diff --git a/ext/TensorKitChainRulesCoreExt.jl b/ext/TensorKitChainRulesCoreExt.jl
index 0d1d0825..27208c3a 100644
--- a/ext/TensorKitChainRulesCoreExt.jl
+++ b/ext/TensorKitChainRulesCoreExt.jl
@@ -385,15 +385,14 @@ function svd_pullback!(ΔA::AbstractMatrix, U::AbstractMatrix, S::AbstractVector
 
     # check whether cotangents arise from gauge-invariance objective function
     mask = abs.(Sp' .- Sp) .< tol
-    gaugepart = view(aUΔU, mask) + view(aVΔV, mask)
-    norm(gaugepart, Inf) < tol || @warn "cotangents sensitive to gauge choice"
+    Δgauge = norm(view(aUΔU, mask) + view(aVΔV, mask), Inf)
     if p > r
         rprange = (r + 1):p
-        norm(view(aUΔU, rprange, rprange), Inf) < tol ||
-            @warn "cotangents sensitive to gauge choice"
-        norm(view(aVΔV, rprange, rprange), Inf) < tol ||
-            @warn "cotangents sensitive to gauge choice"
+        Δgauge = max(Δgauge, norm(view(aUΔU, rprange, rprange), Inf))
+        Δgauge = max(Δgauge, norm(view(aVΔV, rprange, rprange), Inf))
     end
+    Δgauge < tol ||
+        @warn "`svd` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
     UdΔAV = (aUΔU .+ aVΔV) .* safe_inv.(Sp' .- Sp, tol) .+
             (aUΔU .- aVΔV) .* safe_inv.(Sp' .+ Sp, tol)
@@ -461,8 +460,9 @@ function eig_pullback!(ΔA::AbstractMatrix, D::AbstractVector, V::AbstractMatrix
         VdΔV = V' * ΔV
 
         mask = abs.(transpose(D) .- D) .< tol
-        gaugepart = view(VdΔV, mask)
-        norm(gaugepart, Inf) < tol || @warn "cotangents sensitive to gauge choice"
+        Δgauge = norm(view(VdΔV, mask), Inf)
+        Δgauge < tol ||
+            @warn "`eig` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         VdΔV .*= conj.(safe_inv.(transpose(D) .- D, tol))
 
@@ -504,8 +504,9 @@ function eigh_pullback!(ΔA::AbstractMatrix, D::AbstractVector, V::AbstractMatri
         aVdΔV = rmul!(VdΔV - VdΔV', 1 / 2)
 
         mask = abs.(D' .- D) .< tol
-        gaugepart = view(aVdΔV, mask)
-        norm(gaugepart, Inf) < tol || @warn "cotangents sensitive to gauge choice"
+        Δgauge = norm(view(aVdΔV, mask))
+        Δgauge < tol ||
+            @warn "`eigh` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
 
         aVdΔV .*= safe_inv.(D' .- D, tol)
 
@@ -567,8 +568,9 @@ function qr_pullback!(ΔA::AbstractMatrix, Q::AbstractMatrix, R::AbstractMatrix,
         Q2 = view(Q, :, (p + 1):m)
         ΔQ2 = view(ΔQ, :, (p + 1):m)
         Q1dΔQ2 = Q1' * ΔQ2
-        gaugepart = mul!(copy(ΔQ2), Q1, Q1dΔQ2, -1, 1)
-        norm(gaugepart, Inf) < tol || @warn "cotangents sensitive to gauge choice"
+        Δgauge = norm(mul!(copy(ΔQ2), Q1, Q1dΔQ2, -1, 1), Inf)
+        Δgauge < tol ||
+            @warn "`qr` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
         mul!(ΔA1, Q2, Q1dΔQ2', -1, 1)
     end
     rdiv!(ΔA1, UpperTriangular(R11)')
@@ -621,8 +623,9 @@ function lq_pullback!(ΔA::AbstractMatrix, L::AbstractMatrix, Q::AbstractMatrix,
         Q2 = view(Q, (p + 1):n, :)
         ΔQ2 = view(ΔQ, (p + 1):n, :)
         ΔQ2Q1d = ΔQ2 * Q1'
-        gaugepart = mul!(copy(ΔQ2), ΔQ2Q1d, Q1, -1, 1)
-        norm(gaugepart, Inf) < tol || @warn "cotangents sensitive to gauge choice"
+        Δgauge = norm(mul!(copy(ΔQ2), ΔQ2Q1d, Q1, -1, 1))
+        Δgauge < tol ||
+            @warn "`lq` cotangents sensitive to gauge choice: (|Δgauge| = $Δgauge)"
         mul!(ΔA1, ΔQ2Q1d', Q2, -1, 1)
     end
     ldiv!(LowerTriangular(L11)', ΔA1)