google · edwjchen · May 21, 2026
diff --git a/lib/Analysis/ILPBootstrapPlacementAnalysis/ILPBootstrapPlacementAnalysis.cpp b/lib/Analysis/ILPBootstrapPlacementAnalysis/ILPBootstrapPlacementAnalysis.cpp
diff --git a/lib/Analysis/ILPBootstrapPlacementAnalysis/ILPBootstrapPlacementAnalysis.h b/lib/Analysis/ILPBootstrapPlacementAnalysis/ILPBootstrapPlacementAnalysis.h
@@ -16,9 +16,31 @@ namespace mlir {
 namespace heir {
 class ILPBootstrapPlacementAnalysis {
  public:
+  struct OperandLevelReduction {
+    Operation* op;
+    unsigned operandNumber;
+    int levelToDrop;
+  };
+
+  struct OutputLevelReduction {
+    Value value;
+    int levelToDrop;
+  };
+
   ILPBootstrapPlacementAnalysis(Operation* op, DataFlowSolver* solver,
-                                int bootstrapWaterline)
-      : opToRunOn(op), solver(solver), bootstrapWaterline(bootstrapWaterline) {}
+                                int bootstrapWaterline, int scaleWaterline,
+                                int scaleFactorBits,
+                                int bootstrapLevelLowerBound, int bootstrapCost,
+                                int rescaleCost, bool useOrbitCompression)
+      : opToRunOn(op),
+        solver(solver),
+        bootstrapWaterline(bootstrapWaterline),
+        scaleWaterline(scaleWaterline),
+        scaleFactorBits(scaleFactorBits),
+        bootstrapLevelLowerBound(bootstrapLevelLowerBound),
+        bootstrapCost(bootstrapCost),
+        rescaleCost(rescaleCost),
+        useOrbitCompression(useOrbitCompression) {}
   ~ILPBootstrapPlacementAnalysis() = default;
 
   LogicalResult solve();
@@ -29,6 +51,17 @@ class ILPBootstrapPlacementAnalysis {
   // relinearize insertion.
   llvm::SmallVector<Value, 32> getValuesToBootstrap() const;
 
+  // Return per-use level reductions chosen by the ILP.
+  llvm::SmallVector<OperandLevelReduction, 32> getOperandLevelReductions()
+      const {
+    return operandLevelReductions;
+  }
+
+  // Return per-result level reductions chosen by the ILP.
+  llvm::SmallVector<OutputLevelReduction, 32> getOutputLevelReductions() const {
+    return outputLevelReductions;
+  }
+
   // Return the level at the given SSA value, as determined by the
   // solution to the optimization problem. When the input value is the result
   // of an op, and the model solution suggests a bootstrap should be
@@ -47,9 +80,17 @@ class ILPBootstrapPlacementAnalysis {
   Operation* opToRunOn;
   DataFlowSolver* solver;
   int bootstrapWaterline;
+  int scaleWaterline;
+  int scaleFactorBits;
+  int bootstrapLevelLowerBound;
+  int bootstrapCost;
+  int rescaleCost;
+  bool useOrbitCompression;
   llvm::DenseMap<Operation*, bool> solution;
   llvm::DenseMap<Value, int> solutionLevelBeforeBootstrap;
   llvm::DenseMap<Value, int> solutionLevelAfterBootstrap;
+  llvm::SmallVector<OperandLevelReduction, 32> operandLevelReductions;
+  llvm::SmallVector<OutputLevelReduction, 32> outputLevelReductions;
 };
 }  // namespace heir
 }  // namespace mlir

diff --git a/lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.cpp b/lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.cpp
@@ -1,12 +1,19 @@
 #include "lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.h"
 
+#include <cmath>
+#include <optional>
+#include <string>
+#include <utility>
+
 #include "lib/Analysis/ILPBootstrapPlacementAnalysis/ILPBootstrapPlacementAnalysis.h"
 #include "lib/Analysis/SecretnessAnalysis/SecretnessAnalysis.h"
 #include "lib/Dialect/Mgmt/IR/MgmtOps.h"
 #include "lib/Dialect/Mgmt/Transforms/AnnotateMgmt.h"
 #include "lib/Dialect/Secret/IR/SecretOps.h"
 #include "lib/Transforms/SecretInsertMgmt/Pipeline.h"
 #include "llvm/include/llvm/Support/Debug.h"               // from @llvm-project
+#include "llvm/include/llvm/Support/JSON.h"                // from @llvm-project
+#include "llvm/include/llvm/Support/MemoryBuffer.h"        // from @llvm-project
 #include "mlir/include/mlir/Analysis/DataFlow/Utils.h"     // from @llvm-project
 #include "mlir/include/mlir/Analysis/DataFlowFramework.h"  // from @llvm-project
 #include "mlir/include/mlir/IR/Builders.h"                 // from @llvm-project
@@ -26,20 +33,90 @@ namespace heir {
 #define GEN_PASS_DEF_ILPBOOTSTRAPPLACEMENT
 #include "lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.h.inc"
 
