column(self) -> SecureColumn {
+        let length = self.len();
+        let data = self.data.into_iter().map(PackedSecureField::from).collect();
+        SecureColumn { data, length }
+    }
 }
 
 impl Column<BaseField> for BaseColumn {
diff --git a/crates/prover/src/core/fields/qm31.rs b/crates/prover/src/core/fields/qm31.rs
index 4467aeb41..6da19a3c0 100644
--- a/crates/prover/src/core/fields/qm31.rs
+++ b/crates/prover/src/core/fields/qm31.rs
@@ -85,6 +85,24 @@ impl Mul for QM31 {
     }
 }
 
+impl From<usize> for QM31 {
+    fn from(value: usize) -> Self {
+        M31::from(value).into()
+    }
+}
+
+impl From<u32> for QM31 {
+    fn from(value: u32) -> Self {
+        M31::from(value).into()
+    }
+}
+
+impl From<i32> for QM31 {
+    fn from(value: i32) -> Self {
+        M31::from(value).into()
+    }
+}
+
 impl TryInto<M31> for QM31 {
     type Error = ();
 
diff --git a/crates/prover/src/core/lookups/mle.rs b/crates/prover/src/core/lookups/mle.rs
index 7ac7f9eb3..7449f40f2 100644
--- a/crates/prover/src/core/lookups/mle.rs
+++ b/crates/prover/src/core/lookups/mle.rs
@@ -1,4 +1,4 @@
-use std::ops::Deref;
+use std::ops::{Deref, DerefMut};
 
 use educe::Educe;
 
@@ -58,6 +58,12 @@ impl<B: ColumnOps<F>, F: Field> Deref for Mle<B, F> {
     }
 }
 
