diff --git a/examples/ksat.ipynb b/examples/ksat.ipynb
index dd304a4..ddc3b27 100644
--- a/examples/ksat.ipynb
+++ b/examples/ksat.ipynb
@@ -12,7 +12,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -29,7 +29,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -39,7 +39,7 @@
     "k = 3\n",
     "g = rand_regular_factor_graph(rng, n, m, k)\n",
     "ψ = [KSATClause(bitrand(rng, length(neighbors(g, factor(a))))) for a in factors(g)]\n",
-    "bp = BP(g, ψ, fill(2, nvariables(g)));"
+    "bp = fast_ksat_bp(g, ψ);"
    ]
   },
   {
@@ -51,13 +51,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
+   "execution_count": 19,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "40"
+       "43"
       ]
      },
      "metadata": {},
@@ -65,7 +65,7 @@
     }
    ],
    "source": [
-    "iters = iterate!(bp; maxiter=1000, tol=1e-12, rein=5e-2)"
+    "iters = iterate!(bp; maxiter=1000, tol=1e-14, rein=5e-2)"
    ]
   },
   {
@@ -78,14 +78,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "1×100 adjoint(::Vector{Int64}) with eltype Int64:\n",
-       " 0  0  0  1  0  0  1  0  1  0  0  0  1  …  0  0  1  0  0  0  0  1  1  0  0  1"
+       "1×1000 adjoint(::Vector{Int64}) with eltype Int64:\n",
+       " 0  0  0  1  0  0  1  0  1  1  0  0  1  …  0  0  0  0  0  0  0  1  0  0  0  1"
       ]
      },
      "metadata": {},
@@ -106,7 +106,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 112,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
@@ -118,7 +118,7 @@
     }
    ],
    "source": [
-    "nunsat = sum(1 - Int(bp.ψ[a](xstar[i] for i in neighbors(bp.g, factor(a)))) \n",
+    "nunsat = sum(!(Bool(bp.ψ[a](xstar[i]+1 for i in neighbors(bp.g, factor(a))))) \n",
     "    for a in factors(bp.g))\n",
     "println(\"Number of unsatisfied clauses: $nunsat\")"
    ]
@@ -126,15 +126,15 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Julia 1.10.5",
+   "display_name": "Julia 1.11.2",
    "language": "julia",
-   "name": "julia-1.10"
+   "name": "julia-1.11"
   },
   "language_info": {
    "file_extension": ".jl",
    "mimetype": "application/julia",
    "name": "julia",
-   "version": "1.10.5"
+   "version": "1.11.2"
   }
  },
  "nbformat": 4,
diff --git a/src/Models/ksat.jl b/src/Models/ksat.jl
index c514a6b..255ae48 100644
--- a/src/Models/ksat.jl
+++ b/src/Models/ksat.jl
@@ -35,6 +35,7 @@ const BPKSAT = BP{<:KSATClause, <:BPFactor, <:NTuple{2,<:Real}, <:NTuple{2,<:Rea
 @doc raw"""
     fast_ksat_bp(g::AbstractFactorGraph, ψ::Vector{<:KSATClause}, [ϕ])
 
+Return a specialized BP instance with `KSATClause` and messages encoded as tuples of two reals instead of vectors. 
 ```
 """
 function fast_ksat_bp(g::AbstractFactorGraph, ψ::Vector{<:KSATClause},
@@ -55,9 +56,9 @@ Base.eltype(bp::BPKSAT) = eltype(eltype(eltype(bp.b)))
 function BeliefPropagation.reset!(bp::BPKSAT)
     (; u, h, b) = bp
     T = eltype(bp)
-    u .= (T(0.5), T(0.5))
-    h .= (T(0.5), T(0.5))
-    b .= (T(0.5), T(0.5))
+    u .= ((T(0.5), T(0.5)),)
+    h .= ((T(0.5), T(0.5)),)
+    b .= ((T(0.5), T(0.5)),)
     return nothing
 end
 function BeliefPropagation.randomize!(rng::AbstractRNG, bp::BPKSAT)
@@ -68,7 +69,7 @@ function BeliefPropagation.randomize!(rng::AbstractRNG, bp::BPKSAT)
         u[ia] = (ru, 1-ru)
         h[ia] = (rh, 1-rh)
     end
-    b .= (T(0.5), T(0.5))
+    b .= ((T(0.5), T(0.5)),)
     return nothing
 end
 
diff --git a/test/Models/ksat.jl b/test/Models/ksat.jl
index f5d2de0..a77bf22 100644
--- a/test/Models/ksat.jl
+++ b/test/Models/ksat.jl
@@ -39,6 +39,8 @@ end
     g = rand_regular_factor_graph(rng, n, m, k)
     ψ = [KSATClause(bitrand(rng, degree(g, factor(a)))) for a in factors(g)]
     bp = fast_ksat_bp(g, ψ)
+    reset!(bp)
+    randomize!(bp)
     iterate!(bp; maxiter=50, tol=1e-10)
     b = beliefs(bp)
     fb = factor_beliefs(bp)