Deploying high-accuracy neural networks on resource-constrained edge devices remains challenging, as existing approaches treat training, compression, and hardware synthesis as separate stages, leaving a gap between software-trained models and efficient end-to-end deployment with limited support for interpretability. We propose Bern2Edge, an end-to-end framework that uses knowledge distillation to convert a pretrained teacher feed-forward network into hardware-efficient representations via Bernstein polynomial activations. This representation enables two deployment paths: (i) a high-fidelity LUT-based realization that preserves model fidelity under compression, and (ii) a symbolic rule-based representation derived from Bernstein activation geometry, enabling interpretable inference with explicit input-space constraints. The resulting BNNs achieve up to 2.12 percentage-point (pp) accuracy improvement over ReLU under identical compression constraints. At the system level, Bern2Edge achieves up to 99.8% latency reduction and 95.2% BRAM reduction relative to a W8A8 quantized teacher on an AMD Xilinx KV260 FPGA, while maintaining accuracy within 0.5 pp, and further deploys on a low-power Spartan-7 XC7S15 FPGA. The rule-based path reduces DSP usage by up to 89.0% at a cost of 1.5 pp in total accuracy.
Figures & tables
Fig. 1 : Overview of Bern2Edge : A high-accuracy teacher model is distilled into a compressed BNN student via KD. The resulting representation is synthesized and deployed via either exact LUT-based realization or symbolic rule extraction.
Fig. 2 : Decision boundaries learned by a BNN (left) and a ReLU model (right) of equal capacity on the synthetic Two Moons dataset [ 24 ] . The BNN captures the curved structure of the data, while the ReLU model produces a simpler, predominantly linear boundary.
Fig. 3 : Per-neuron LUT behavior vs. table size on Covertype: test accuracy (top) and error rate (bottom) vs. LUT entries per neuron. Error% is the fraction of samples where LUT output differs from full-precision inference.
Fig. 4 : Bernstein activation curves with analytically derived regime breakpoints. Six representative neuron activations from a BNN ( h=64 ) trained on Adult [ 26 ] , with breakpoints from derivative roots and inflection points marked.
Fig. 5 : Activation-geometry-based rule formation. A selected regime in normalized activation space ( t ) maps through z -space to an affine constraint in input space, forming interpretable oblique regions.
Fig. 6 : Activation-geometry rule regions on the Two Moons dataset [ 24 ] . Rules align with the curved decision boundary via Bernstein-derived breakpoints, enabling compact partitioning.
Dataset
Arch.
Act.
Acc. (%)
CE Loss
Δ Acc / Δ CE
Latency
DSPs
BRAMs
LUTs
HIGGS-Small
{28,16,2}
ReLU
70.98 ± 0.20
0.553
+0.94 / −0.013
85
108
0
5397
Bern
71.92 ± 0.26
0.540
87
106
2
5682
{28,16,8,2}
ReLU
71.84 ± 0.24
0.540
+0.48 / −0.008
121
156
0
6852
Bern
72.32 ± 0.18
0.532
125
135
3
7294
{28,128,2}
ReLU
72.08 ± 0.27
0.524
+0.45 / −0.012
337
108
34
5114
Bern
72.53 ± 0.18
0.512
339
103
44
5410
TABLE I : Accuracy and synthesis metrics on AMD KV260 (5-fold CV). Latency in clock cycles. Δ Acc / Δ CE: BNN minus ReLU.
Fig. 7 : Test accuracy vs. KD weight α ( T=2 ) on HIGGS-Small for students with single layer h=16 (top) and h=128 (bottom). Dashed line: teacher baseline ( 72.32% ).
Latency
BRAMs
Bernstein
ReLU
Δ Acc
(cyc)
Acc (%)
(cyc, BRAM)
Acc (%)
(cyc, BRAM)
(pp)
≤200
≤30
76.50 ± 0.44
(189, 26)
74.93 ± 0.08
(188, 25)
+1.57
≤400
≤55
82.98 ± 0.16
(397, 52)
81.87 ± 0.37
(396, 49)
+1.11
≤1000
≤120
91.09 ± 0.27
(963, 105)
88.97 ± 0.82
(960, 113)
+2.12
≤2500
≤140
95.05 ± 0.05
(2481, 136)
93.53 ± 0.18
(2477, 137)
+1.52
≤7500
≤180
96.39 ± 0.02
(7433, 179)
95.62 ± 0.12
(7429, 169)
+0.77
TABLE II : Covertype accuracy under matched latency and BRAM budgets. Parentheses: actual synthesis values (cycles, BRAMs).
