pith. sign in

arxiv: 2507.07763 · v2 · submitted 2025-07-10 · ❄️ cond-mat.dis-nn

Improving deep neural network performance through sampling

Lakshmi A. Ghantasala , Ming-Che Li , Risi Jaiswal , Behtash Behin-Aein , Joseph Makin , Shreyas Sen , Supriyo Datta This is my paper

Pith reviewed 2026-05-19 05:42 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn
keywords deep neural networksprobabilistic samplingp-bitsenergy efficiencyaccuracy improvementgenerative AIBoltzmann machinesenergy tradeoffs
0
0 comments X

The pith

Multiple samples from probabilistic networks can deliver superior accuracy in deep neural networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper asks whether energy-efficient sampling using probabilistic neurons, already shown in Boltzmann machines, can be brought to deep neural networks that currently rely on deterministic multi-bit neurons. It first establishes that repeated sampling from probabilistic networks can produce higher accuracy than a single deterministic pass. It then supplies a simple expression to compare the energy cost of adding more samples against the cost of adding more bits to one deterministic sample, and demonstrates the expression on several algorithms and architectures. A reader would care because generative AI energy use is rising rapidly and this work offers a concrete way to decide when probabilistic hardware might be the lower-energy route to better performance.

Core claim

It is feasible to obtain superior accuracy through the use of multiple samples generated by probabilistic networks. This possibility raises the question of which option is energetically preferable for improving accuracy: generating more samples, or adding more bits to a single deterministic sample. The authors provide a simple expression that can be used to estimate these energy tradeoffs and illustrate it with results for different algorithms and architectures.

What carries the argument

A simple closed-form expression that equates the accuracy gain from additional probabilistic samples to the accuracy gain from additional bits in a deterministic neuron and solves for the energy crossover point.

If this is right

  • Accuracy in feedforward DNNs can be raised by drawing multiple low-precision probabilistic samples instead of widening a single deterministic sample.
  • Hardware designers can use the given expression to decide whether to allocate resources to faster sampling or to higher bit precision.
  • The same sampling approach shown for Boltzmann machines can be carried over to modern generative models without changing the core network topology.
  • Energy accounting for AI inference can now include sample count as a tunable parameter alongside bit width.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the expression holds on real p-bit hardware, chip architects may shift some resources from wider multipliers toward faster random-number generation and sampling circuitry.
  • Training procedures may need to be modified so that the network learns to produce useful diversity across its probabilistic samples rather than converging to a single high-confidence output.
  • The tradeoff analysis could be repeated for other model families such as transformers or graph networks to see whether the same sample-versus-bit crossover appears.

Load-bearing premise

The accuracy gains observed with probabilistic sampling and the energy costs of p-bit hardware can be compared directly via a simple closed-form expression without hidden implementation overheads or training differences.

What would settle it

A side-by-side measurement on the same task and hardware that records both final accuracy and total energy for (a) one deterministic network with increasing bit width and (b) a probabilistic network with increasing number of independent samples, then checks whether the measured crossover matches the paper's closed-form prediction.

Figures

Figures reproduced from arXiv: 2507.07763 by Behtash Behin-Aein, Joseph Makin, Lakshmi A. Ghantasala, Ming-Che Li, Risi Jaiswal, Shreyas Sen, Supriyo Datta.

Figure 1
Figure 1. Figure 1: The digital ASIC for Boltzmann machine and QUBO problems from [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Both p-bit and q-bit networks with N units generate samples from a probability distribution with 2N possibilities. repeated T times resulting in N × T applications of the same elementary operation. Energy per elementary operation: We can write the total energy E needed to implement a particular algorithm in terms of the energy ϵp per probabilistic elementary operation which can be written as (see Fig.3b): … view at source ↗
Figure 4
Figure 4. Figure 4: Energy cost of component operations of building block for QMC from [PITH_FULL_IMAGE:figures/full_fig_p002_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Image generation with a standard DNN network compared to p-bit [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Quantitative comparison of generated images in Fig.5 using FID [PITH_FULL_IMAGE:figures/full_fig_p003_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Energy of component operations of building block for DNN p-bit [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
read the original abstract

Energy efficient sampling with probabilistic neurons or p-bits has been demonstrated in the context of Boltzmann machines and it is natural to ask if these approaches can be extended to the field of generative AI where energy costs have become prohibitively large. However, this very active field is dominated by feedforward deep neural networks (DNNs) which primarily use multi-bit deterministic neurons with no role for sampling. In this paper we first show that it is feasible to obtain superior accuracy through the use of multiple samples generated by probabilistic networks. This possibility raises the question of which option is energetically preferable for improving accuracy: generating more samples, or adding more bits to a single deterministic sample. We provide a simple expression that can be used to estimate these energy tradeoffs and illustrate it with results for different algorithms and architectures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes extending probabilistic sampling with p-bits (previously shown in Boltzmann machines) to feedforward deep neural networks for generative AI. It asserts that multiple samples from probabilistic networks can deliver superior accuracy relative to deterministic multi-bit neurons, then introduces a simple closed-form expression to compare the energy cost of generating additional samples versus increasing bit precision in a single deterministic sample; the expression is illustrated with results across algorithms and architectures.

