EFA-RFC-002: RELAX/1

A relaxation dialect and cross-paradigm exchange for energy-native computing

Status	Draft v0.1 — for public comment
Date	2026-08-02
License	CC0 1.0 — adopt, fork, or absorb without permission
Companion	EFA-RFC-001 (OER/1 receipts + DRIFT/1 benchmark) — every executing op in this dialect emits an OER receipt stub
Intended audience	MLIR community · NIR maintainers · Intel Lava · Extropic thrml · Klere flowg/Joule · Ferric · UXL Foundation · vendors of settling, sampling, annealing, crossbar, and neuromorphic hardware · GPU-simulation implementers

RFC 2119 keywords apply.

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1. Motivation

Every portability layer in production — Triton, StableHLO/IREE, SYCL, Mojo/MAX, CANN, MUSA, Vulkan compute, ggml — shares one assumption: the primitive of computation is a kernel applied to tensors on a clock. A thermodynamic sampling unit, an Ising annealer, a memristor crossbar doing in-situ writes, or a ternary settling fabric has no representation in any of them. You cannot lower a matmul onto a device whose native operation is relax until stable. The consequence is structural: the entire make-hardware-fungible movement commoditizes GPU-class hardware while leaving the energy-native paradigm without a compiler target, so every new substrate rebuilds its stack from zero — the precise failure mode that killed the first neuromorphic wave.

One shipping counterexample proves the fix: NIR, the Neuromorphic Intermediate Representation, runs one spiking model across Loihi 2, SpiNNaker2, Xylo, Speck, and simulators — because its primitives match the physics (stateful neurons and spikes, not kernels). RELAX/1 is the analogous object for relaxation and sampling computation: a small op set whose primitives are settle, sample, anneal, local write, verify, certify — declarative about what equilibrium or distribution is sought, silent about how the substrate reaches it. It is specified as (a) an MLIR dialect (relax) so it lands inside the compiler commons the industry already runs, and (b) a JSON graph-exchange form (mirroring NIR) for runtimes without MLIR.

Design north star: a model expressed once in RELAX/1 runs today on a GPU in simulation, tomorrow on any conforming physical substrate, and produces an OER/1 receipt either way — with the provenance axes telling you honestly which one you got.

2. Design principles

1. Physics-neutral semantics. Ops define fixed points, distributions, and update rules mathematically; substrates satisfy them by any means (gradient descent, analog dynamics, thermal noise, optical interference).
2. Mandatory simulation lowering. Every op MUST have a reference GPU/CPU lowering (via StableHLO/Triton). This is the adoption strategy — no exotic hardware required to use the dialect — and the correctness oracle for physical targets. Simulated executions are auto-tagged provenance: simulated × emulation.
3. Energy-typed execution. Every executing op takes a budget (joules, steps, seconds, or a temperature schedule) and MUST either satisfy it or refuse — refusal is a first-class, receipted outcome (semantics after Klere’s Joule/flowg).
4. Receipts native. Executing ops emit OER/1 receipt stubs; the runtime completes and signs them. Compilation without receipts is legal; execution without receipts is nonconforming above RELAX-C1.
5. Stochasticity in the type system. Sampling ops are effectful and seeded where the substrate permits; native-thermal sources declare non-reproducibility explicitly rather than faking seeds.
6. Small on purpose. Ten core ops. Anything expressible as composition stays out of the core.

3. Core abstractions

• Energy (!relax.energy<form, state_type, N>): a scalar function over states. Forms: ising (pairwise couplings + biases), hopfield (dense/ternary associative), factor_graph (sparse local factors), ebm_net (learned neural E_θ, carried as a StableHLO/ONNX sub-module), composite (sum/min of energies).
• State (!relax.state<domain, N>): binary, ternary, continuous<fN>, spiking (bridged to/from NIR).
• Budget (!relax.budget<joules|steps|seconds|schedule>): compile-time-checked where static; runtime-metered otherwise.
• FastWeights (!relax.fastweights<N, M>): inference-time-mutable coupling store — the Hebbian target; on crossbar substrates this is physical memory.
• Certificate, Receipt: as defined in RFC-001.

4. Op set (v0.1 core)

Op	Signature (informal)	Semantics
relax.define_energy	attrs(form, params/URI) → energy	Declare/bind an energy landscape
relax.encode / relax.decode	tensor ⇄ state	Move between tensor world and state world
relax.settle	(energy, state, budget, tol) → (state, receipt)	Reach a local fixed point: E non-increasing along the trajectory; stop at tol or budget; MAY refuse
relax.sample	(energy, n, temp, method, seed?) → (states, receipt)	Draw n samples ~ e^(−E/T); method ∈ gibbs | langevin | metropolis | native_thermal
relax.anneal	(energy, schedule, budget) → (state, receipt)	Settle under a declared temperature path; the op where the coupled-chain/annealing question is answered on hardware
relax.local_write	(fastweights, x, y?, rule, α, gate?) → fastweights′	Gradient-free write: rule ∈ hebbian(αxxᵀ) | delta | decay | surprise_gated; the native crossbar/settle×2 op
relax.nudge	(energy, target, β) → energy′	Clamp/bias toward a target (EqProp phase two)
relax.eqprop_grad	(x_free, x_nudged) → local Δcouplings	Learning signal from two relaxations
relax.verify	(energy, state, τ) → (bool, margin, receipt)	Energy-as-verifier: accept iff E(x) ≤ τ
relax.certify	(energy, region, type) → certificate	type ∈ energy_monotone | contraction_region; populates OER certificate
relax.compose	(E₁, E₂, mode) → energy	mode ∈ sum (conjunction) | min (disjunction) — zero-shot compositionality