Fig. 8 : FPGA resource utilization on Adult ( h=128 ) for naive Bernstein evaluation and LUT-based inference across polynomial degrees n∈{3,5,7,9,11} .
Arch
BNN Acc. (%)
αsc
Rules
ℓ
Cov. (%)
Cov. Acc. (%)
Acc t (%)
{14,16,2}
84.33
0.5
37
1.76
78.2
86.8
82.6
0.1
45
1.67
91.5
84.5
81.7
{14,32,2}
84.42
0.5
45
2.04
84.9
87.2
83.2
0.1
53
2.02
94.0
85.3
82.1
{14,128,2}
84.63
0.5
61
1.64
89.5
85.9
82.8
0.1
85
1.75
95.8
85.3
82.0
TABLE III : Rule extraction on Adult across five BNN architectures. αconf : conflict penalty constant = 0.1. CART fallback. αsc : same-coverage penalty; ℓ : avg. conditions per rule; Cov.: coverage; Cov. Acc.: covered accuracy; Acc t : total accuracy.
Arch
Method
Acc (%)
Latency
DSP
BRAM
LUT
FF
{14,16,2}
LUT
84.33
77
77
2
4,329
5,582
Rules
82.59
183
30
5
2,997
2,290
{14,32,2}
LUT
84.42
119
109
4
6,019
8,333
Rules
83.16
215
30
8
3,009
2,218
{14,128,2}
LUT
84.63
376
301
28
15,609
22,865
Rules
82.76
279
30
8
3,002
2,217
TABLE IV : LUT-based BNNs vs. rule networks HW results on Adult (AMD KV260).
Type
Method
Rules
ℓ
Acc (%)
Fid (%)
Decompositional
DeepRED [ 19 ]
5143±9799
5.43
78.7
89.3
REM-D [ 35 ]
3617±6748
5.41
78.6
89.4
ECLAIRE [ 20 ]
396±75
3.82
84.6
89.4
Bern2Edge
no-KD ( αsc=0.1 )
46±4
1.84
84.2
91.8
no-KD ( αsc=0.5 )
24±3
1.81
82.9
94.3
KD ( αsc=0.1 )
44±4
1.86
84.4
91.8
TABLE V : Rule extraction on MAGIC Gamma Telescope. Baselines from Zarlenga et al. [ 20 ] (mean ± std, 5 folds); Decompositional: rule extraction from intermediate layers; ℓ : avg. conditions per rule; Fid: fidelity to baseline network.
Method
Acc (%)
Latency (cycles)
DSPs
BRAMs
URAMs
HIGGS-Small
Teacher (W8A8)
72.3
6,981
186
50
–
Bern2Edge (LUT)
72.3
125 ( ↓ 98.2%)
135 ( ↓ 27.4%)
3 ( ↓ 94.0%)
–
Covertype
Teacher (W8A8)
96.9
91,634
389
128
52
Bern2Edge (LUT)
96.4
7,433 ( ↓ 91.9%)
326 ( ↓ 16.2%)
149 ( ↑ 16.4%)
3 ( ↓ 94.2%)
TABLE VI : Post-synthesis accuracy and end-to-end hardware results for Bern2Edge across three datasets. Percentages indicate change relative to the W8A8 teacher baseline. Rule deployment path reported for Adult only.
Model
Config.
LUT
FF
DSP
BRAM
Lat.
Pwr
Acc
Acc fp
18K
(cyc)
(mW)
(%)
(%)
Rules
R50
1,086
844
16
6
340
62
83.02
—
R29
710
765
16
4
156
59
83.01
—
Bern. {14,h,2}
h=4
553
883
18
1
61
51
84.18
84.25
h=8
635
804
19
1
82
63
84.57
84.64
h=16
662
777
19
1
115
63
84.88
84.86
TABLE VII : Deployment on XC7S15. R50 and R29 denote the 50-rule and 29-rule symbolic classifiers, respectively. Acc is test accuracy; Acc fp the fp32 reference for BNNs.
