Constrained Image Generation Using Binarized Neural Networks with Decision Procedures

Abstract

We consider the problem of binary image generation with given properties. This problem arises in a number of practical applications, including generation of artificial porous medium for an electrode of lithium-ion batteries, for composed materials, etc. A generated image represents a porous medium and, as such, it is subject to two sets of constraints: topological constraints on the structure and process constraints on the physical process over this structure. To perform image generation we need to define a mapping from a porous medium to its physical process parameters. For a given geometry of a porous medium, this mapping can be done by solving a partial differential equation (PDE). However, embedding a PDE solver into the search procedure is computationally expensive. We use a binarized neural network to approximate a PDE solver. This allows us to encode the entire problem as a logical formula. Our main contribution is that, for the first time, we show that this problem can be tackled using decision procedures. Our experiments show that our model is able to produce random constrained images that satisfy both topological and process constraints.

BDD4BNN: A BDD-Based Quantitative Analysis Framework for Binarized Neural Networks

“…For decision explanation, we show the effectiveness of BDD4BNN in computing prime-implicant explanations and essential features of the given input region for some target classes. Note that this work focuses on quantitative verification and interpretability of BNNs and may underperform SAT/SMT-based methods [12,33,45,46] for qualitative verification of BNNs.…”

“…Existing techniques for quantized DNNs are mostly based on constraint solving, in particular, SAT/SMT solving [12,33,45,46]. Following this line, verification of BNNs with ternary weights [28,48] and quantized DNNs with multiple bits [7,22,24] were also studied.…”

“…A majority of work resorts to SAT/SMT solving. For the 1-bit quantization (i.e., BNNs), typically BNNs are transformed into Boolean formulas where SAT solving is harnessed [12,33,45,46]. Some recent work also studies variants of BNNs [28,48], i.e., BNNs with ternary weights.…”

BDD4BNN: A BDD-based Quantitative Analysis Framework for Binarized Neural Networks

“…A majority of work resorts to SAT/SMT solving. For the 1-bit quantization (i.e., BNNs), typically BNNs are transformed into Boolean formulas where SAT solving is harnessed [42,10,32,41]. Some recent work also studies variants of BNNs [44,27], for instance, three-valued BNNs.…”

Accelerating Binarized Neural Networks via Bit-Tensor-Cores in Turing GPUs

“…Although BNN is not likely to substitute DNNs because of reduced model capacity, for many HPC [14], [15], [16], [17] and cloud applications [18], [19], when certain accuracy levels can be achieved, alternative factors such as latency, energy, hardware cost, resilience, etc. become more prominent.…”