diff --git a/Cargo.toml b/Cargo.toml
index b68e1f6d..fdc91633 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -165,4 +165,4 @@ spongefish = { git = "https://github.com/arkworks-rs/spongefish", features = [
   "ark-ff", "sha2",
 ], rev = "fcc277f8a857fdeeadd7cca92ab08de63b1ff1a1" }
 spongefish-pow = { git = "https://github.com/arkworks-rs/spongefish", rev = "fcc277f8a857fdeeadd7cca92ab08de63b1ff1a1" }
-whir = { git = "https://github.com/WizardOfMenlo/whir/", rev = "3056565b90931c28f725f6655d954bd8f17eaaf6", features = ["tracing"] }
+whir = { git = "https://github.com/WizardOfMenlo/whir/", rev = "ec295ced976c3dc2277a20e1048f928dbfd03bbd", features = ["tracing"] }
diff --git a/provekit/common/src/utils/zk_utils.rs b/provekit/common/src/utils/zk_utils.rs
index f6b7b6f0..7d354eb5 100644
--- a/provekit/common/src/utils/zk_utils.rs
+++ b/provekit/common/src/utils/zk_utils.rs
@@ -4,9 +4,9 @@ use {
     rayon::prelude::*,
     whir::algebra::{
         dot,
+        linear_form::Covector,
         ntt::wavelet_transform,
         polynomials::{CoefficientList, EvaluationsList},
-        weights::Covector,
     },
 };
 
diff --git a/provekit/prover/src/whir_r1cs.rs b/provekit/prover/src/whir_r1cs.rs
index 82c7c2b2..c8317ab7 100644
--- a/provekit/prover/src/whir_r1cs.rs
+++ b/provekit/prover/src/whir_r1cs.rs
@@ -23,9 +23,8 @@ use {
     tracing::{debug, instrument},
     whir::{
         algebra::{
-            embedding::Basefield,
+            linear_form::{Covector, LinearForm},
             polynomials::{CoefficientList, EvaluationsList, MultilinearPoint},
-            weights::{Covector, Evaluate},
         },
         protocols::whir::Witness,
         transcript::{ProverState, VerifierMessage},
@@ -191,9 +190,9 @@ impl WhirR1CSProver for WhirR1CSScheme {
                 &commitment.random_polynomial_coeff,
             );
 
-            let weight_refs: Vec<&dyn Evaluate<Basefield<FieldElement>>> = weights
+            let weight_refs: Vec<&dyn LinearForm<FieldElement>> = weights
                 .iter()
-                .map(|w| w as &dyn Evaluate<Basefield<FieldElement>>)
+                .map(|w| w as &dyn LinearForm<FieldElement>)
                 .collect();
 
             run_zk_whir_pcs_prover(
@@ -305,9 +304,9 @@ impl WhirR1CSProver for WhirR1CSScheme {
                 .flat_map(|w| poly_evals.iter().map(|pe| covector_dot(w, pe)))
                 .collect();
 
-            let weight_refs: Vec<&dyn Evaluate<Basefield<FieldElement>>> = all_weights
+            let weight_refs: Vec<&dyn LinearForm<FieldElement>> = all_weights
                 .iter()
-                .map(|w| w as &dyn Evaluate<Basefield<FieldElement>>)
+                .map(|w| w as &dyn LinearForm<FieldElement>)
                 .collect();
 
             run_zk_whir_pcs_prover(
@@ -619,9 +618,9 @@ pub fn run_zk_sumcheck_prover(
         &blindings_blind_polynomial,
     );
 
