The pitch for event-driven compute has been stable for a decade. Sparse activity replaces dense multiply-accumulates with cheap accumulates, so energy falls with the firing rate, so a spiking substrate wins wherever power is the binding constraint. The pitch has been supported almost entirely by demonstrations: a model, a chip, a number, a comparison against a GPU baseline chosen by the same group that built the chip.
Four papers posted over the past two weeks do something different. Each replaces a demonstration with a bound. Taken separately they read as housekeeping. Taken together they mark the point at which non-von-Neumann compute stops being sold and starts being specified.
The firing floor
The sharpest of the four is Zeyu Wang’s Sparsity Ceiling, which asks how far activity can actually be pushed down before task quality breaks. The experimental design is the part worth copying: hold the architecture fixed, swap only the hidden unit between a continuous unit and a leaky-integrate-and-fire unit, and drive the network with a two-sided target-firing-rate probe that pushes activity down until accuracy gives way.
The answer is that there is no single answer, and the spread is large. Low-load feed-forward perception sparsifies to 5% firing at no accuracy cost. A recurrent language model cannot go below roughly 50% — the recurrent state has to stay active because the state is the memory. A spiking Transformer, on the same probe, sparsifies freely to 2% across three seeds.
That last result is what makes the paper more than a negative finding. If the floor were a property of sequence modelling, the spiking Transformer would hit it too. It does not. The floor is a property of recurrent compression specifically: a fixed-width state that must carry information forward through time cannot be quiet. Wang formalises this as an information-theoretic bound — the firing rate ρ is at least the inverse binary entropy of the ratio of stored bits to state width — and then confirms the three predictions that follow from it — the floor rises with memory load, falls with state width, and rises with task difficulty. That third prediction refutes a naive memory-only reading of the bound, which is the kind of check that separates a derived result from a fitted one.
Attention escapes the floor, but the escape is not free. It buys low firing by storing the full key-value cache, which converts a firing floor into a memory wall. On neuromorphic hardware, recurrence and attention pay on different axes, and neither pays nothing. A further layer-wise input floor caps op reduction whenever the input itself is dense, which isolates event-driven perception — sparse input, shallow load, no compressed state — as the regime where neuromorphic hardware wins outright.
The number that gets quoted versus the number that matters
The Sparsity Ceiling landed the same week as a good illustration of the problem it addresses. Xiubo Liang and colleagues’ SMM Transformer is a competent piece of work: a spiking multimodal Transformer built from a parallel LIF neuron with multistage learnable parameters, a spike-driven token-mixing module that replaces dense pairwise softmax attention with channel-wise spike co-activation, and a spiking mixture-of-experts for modality-aware fusion. It reports accuracy competitive with ANN baselines across visual and multimodal benchmarks, which is not trivial for a deep spiking stack.
It also reports that its token-mixing module reduces the estimated operator-level compute energy of the attention module by up to 97% under a standard MAC/AC arithmetic model. That is the number that will travel. The authors are explicit that whole-model profiling shows “more moderate but consistent” efficiency gains, and they deserve credit for saying so in the abstract rather than burying it in a table.
The gap between those two figures is the entire subject of this piece. A 97% reduction on one module under an arithmetic model is a statement about the module. The whole-model number is a statement about the system. The field has spent years quoting the first and shipping the second, and Wang’s bound explains structurally why the two diverge: the components that resist sparsification are exactly the ones that carry state, and every real model has some.
Analog arrays acquire error bars
The same shift is visible on the analog side, where Mirko Brazzini, Giulio Filippeschi, Alessandro Catania, Sebastiano Strangio and Giuseppe Iannaccone address retention loss in a single-poly floating-gate analog non-volatile memory array fabricated in standard 65 nm CMOS. Analog in-memory computing has a well-known failure mode: the stored weight drifts, so the accuracy measured at programming time is not the accuracy the deployed part delivers.
The contribution is a model of retention-loss statistics calibrated against measurements on real silicon, then propagated through system-level simulation of VGG-10 on CIFAR-10 and WideResNet-28-10 on CIFAR-100. With circuit-level compensation and batch-normalisation recalibration at the algorithmic level combined, baseline inference accuracy is recovered to within 2–4% at 60 days after programming.
Two to four percent at sixty days is not a headline. It is a specification. A procurement conversation can be had about a part that degrades by a bounded amount over a stated interval with a stated mitigation stack. It cannot be had about a part characterised only at t = 0.
Optics gets its approximation theory
Md Sadman Sakib Rahman, Che-Yung Shen and Aydogan Ozcan perform the analogous move for diffractive optical processors, and go further, because optics had been running on a universal-approximation argument with no attached cost model. Their framework shows that phase-encoded diffractive processors implement finite Fourier-feature expansions whose completeness follows from Fourier and Stone-Weierstrass arguments — expressivity is not in question — while physical realisability is governed by finite coefficient synthesis through optimised spatially varying coherent point-spread functions.
The useful output is the decomposition of the approximation error into separately attributable terms: Fourier truncation, PSF synthesis, input phase error, optical hardware, readout, and noise. Alongside it sit scaling relationships tying approximation complexity to optical degrees of freedom and space-bandwidth products, photon-budget and throughput limits imposed by photon statistics, and finite-class statistical learnability bounds for phase-quantised approximators. The paper also separates coherent cascadability and quadratic feature expansion through coherent mixing from the depth-separation results established for digital networks, which closes off a tempting but unsupported analogy.
An engineer can now ask which term dominates a given optical design and spend the budget there. That is a different activity from demonstrating that an optical stack can classify MNIST.
The exception that shows the pattern
Not everything this fortnight was a bound. Jonas Mensing, Wilfred van der Wiel and Andreas Heuer report on networks of metallic nanoparticles connected by molecular junctions, in which static control electrodes convert a passive network into a tunable nonlinear dynamical system. Their design principles are physical rather than architectural: operating near the system’s cutoff frequency balances nonlinear against linear response, SiO₂ thickness sets electrostatic screening and therefore memory, and structural disorder from heterogeneous junctions increases computational expressivity rather than degrading it.
That last point is the one to hold. In a digital substrate, device variation is a yield problem. Here it is the source of the expressivity that makes the network useful, and control voltages can independently manipulate specific signal amplitudes and phases on top of it. This is early-stage work at the demonstration end of the spectrum — precisely the stage the other three papers have graduated from — and it is included here because it shows what the graduation costs. Nanoparticle networks do not yet have a retention model, a photon budget, or a firing floor. In three years, if the substrate matters, someone will have to derive them.
What the bounds are for
The reflexive reading of these results is deflationary: spiking networks cannot sparsify as far as advertised, analog weights drift, optical processors are photon-limited. That reading misses the direction of travel.
A field that only produces demonstrations cannot be designed against. Every deployment decision is a bet on whether the demo’s regime resembles the deployment’s regime, and there is no way to check without rebuilding the demo. A field that produces bounds can be designed against directly. Wang’s result tells a system architect to put event-driven perception on neuromorphic silicon and leave the compressed recurrent state on a conventional part. Brazzini’s retention statistics tell an integrator how often the array must be reprogrammed for a given accuracy target. The Ozcan group’s error decomposition tells an optical designer which of six terms is currently the binding one.
The energy dividend is real and it is bounded, and the second half of that sentence is what makes the first half worth acting on.