+struct OrbitCostModel {
+  int bootstrapCost;
+  int rescaleCost;
+};
+
+static std::optional<int> averagePositiveLatency(const llvm::json::Object& root,
+                                                 llvm::StringRef opName) {
+  const llvm::json::Object* latencyTable = root.getObject("latencyTable");
+  if (!latencyTable) return std::nullopt;
+
+  const llvm::json::Array* latencies = latencyTable->getArray(opName);
+  if (!latencies) return std::nullopt;
+
+  double sum = 0;
+  int count = 0;
+  for (const llvm::json::Value& latencyValue : *latencies) {
+    std::optional<double> latency = latencyValue.getAsNumber();
+    if (!latency || *latency <= 0) continue;
+    sum += *latency;
+    ++count;
+  }
+  if (count == 0) return std::nullopt;
+  return static_cast<int>(std::llround(sum / count));
+}
+
+static FailureOr<OrbitCostModel> loadOrbitCostModel(llvm::StringRef path) {
+  auto bufferOrError = llvm::MemoryBuffer::getFile(path);
+  if (!bufferOrError) return failure();
+
+  llvm::Expected<llvm::json::Value> parsed =
+      llvm::json::parse((*bufferOrError)->getBuffer());
+  if (!parsed) {
+    llvm::consumeError(parsed.takeError());
+    return failure();
+  }
+
+  const llvm::json::Object* root = parsed->getAsObject();
+  if (!root) return failure();
+
+  std::optional<int> parsedBootstrapCost =
+      averagePositiveLatency(*root, "earth.bootstrap_single");
+  std::optional<int> parsedRescaleCost =
+      averagePositiveLatency(*root, "earth.rescale_single");
+  if (!parsedBootstrapCost || !parsedRescaleCost) return failure();
+
+  return OrbitCostModel{*parsedBootstrapCost, *parsedRescaleCost};
+}
+
 struct ILPBootstrapPlacement
     : impl::ILPBootstrapPlacementBase<ILPBootstrapPlacement> {
   using ILPBootstrapPlacementBase::ILPBootstrapPlacementBase;
 
   LogicalResult processSecretGenericOp(
       secret::GenericOp genericOp, DataFlowSolver* solver,
-      SmallVector<Value, 32>* valuesToBootstrap) {
+      SmallVector<Value, 32>* valuesToBootstrap,
+      SmallVector<ILPBootstrapPlacementAnalysis::OutputLevelReduction, 32>*
+          outputLevelReductions,
+      SmallVector<ILPBootstrapPlacementAnalysis::OperandLevelReduction, 32>*
+          operandLevelReductions) {
     genericOp->walk([&](mgmt::BootstrapOp op) {
       op.getResult().replaceAllUsesWith(op.getOperand());
       op.erase();
     });
 
-    ILPBootstrapPlacementAnalysis analysis(genericOp, solver,
-                                           bootstrapWaterline);
+    int effectiveBootstrapCost = bootstrapCost;
+    int effectiveRescaleCost = rescaleCost;
+    if (!orbitCostModel.empty()) {
+      FailureOr<OrbitCostModel> loadedCostModel =
+          loadOrbitCostModel(orbitCostModel);
+      if (failed(loadedCostModel)) {
+        llvm::errs() << "failed to load Orbit cost model from `"
+                     << orbitCostModel << "`\n";
+        genericOp->emitError() << "failed to load Orbit cost model from `"
+                               << orbitCostModel << "`";
+        return failure();
+      }
+      effectiveBootstrapCost = loadedCostModel->bootstrapCost;
+      effectiveRescaleCost = loadedCostModel->rescaleCost;
+    }
+
+    ILPBootstrapPlacementAnalysis analysis(
+        genericOp, solver, bootstrapWaterline, scaleWaterline, scaleFactorBits,
+        bootstrapLevelLowerBound, effectiveBootstrapCost, effectiveRescaleCost,
+        useOrbitCompression);
     if (failed(analysis.solve())) {
       genericOp->emitError(
           "Failed to solve the bootstrap placement optimization problem");
@@ -48,26 +125,69 @@ struct ILPBootstrapPlacement
     LLVM_DEBUG(analysis.printSolution(llvm::dbgs()));
     for (Value v : analysis.getValuesToBootstrap())
       valuesToBootstrap->push_back(v);
+    for (auto reduction : analysis.getOutputLevelReductions())
+      outputLevelReductions->push_back(reduction);
+    for (auto reduction : analysis.getOperandLevelReductions())
+      operandLevelReductions->push_back(reduction);
     return success();
   }
 