αconf
αsc
Conf.
Cov. (%)
Cov. Acc. (%)
Acc t (%)
Rules
ℓ
0.1
0.1
308
94.01
85.26
82.10
53
2.02
1.0
0.1
156
92.60
84.67
82.39
50
2.06
0.1
0.3
136
87.15
86.72
83.16
53
2.06
1.0
0.3
111
86.99
86.77
83.16
52
2.04
0.1
0.5
121
84.86
87.18
83.16
45
2.04
1.0
0.5
106
84.42
87.18
83.39
46
2.09
TABLE VIII : Joint penalty sweep on Adult ( h=32 , BNN acc. 84.42 %). Conf.: conflicting samples; Cov.: coverage; Cov. Acc.: covered accuracy; Acc t : total accuracy; ℓ : avg. conditions per rule.
Fig. 9 : Coverage and covered accuracy as functions of the two rule-extraction penalty parameters on Adult, averaged across five network architectures ( h∈{16,32,128,16×8,32×16} ).
Fig. 10 : BRAM and total accuracy vs. sparsity threshold k on Adult ( h=32 ).
Fallback
Acc.
Acc unc
Fid unc
LUT
FF
DSP
Lat.
Linear Regression
81.67
67.4
84.1
1749
520
10
13
Full BNN
82.91
71.9
100.0
1887
2318
40
68
Small BNN
82.23
71.3
90.5
1129
2178
38
46
CART
83.02
72.1
87.7
714
471
0
26
TABLE IX : Fallback strategy ablation on the Adult dataset ( h=32 , αsc=0.5 , αconf=0.1 ). Resource columns report the fallback component only. Acc unc and Fid unc are on uncovered samples. All accuracy and fidelity values in %.
Empirical (%)
Certified (%)
c
Rule Acc.
Fid.
Rules
BNN
ReLU
0.00
100.0
98.2
100.0
100.0
100.0
0.01
99.6
97.8
83.4
82.1
80.1
0.03
99.0
97.2
59.4
41.3
27.1
0.05
98.4
96.4
42.7
16.0
12.4
0.10
97.0
94.7
22.7
6.6
4.8
TABLE X : Robustness certification on MAGIC. Empirical columns show rule accuracy and rule–BNN fidelity under sampled noise; certified columns show provably stable fractions for rules and networks.
Geographic shift
Temporal shift (CA)
System
Metric
ID (CA-18)
GEO-AVG
Δ
MS
WY
WV
TEMP-AVG
Δ
2019
2021
2022
ReLU Teacher
Acc. (%)
81.28 ± 0.09
74.32 ± 0.64
− 7.0
73.73
74.61
74.61
80.00 ± 0.09
− 1.3
80.74
79.82
79.44
ReLU
Acc. (%)
80.55 ± 0.15
74.10 ± 0.76
− 6.5
73.42
74.45
74.43
79.37 ± 0.19
− 1.2
80.03
79.23
78.84
BNN
Acc. (%)
80.89 ± 0.29
74.45 ± 0.69
− 6.4
73.79
74.77
74.79
79.81 ± 0.36
− 1.1
80.49
79.67
79.26
Rules
Coverage (%)
90.09 ± 0.86
85.82 ± 1.38
− 4.3
86.10
85.07
86.29
90.24 ± 0.78
+ 0.2
90.01
90.35
90.35
Covered acc. (%)
80.29 ± 0.20
76.41 ± 1.07
− 3.9
77.31
74.82
77.09
78.67 ± 0.42
− 1.6
79.38
78.62
78.00
TABLE XI : Distribution-shift robustness on ACS Income, training on CA-2018. ID = held-out CA-2018 test set; GEO-AVG and TEMP-AVG are means over shifted conditions; Δ = AVG − ID (pp). Means ± std over 5 seeds.