Illustrative MLIR-style listing (drift-benchmark inner loop, RFC-001 task D-A):

%E   = relax.define_energy ising couplings(@W_world) : !relax.energy<ising, ternary, 4096>
%z   = relax.encode %obs : tensor<4096xf32> -> !relax.state<ternary, 4096>
// think: K-step settle under a joule budget — may refuse
%z*, %r1 = relax.settle %E, %z budget(#relax.budget<joules 2.0e-6>) tol(1.0e-4)
// plan: sample candidate futures, verify with the same energy
%cands, %r2 = relax.sample %E_goal, 64 temp(0.8) method(metropolis) seed(17)
%ok, %m, %r3 = relax.verify %E_goal, %best threshold(0.12)
// adapt on surprise: gradient-free write to fast weights (native crossbar op)
%Z1 = relax.local_write %Z, %z* rule(hebbian) alpha(0.02) gate(surprise > 0.7)
// receipts %r1..%r3 aggregate under RFC-001 §3.3 min-grade composition

5. Lowering targets (v0.1 matrix)

Substrate family	settle	sample	anneal	local_write	Notes
gpu_sim (reference, REQUIRED)	unrolled descent (Triton/StableHLO)	Gibbs/Langevin kernels	scheduled Langevin	tensor update	Correctness oracle; auto-tag simulated×emulation
fpga_settling (Klere-class ternary fabric)	native	via settle+noise inject	clocked schedule	settle×2 / direct SRAM write	First physical conformance target; receipts via frequency-sweep (OER-L1)
tsu_pbit (Extropic-class; thrml bridge)	zero-T limit	native_thermal	native schedule control	host-side	DTM = chained relax.sample; seedless native sampling declared
ising_annealer (SBM / DA / CIM / D-Wave)	zero-T anneal	repeated anneal reads	native	n/a (couplings reload)	Latency-record substrate; QUBO adapter
cim_crossbar (memristor/PCM)	analog matvec iteration	+ noise	scheduled	in-situ outer product — native	The write IS the physics; endurance budget declared
neuromorphic_snn (via NIR bridge)	attractor nets	stochastic neurons	intrinsic	on-chip plasticity rules	state<spiking> round-trips through NIR
photonic	iterative optical loop (exp.)	optical noise (exp.)	exp.	n/a	Marked experimental in v0.1

A conforming physical backend implements ≥1 column natively and MAY delegate the rest to gpu_sim with correct provenance tags — mixed executions compose under RFC-001 min-grade rules.

6. Exchange form and interop

• JSON graph (NIR-mirroring): nodes = ops above; edges = states/energies; energies-by-reference (URI + hash) so learned E_θ travels as ONNX/StableHLO payload.
• ONNX: custom domain org.efa.relax for the ten ops (opset 1).
• NIR bridge: state<spiking> encode/decode is specified against NIR node types; a spiking policy can be verified by a relax.verify energy and vice versa.
• thrml / Lava adapters: thin mappings published as reference code; neither project need change to be targeted.
• Receipts: every runtime boundary above is an OER emission point (RFC-001 §5).

7. Conformance

Level	Meaning
RELAX-C0	Dialect-valid programs run on gpu_sim reference lowering
RELAX-C1	≥1 op lowered to a physical substrate, oracle-checked against gpu_sim
RELAX-C2	C1 + OER-L1 receipts emitted on every executing op
RELAX-C3	C2 + relax.certify implemented for actuation-class workloads; DRIFT/1-eligible

8. Anti-goals

Not a kernel language (Triton/Mojo remain the right tools inside ebm_net). Not a spiking format (NIR owns that; we bridge). Not a quantum IR (annealers enter only through their classical interface). Not a scheduler — placement/routing across substrates is the runtime’s job (flowg-class systems), for which this dialect is the instruction set.

9. Reference-implementation plan before v1.0

JSON-Schema + MLIR dialect definition (TableGen); gpu_sim lowerings for all ten ops; two physical backends on dissimilar substrates (one settling fabric, one sampler); the RFC-001 D-A task expressed end-to-end with receipts; conformance test suite with oracle tolerances.

Acknowledgments

Primitive set distilled from: EBT descent-as-thinking (Gladstone/Du); EqProp (Scellier–Bengio); fast-weight/delta-rule lineage (Schmidhuber; Ba; Yang; Behrouz); EFA’s unified readings (settle/verify/certify/write) and published negatives; Klere’s budget-refusal and receipt semantics; NIR’s proof that paradigm-matched primitives portabilize; Extropic’s DTM as chained sampling. CC0 — the point is adoption, not attribution. Drafted with AI assistance (Claude, Anthropic) at the direction of the EFA program.