+  std::pair<Value, Operation*> followRelinearizeModReduceChain(Value value) {
+    Value chainValue = value;
+    Operation* chainEnd = value.getDefiningOp();
+    while (chainValue.hasOneUse()) {
+      Operation* user = *chainValue.getUsers().begin();
+      if (isa<mgmt::RelinearizeOp>(user) || isa<mgmt::ModReduceOp>(user)) {
+        chainValue = user->getResult(0);
+        chainEnd = user;
+        continue;
+      }
+      break;
+    }
+    return {chainValue, chainEnd};
+  }
+
+  void insertOutputLevelReductions(
+      ArrayRef<ILPBootstrapPlacementAnalysis::OutputLevelReduction>
+          outputLevelReductions) {
+    OpBuilder b(&getContext());
+    for (auto reduction : outputLevelReductions) {
+      auto [toReduce, insertAfter] =
+          followRelinearizeModReduceChain(reduction.value);
+      if (!insertAfter) continue;
+
+      b.setInsertionPointAfter(insertAfter);
+      auto levelReduceOp = mgmt::LevelReduceOp::create(
+          b, insertAfter->getLoc(), toReduce,
+          b.getI64IntegerAttr(reduction.levelToDrop));
+      toReduce.replaceAllUsesExcept(levelReduceOp.getResult(), {levelReduceOp});
+    }
+  }
+
+  void insertOperandLevelReductions(
+      ArrayRef<ILPBootstrapPlacementAnalysis::OperandLevelReduction>
+          operandLevelReductions) {
+    OpBuilder b(&getContext());
+    for (auto reduction : operandLevelReductions) {
+      Operation* op = reduction.op;
+      if (!op || reduction.operandNumber >= op->getNumOperands()) continue;
+
+      Value operand = op->getOperand(reduction.operandNumber);
+      b.setInsertionPoint(op);
+      auto levelReduceOp = mgmt::LevelReduceOp::create(
+          b, op->getLoc(), operand, b.getI64IntegerAttr(reduction.levelToDrop));
+      op->setOperand(reduction.operandNumber, levelReduceOp.getResult());
+    }
+  }
+
   void insertBootstrapsForValues(ArrayRef<Value> valuesToBootstrap) {
     OpBuilder b(&getContext());
     for (Value v : valuesToBootstrap) {
       // After modreduce/relinearize we have mul -> relinearize -> modreduce.
       // Follow the chain so we bootstrap the modreduce result (correct level
       // refresh) and insert after it.
-      Value toBootstrap = v;
-      Operation* insertAfter = v.getDefiningOp();
-      while (toBootstrap.hasOneUse()) {
-        Operation* user = *toBootstrap.getUsers().begin();
-        if (isa<mgmt::RelinearizeOp>(user) || isa<mgmt::ModReduceOp>(user)) {
-          toBootstrap = user->getResult(0);
-          insertAfter = user;
-        } else {
-          break;
-        }
-      }
+      auto [toBootstrap, insertAfter] = followRelinearizeModReduceChain(v);
+      if (!insertAfter) continue;
       b.setInsertionPointAfter(insertAfter);
       auto bootstrapOp =
           mgmt::BootstrapOp::create(b, insertAfter->getLoc(), toBootstrap);
@@ -89,9 +209,14 @@ struct ILPBootstrapPlacement
     }
 
     SmallVector<Value, 32> valuesToBootstrap;
+    SmallVector<ILPBootstrapPlacementAnalysis::OutputLevelReduction, 32>
+        outputLevelReductions;
+    SmallVector<ILPBootstrapPlacementAnalysis::OperandLevelReduction, 32>
+        operandLevelReductions;
     auto result = module->walk([&](secret::GenericOp genericOp) {
-      if (failed(
-              processSecretGenericOp(genericOp, &solver, &valuesToBootstrap)))
+      if (failed(processSecretGenericOp(genericOp, &solver, &valuesToBootstrap,
+                                        &outputLevelReductions,
+                                        &operandLevelReductions)))
         return WalkResult::interrupt();
       return WalkResult::advance();
     });
@@ -100,6 +225,10 @@ struct ILPBootstrapPlacement
       return;
     }
 
+    // Insert per-use level reductions before consumers, matching Orbit-style
+    // edge rescale placement.
+    insertOperandLevelReductions(operandLevelReductions);
+
     // Modreduce after every mul.
     insertModReduceBeforeOrAfterMult(getOperation(), /*afterMul=*/true,
                                      /*beforeMulIncludeFirstMul=*/false,
@@ -108,6 +237,10 @@ struct ILPBootstrapPlacement
     // Relinearize after every mul.
     insertRelinearizeAfterMult(getOperation(), /*includeFloats=*/true);
 