TinyBERT4
h=600
h=312
Scope
Metric
GeLU
Bern
GeLU
Bern
SST-2 Acc. (%)
90.37
90.02
90.48
89.11
90.02
FFN
Lat. (cycles)
6,413,520
3,282,640 ( ↓ 48.8%)
3,278,288 ( ↓ 48.9%)
1,789,648 ( ↓ 72.1%)
1,785,296 ( ↓ 72.2%)
DSP
121
121 (0.0%)
80 ( ↓ 33.9%)
121 (0.0%)
80 ( ↓ 33.9%)
BRAM
155
82 ( ↓ 47.1%)
128 ( ↓ 17.4%)
80 ( ↓ 48.4%)
108 ( ↓ 30.3%)
FF
17,746
19,580 ( ↑ 10.3%)
15,654 ( ↓ 11.8%)
19,528 ( ↑ 10.0%)
15,568 ( ↓ 12.3%)
TABLE XII : SST-2 accuracy, latency, and FPGA resource utilization for full 4-layer FFN substitution. FFN : FFN sublayers only; Full : complete encoder. Resource reductions are relative to TinyBERT4.
Edge inference runs trained AI models on nearby devices such as phones, cameras, robots, and embedded computers under tight resource and latency limits.
Federated Learning (FL) preserves privacy by distributing training across devices. However, using DNNs is computationally intensive at the low-powered edge during inference. Edge deployment demands models that simultaneously optimize memory footprint and computational efficiency, a dilemma where conventional DNNs fail by exceeding resource limits. Traditional post-training binarization reduces model size but suffers from severe accuracy loss due to quantization errors. To address these challenges, we propose FedBNN, a rotation-aware binary neural network framework that learns binary representations directly during local training. By encoding each weight as a single bit {+1,−1} instead of a 32-bit float, FedBNN shrinks the model footprint, significantly reducing runtime (during inference) FLOPs and memory requirements in comparison to federated methods using real models. Evaluations across multiple benchmark datasets demonstrate that FedBNN significantly reduces resource consumption while performing similarly to existing federated methods using real-valued models.
This paper examines the use of Quantized Neural Networks (QNNs) for two resource-constrained scientific applications: automated calibration of semiconductor quantum bits (qubits) and scientific particle detectors. We evaluate the trade-offs between Post-Training Quantization (PTQ), Quantization-Aware Training (QAT), and ultra-low-bit Binary Neural Networks (BNNs) with respect to latency and resource usage. Our results demonstrate that PTQ and QAT are easily implementable solutions achieving a four-fold reduction in memory usage for Ushaped CNN (U-Net) architectures, whereas BNNs are better suitable for use cases with challenging latency requirements. For the training of non-differentiable custom BNNs, we propose a novel, hardware-constrained learning approach using Genetic Algorithms (GAs). We showcase a Look-Up Table (LUT)-based BNN architecture suitable for direct conversion to Very High-Speed Integrated Circuit Hardware Description Language (VHDL) via the HCL4BNN framework. This method achieves nanosecond-scale inference latencies at 10 ns to 15 ns without requiring specialized Digital Signal Processor (DSP) or Block RAM (BRAM) resources.
Alperen Aksoy, Ilja Bekman, Vesselin Dimitrov +6
Peter Grünberg Institute (PGI), Integrated Computing Architectures (ICA | PGI-4), Forschungszentrum Jülich GmbH, Germany · Center for Particle Physics Siegen, Department für Physik, Universität Siegen, Germany · Faculty of Engineering, JARA-FIT Institute for Quantum Information, Forschungszentrum Jülich GmbH and RWTH Aachen University, Germany +1
Edge devices are increasingly utilized for deploying deep learning applications on embedded systems. The real-time nature of many applications and the limited resources of edge devices necessitate latency-targeted neural network compression. However, measuring latency on real devices is challenging and expensive. Therefore, this letter presents a novel and efficient framework, named EvoLP, to accurately predict the inference latency of models on edge devices. This predictor can evolve to achieve higher latency prediction precision during the network compression process. Experimental results demonstrate that EvoLP outperforms previous state-of-the-art approaches by being evaluated on three edge devices and four model variants. Moreover, when incorporated into a model compression framework, it effectively guides the compression process for higher model accuracy while satisfying strict latency constraints. We open source EvoLP at https://github.com/ntuliuteam/EvoLP.
Shuo Huai, Hao Kong, Shiqing Li +5
School of Computer Science and Engineering, Nanyang Technological University, Singapore · HP-NTU Digital Manufacturing Corporate Lab, Nanyang Technological University, Singapore · HP Inc., Palo Alto, California, USA