Significance. If the quantitative results and the energy expression hold under matched training budgets, the work could provide a useful framework for energy-accuracy tradeoffs in AI hardware, highlighting a potential advantage of probabilistic p-bit implementations over conventional precision scaling.

major comments (2)
  1. [Abstract] Abstract: the central feasibility claim ('it is feasible to obtain superior accuracy through the use of multiple samples generated by probabilistic networks') is stated without any numerical accuracy deltas, error bars, baseline comparisons, or dataset details; the claim is therefore load-bearing yet unsupported in the given text.
  2. [Energy tradeoff expression] Energy tradeoff expression: the simple expression is presented as directly usable for ranking 'more samples' versus 'more bits,' but the manuscript does not indicate whether the underlying accuracy gains were obtained under matched training epochs or whether p-bit sampling incurs unmodeled control/communication overhead; if either is true the ranking is no longer reliable.
minor comments (2)
  1. Add explicit statements of the training protocol (epochs, optimizer, loss) used for the probabilistic networks so that readers can judge whether the accuracy gains are fairly compared to deterministic baselines.
  2. Clarify the exact functional form of the energy expression (including any normalization or fitted constants) and state the hardware assumptions (e.g., energy per p-bit sample versus energy per additional bit).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. Below we respond point by point to the major comments and indicate the planned revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central feasibility claim ('it is feasible to obtain superior accuracy through the use of multiple samples generated by probabilistic networks') is stated without any numerical accuracy deltas, error bars, baseline comparisons, or dataset details; the claim is therefore load-bearing yet unsupported in the given text.

    Authors: We agree that the abstract would be strengthened by the inclusion of quantitative support for the central claim. In the revised manuscript we will incorporate specific accuracy improvements, error bars, baseline comparisons, and dataset details into the abstract while preserving its brevity. revision: yes

  2. Referee: [Energy tradeoff expression] Energy tradeoff expression: the simple expression is presented as directly usable for ranking 'more samples' versus 'more bits,' but the manuscript does not indicate whether the underlying accuracy gains were obtained under matched training epochs or whether p-bit sampling incurs unmodeled control/communication overhead; if either is true the ranking is no longer reliable.

    Authors: The reported accuracy gains are obtained from the same trained networks, with the only difference being the inference procedure (multiple probabilistic samples versus a single higher-precision deterministic sample); training epochs and conditions are therefore matched by construction. We will add an explicit statement clarifying this point. The energy expression focuses on neuron-level computational cost and does not include control or communication overhead for sampling; we will revise the text to note this limitation explicitly and describe the expression as providing a baseline tradeoff estimate under the assumption that such overheads are either comparable or accounted for separately in a full hardware implementation. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper claims superior accuracy from multiple probabilistic samples and introduces a simple closed-form energy tradeoff expression illustrated across algorithms and architectures. No quoted equations, self-citations, or steps in the provided abstract or description reduce a prediction to a fitted input by construction, import uniqueness from prior author work, or smuggle an ansatz via citation. The central comparison of sampling versus bit-precision appears as an independent estimation tool rather than a self-referential loop, making the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; therefore the ledger is necessarily incomplete and limited to assumptions visible in the summary text.

axioms (1)
  • domain assumption Probabilistic p-bit networks can be run repeatedly to produce independent samples whose combination improves accuracy over a single deterministic neuron.
    This premise is required to extend the Boltzmann-machine results to feedforward DNNs and is stated without further justification in the abstract.

pith-pipeline@v0.9.0 · 5686 in / 992 out tokens · 62582 ms · 2026-05-19T05:42:38.713075+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

6 extracted references · 6 canonical work pages

  1. [1]

    M.-C. Li, A. Ghosh, R. Jaiswal, L. A. Ghantasala, B. Behin-Aein, S. Sen, and S. Datta, ``12.2 p- Circuits : Neither Digital Nor Analog ,'' in 2025 IEEE International Solid - State Circuits Conference ( ISSCC ) , vol. 68, Feb. 2025, pp. 1--3, iSSN: 2376-8606. [Online]. Available: https://ieeexplore.ieee.org/abstract/document/10904553

    work page arXiv 2025

  2. [2]

    Chowdhury, K

    S. Chowdhury, K. Y. Camsari, and S. Datta, `` en Accelerated quantum Monte Carlo with probabilistic computers ,'' en Communications Physics , vol. 6, no. 1, pp. 1--9, Apr. 2023, 1 citations (Semantic Scholar/DOI) [2023-06-05] Number: 1 Publisher: Nature Publishing Group. [Online]. Available: https://www.nature.com/articles/s42005-023-01202-3

    work page 2023

  3. [3]

    Raiko, M

    T. Raiko, M. Berglund, G. Alain, and L. Dinh, `` Techniques for learning binary stochastic feedforward neural networks ,'' 3rd International Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings, pp. 1--10, 2015

    work page 2015

  4. [4]

    O'Connor, N

    M. O'Connor, N. Chatterjee, D. Lee, J. Wilson, A. Agrawal, S. W. Keckler, and W. J. Dally, `` en Fine-grained DRAM : energy-efficient DRAM for extreme bandwidth systems ,'' in en Proceedings of the 50th Annual IEEE / ACM International Symposium on Microarchitecture . 1em plus 0.5em minus 0.4em Cambridge Massachusetts: ACM, Oct. 2017, pp. 41--54. [Online]....

    work page doi:10.1145/3123939.3124545 2017

  5. [5]

    Letourneau and J

    M. Letourneau and J. W. Sharp, AMS-StyleGuide-online.pdf, American Mathematical Society, Providence, RI, USA, [Online]. Available: http://www.ams.org/arc/styleguide/index.html

    work page

  6. [6]

    11em plus .33em minus .07em 4000 4000 100 4000 4000 500 `\.=1000 = #1 \@IEEEnotcompsoconly \@IEEEcompsoconly #1 * [1] 0pt [0pt][0pt] #1 * [1] 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEcompsocnotconfonly \@IEEEauthorblockAstyle \@IEEEcompsocnotconfonly \@IEEEcompsocconfonly \@IEEEauthordefaulttextstyle \@IEEEcompsocnotconfonly \@IEEEauthor...

    work page