-    let blinding_weight_refs: Vec<&dyn Evaluate<Basefield<FieldElement>>> = blinding_weights
+    let blinding_weight_refs: Vec<&dyn LinearForm<FieldElement>> = blinding_weights
         .iter()
-        .map(|w| w as &dyn Evaluate<Basefield<FieldElement>>)
+        .map(|w| w as &dyn LinearForm<FieldElement>)
         .collect();
 
     let (_sums, _deferred) = run_zk_whir_pcs_prover(
@@ -711,14 +710,15 @@ fn compute_evaluations_single(
 pub fn run_zk_whir_pcs_prover(
     witnesses: &[&Witness<FieldElement>],
     polynomials: &[&CoefficientList<FieldElement>],
-    weights: &[&dyn Evaluate<Basefield<FieldElement>>],
+    linear_forms: &[&dyn LinearForm<FieldElement>],
     evaluations: &[FieldElement],
     params: &WhirConfig,
     merlin: &mut ProverState<TranscriptSponge>,
 ) -> (MultilinearPoint<FieldElement>, Vec<FieldElement>) {
     debug!("WHIR Parameters: {params}");
 
-    let (randomness, deferred) = params.prove(merlin, polynomials, witnesses, weights, evaluations);
+    let (randomness, deferred) =
+        params.prove(merlin, polynomials, witnesses, linear_forms, evaluations);
 
     (randomness, deferred)
 }
diff --git a/provekit/verifier/src/whir_r1cs.rs b/provekit/verifier/src/whir_r1cs.rs
index 83163c94..cb860bed 100644
--- a/provekit/verifier/src/whir_r1cs.rs
+++ b/provekit/verifier/src/whir_r1cs.rs
@@ -11,8 +11,8 @@ use {
     tracing::instrument,
     whir::{
         algebra::{
+            linear_form::{Covector, LinearForm},
             polynomials::MultilinearPoint,
-            weights::{Covector, Weights},
         },
         protocols::whir::Commitment,
         transcript::{codecs::Empty, Proof, VerifierMessage, VerifierState},
@@ -153,9 +153,9 @@ impl WhirR1CSVerifier for WhirR1CSScheme {
                 let mut all_evaluations = evaluations_1;
                 all_evaluations.extend(evaluations_2);
 
-                let weight_refs: Vec<&dyn Weights<FieldElement>> = all_weights
+                let weight_refs: Vec<&dyn LinearForm<FieldElement>> = all_weights
                     .iter()
-                    .map(|w| w as &dyn Weights<FieldElement>)
+                    .map(|w| w as &dyn LinearForm<FieldElement>)
                     .collect();
                 let commitment_refs: Vec<&Commitment<FieldElement>> =
                     vec![&commitment_1, &commitment_2];
@@ -202,9 +202,9 @@ impl WhirR1CSVerifier for WhirR1CSScheme {
                     );
                 }
 
-                let weight_refs: Vec<&dyn Weights<FieldElement>> = weights
+                let weight_refs: Vec<&dyn LinearForm<FieldElement>> = weights
                     .iter()
-                    .map(|w| w as &dyn Weights<FieldElement>)
+                    .map(|w| w as &dyn LinearForm<FieldElement>)
                     .collect();
 
                 let (whir_folding_randomness, deferred_evals) = run_whir_pcs_verifier(
@@ -464,9 +464,9 @@ pub fn run_sumcheck_verifier(
         ]),
     );
 
-    let blinding_weight_refs: Vec<&dyn Weights<FieldElement>> = blinding_weights
+    let blinding_weight_refs: Vec<&dyn LinearForm<FieldElement>> = blinding_weights
         .iter()
-        .map(|w| w as &dyn Weights<FieldElement>)
+        .map(|w| w as &dyn LinearForm<FieldElement>)
         .collect();
 
     run_whir_pcs_verifier(
@@ -492,7 +492,7 @@ pub fn run_whir_pcs_verifier(
     arthur: &mut VerifierState<'_, TranscriptSponge>,
     params: &WhirConfig,
     commitments: &[&Commitment<FieldElement>],
-    weights: &[&dyn Weights<FieldElement>],
+    weights: &[&dyn LinearForm<FieldElement>],
     evaluations: &[FieldElement],
 ) -> Result<(MultilinearPoint<FieldElement>, Vec<FieldElement>)> {
     let (folding_randomness, deferred) =