+impl<B: ColumnOps<F>, F: Field> DerefMut for Mle<B, F> {
+    fn deref_mut(&mut self) -> &mut Self::Target {
+        &mut self.evals
+    }
+}
+
 #[cfg(test)]
 mod test {
     use super::{Mle, MleOps};
diff --git a/crates/prover/src/examples/xor/gkr_lookups/accumulation.rs b/crates/prover/src/examples/xor/gkr_lookups/accumulation.rs
new file mode 100644
index 000000000..178c0b8bf
--- /dev/null
+++ b/crates/prover/src/examples/xor/gkr_lookups/accumulation.rs
@@ -0,0 +1,186 @@
+use std::iter::zip;
+use std::ops::{AddAssign, Mul};
+
+use educe::Educe;
+use num_traits::One;
+
+use crate::core::backend::simd::SimdBackend;
+use crate::core::backend::Backend;
+use crate::core::circle::M31_CIRCLE_LOG_ORDER;
+use crate::core::fields::m31::BaseField;
+use crate::core::fields::qm31::SecureField;
+use crate::core::lookups::mle::Mle;
+use crate::core::utils::generate_secure_powers;
+
+pub const MIN_LOG_BLOWUP_FACTOR: u32 = 1;
+
+/// Max number of [`Mle`] variables for multilinear polynomials that get compiled into a univariate
+/// IOP.
+pub const MAX_MLE_N_VARIABLES: u32 = M31_CIRCLE_LOG_ORDER - MIN_LOG_BLOWUP_FACTOR;
+
+/// Accumulates [`Mle`]s grouped by their number of variables.
+pub struct MleCollection<B: Backend> {
+    mles_by_n_variables: Vec<Option<Vec<DynMle<B>>>>,
+}
+
+impl<B: Backend> MleCollection<B> {
+    /// Appends an [`Mle`] to the collection.
+    pub fn push(&mut self, mle: impl Into<DynMle<B>>) {
+        let mle = mle.into();
+        let mles = self.mles_by_n_variables[mle.n_variables()].get_or_insert(Vec::new());
+        mles.push(mle);
+    }
+}
+
+impl MleCollection<SimdBackend> {
+    /// Performs a random linear combination of all MLEs, grouped by their number of variables.
+    ///
+    /// MLEs are returned in ascending order by number of variables.
+    pub fn random_linear_combine_by_n_variables(
+        self,
+        alpha: SecureField,
+    ) -> Vec<Mle<SimdBackend, SecureField>> {
+        self.mles_by_n_variables
+            .into_iter()
+            .flatten()
+            .map(|mles| mle_random_linear_combination(mles, alpha))
+            .collect()
+    }
+}
+
+/// # Panics
+///
+/// Panics if `mles` is empty or all MLEs don't have the same number of variables.
+fn mle_random_linear_combination(
+    mles: Vec<DynMle<SimdBackend>>,
+    alpha: SecureField,
+) -> Mle<SimdBackend, SecureField> {
+    assert!(!mles.is_empty());
+    let n_variables = mles[0].n_variables();
+    assert!(mles.iter().all(|mle| mle.n_variables() == n_variables));
+    let alpha_powers = generate_secure_powers(alpha, mles.len()).into_iter().rev();
+    let mut mle_and_coeff = zip(mles, alpha_powers);
+
+    // The last value can initialize the accumulator.
+    let (mle, coeff) = mle_and_coeff.next_back().unwrap();
+    assert!(coeff.is_one());
+    let mut acc_mle = mle.into_secure_mle();
+
+    for (mle, coeff) in mle_and_coeff {
+        match mle {
+            DynMle::Base(mle) => combine(&mut acc_mle.data, &mle.data, coeff.into()),
+            DynMle::Secure(mle) => combine(&mut acc_mle.data, &mle.data, coeff.into()),
+        }
+    }
+
+    acc_mle
+}
+
+/// Computes all `acc[i] += alpha * v[i]`.
+pub fn combine<EF: AddAssign + Mul<F, Output = EF> + Copy, F: Copy>(
+    acc: &mut [EF],
+    v: &[F],
+    alpha: EF,
+) {
+    assert_eq!(acc.len(), v.len());
+    zip(acc, v).for_each(|(acc, &v)| *acc += alpha * v);
+}
+
+impl<B: Backend> Default for MleCollection<B> {
+    fn default() -> Self {
+        Self {
+            mles_by_n_variables: vec![None; MAX_MLE_N_VARIABLES as usize + 1],
+        }
+    }
+}
+
+/// Dynamic dispatch for [`Mle`] types.
+#[derive(Educe)]
+#[educe(Debug, Clone)]
+pub enum DynMle<B: Backend> {
+    Base(Mle<B, BaseField>),
+    Secure(Mle<B, SecureField>),
+}
+
+impl<B: Backend> DynMle<B> {
+    fn n_variables(&self) -> usize {
+        match self {
+            DynMle::Base(mle) => mle.n_variables(),
+            DynMle::Secure(mle) => mle.n_variables(),
+        }
+    }
+}
+
+impl<B: Backend> From<Mle<B, SecureField>> for DynMle<B> {
+    fn from(mle: Mle<B, SecureField>) -> Self {
+        DynMle::Secure(mle)
+    }
+}
+
+impl<B: Backend> From<Mle<B, BaseField>> for DynMle<B> {
+    fn from(mle: Mle<B, BaseField>) -> Self {
+        DynMle::Base(mle)
+    }
+}
+
+impl DynMle<SimdBackend> {
+    fn into_secure_mle(self) -> Mle<SimdBackend, SecureField> {
+        match self {
+            Self::Base(mle) => Mle::new(mle.into_evals().into_secure_column()),
+            Self::Secure(mle) => mle,
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use std::iter::repeat;
+
+    use num_traits::Zero;
+
+    use crate::core::backend::simd::SimdBackend;
+    use crate::core::fields::m31::BaseField;
+    use crate::core::fields::qm31::SecureField;
+    use crate::core::fields::Field;
+    use crate::core::lookups::mle::{Mle, MleOps};
+    use crate::examples::xor::gkr_lookups::accumulation::MleCollection;
+
+    #[test]
+    fn random_linear_combine_by_n_variables() {
+        const SMALL_N_VARS: usize = 4;
+        const LARGE_N_VARS: usize = 6;
+        let alpha = SecureField::from(10);
+        let mut mle_collection = MleCollection::<SimdBackend>::default();
+        mle_collection.push(const_mle(SMALL_N_VARS, BaseField::from(1)));
+        mle_collection.push(const_mle(SMALL_N_VARS, SecureField::from(2)));
+        mle_collection.push(const_mle(LARGE_N_VARS, BaseField::from(3)));
+        mle_collection.push(const_mle(LARGE_N_VARS, SecureField::from(4)));
+        mle_collection.push(const_mle(LARGE_N_VARS, SecureField::from(5)));
+        let small_eval_point = [SecureField::zero(); SMALL_N_VARS];
+        let large_eval_point = [SecureField::zero(); LARGE_N_VARS];
+
+        let [small_mle, large_mle] = mle_collection
+            .random_linear_combine_by_n_variables(alpha)
+            .try_into()
+            .unwrap();
+
+        assert_eq!(small_mle.n_variables(), SMALL_N_VARS);
+        assert_eq!(large_mle.n_variables(), LARGE_N_VARS);
+        assert_eq!(
+            small_mle.eval_at_point(&small_eval_point),
+            SecureField::from(1) * alpha + SecureField::from(2)
+        );
+        assert_eq!(
+            large_mle.eval_at_point(&large_eval_point),
+            (SecureField::from(3) * alpha + SecureField::from(4)) * alpha + SecureField::from(5)
+        );
+    }
+
+    fn const_mle<B, F>(n_variables: usize, v: F) -> Mle<B, F>
+    where
+        B: MleOps<F>,
+        F: Field,
+    {
+        Mle::new(repeat(v).take(1 << n_variables).collect())
+    }
+}
diff --git a/crates/prover/src/examples/xor/gkr_lookups/mod.rs b/crates/prover/src/examples/xor/gkr_lookups/mod.rs
index 8c570c3ba..6ee603eb0 100644
--- a/crates/prover/src/examples/xor/gkr_lookups/mod.rs
+++ b/crates/prover/src/examples/xor/gkr_lookups/mod.rs
@@ -1 +1,2 @@
+pub mod accumulation;
 pub mod mle_eval;