+    // Insert shared producer-output level reductions after mul management and
+    // before bootstraps, matching Orbit's node rescale decisions.
+    insertOutputLevelReductions(outputLevelReductions);
+
     // Insert bootstraps at the Values the ILP chose. Values remain valid.
     insertBootstrapsForValues(valuesToBootstrap);
 

diff --git a/lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.td b/lib/Transforms/ILPBootstrapPlacement/ILPBootstrapPlacement.td
@@ -6,19 +6,23 @@ include "mlir/Pass/PassBase.td"
 def ILPBootstrapPlacement : Pass <"ilp-bootstrap-placement"> {
     let summary = "Optimize placement of bootstrap ops using ILP";
     let description = [{
-        This pass uses an integer linear program to determine the optimal level
-        of each term in the MLIR, and thus the placement of bootstrap and
-        modreduce operations.
+        This pass uses an integer linear program to determine feasible levels
+        and CKKS-style scales for each term in the MLIR, and thus the placement
+        of bootstrap and level-reduction operations.
 
         The pass runs on [ciphertext-semantic](https://heir.dev/docs/design/layout/#data-semantic-and-ciphertext-semantic-tensors)
         IR (secret.generic with arith ops operating on pre-packed tensors). It
         1) Inserts mgmt.modreduce after each level-consuming op (e.g. mul in
            CKKS, where level drops only at multiplications).
-        2) Inserts mgmt.bootstrap at the positions chosen by the ILP.
-        3) Inserts mgmt.relinearize after each mul. Resulting order is mul ->
+        2) Inserts per-use mgmt.level_reduce ops for edge rescale decisions
+           chosen by the ILP.
+        3) Inserts mgmt.bootstrap at the positions chosen by the ILP.
+        4) Inserts mgmt.relinearize after each mul. Resulting order is mul ->
            relinearize -> modreduce, with bootstrap after modreduce or after
            the op where the ILP chose.
 
+        The ILP formulation is inspired by [Orbit](https://eprint.iacr.org/2026/213.pdf).
+
         Note: The ILP formulation does not account for a freshly encrypted
         ciphertext starting at a higher level than the bootstrap waterline.
         This will be implemented as future work.
@@ -32,6 +36,41 @@ def ILPBootstrapPlacement : Pass <"ilp-bootstrap-placement"> {
            "int",
            /*default=*/"3",
            "Bootstrap waterline (max level). Levels are 0..bootstrap-waterline (inclusive); inputs start at bootstrap-waterline.">,
+    Option<"scaleWaterline",
+           "scale-waterline",
+           "int",
+           /*default=*/"40",
+           "Minimum CKKS scale budget used by the Orbit-inspired scale constraints.">,
+    Option<"scaleFactorBits",
+           "scale-factor-bits",
+           "int",
+           /*default=*/"51",
+           "Scale bits dropped by one rescale/modreduce in the Orbit-inspired scale constraints.">,
+    Option<"bootstrapLevelLowerBound",
+           "bootstrap-level-lower-bound",
+           "int",
+           /*default=*/"0",
+           "Minimum input level at which bootstrap is allowed in the Orbit-inspired scale constraints.">,
+    Option<"orbitCostModel",
+           "orbit-cost-model",
+           "std::string",
+           /*default=*/"""",
+           "Path to an Orbit JSON cost model. When provided, bootstrap-cost and rescale-cost are loaded from latencyTable.">,
+    Option<"bootstrapCost",
+           "bootstrap-cost",
+           "int",
+           /*default=*/"69320650",
+           "Cost of one bootstrap in the ILP objective. Default is the positive-latency average from Orbit's profiled 64k Lattigo base cost model.">,
+    Option<"rescaleCost",
+           "rescale-cost",
+           "int",
+           /*default=*/"40988",
+           "Cost of one level-reduction/rescale in the ILP objective. Default is the positive-latency average from Orbit's profiled 64k Lattigo base cost model.">,
+    Option<"useOrbitCompression",
+           "use-orbit-compression",
+           "bool",
+           /*default=*/"true",
+           "When true, add Orbit-inspired structural compression constraints so equivalent ops share ILP state and bootstrap decisions.">,
   ];
 }
 

diff --git a/tests/Transforms/ilp_bootstrap_placement/BUILD b/tests/Transforms/ilp_bootstrap_placement/BUILD
@@ -2,9 +2,20 @@ load("//bazel:lit.bzl", "glob_lit_tests")
 
 package(default_applicable_licenses = ["@heir//:license"])
 
+filegroup(
+    name = "orbit_cost_model",
+    srcs = [
+        "orbit_bad_cost_model.json",
+        "orbit_cost_model.json",
+    ],
+)
+
 glob_lit_tests(
     name = "all_tests",
-    data = ["@heir//tests:test_utilities"],
+    data = [
+        ":orbit_cost_model",
+        "@heir//tests:test_utilities",
+    ],
     driver = "@heir//tests:run_lit.sh",
     test_file_exts = ["mlir"],
 )