arXiv subjects

Zachary Tatlock

Publications and source records attributed to Zachary Tatlock.

34 records · Page 2Linked to original sources

arXiv2021

Rewrite Rule Inference Using Equality Saturation

Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed ruler. Compared to a similar tool built on CVC4, ruler synthesizes 5.8X smaller rulesets 25X faster without compromising on proving power. In an end-to-end case study, we show ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.

cs.PL↗

arXiv2021

Co-Optimization of Design and Fabrication Plans for Carpentry

Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design, instead considering families of design variations, sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts(BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs(ICEE) can keep the size of the e-graph manage-able and direct the search toward promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.

cs.GR↗

arXiv2021

Co-Optimization of Design and Fabrication Plans for Carpentry: Supplemental Material

Past work on optimizing fabrication plans given a carpentry design can provide Pareto-optimal plans trading off between material waste, fabrication time, precision, and other considerations. However, when developing fabrication plans, experts rarely restrict to a single design, instead considering families of design variations, sometimes adjusting designs to simplify fabrication. Jointly exploring the design and fabrication plan spaces for each design is intractable using current techniques. We present a new approach to jointly optimize design and fabrication plans for carpentered objects. To make this bi-level optimization tractable, we adapt recent work from program synthesis based on equality graphs (e-graphs), which encode sets of equivalent programs. Our insight is that subproblems within our bi-level problem share significant substructures. By representing both designs and fabrication plans in a new bag of parts(BOP) e-graph, we amortize the cost of optimizing design components shared among multiple candidates. Even using BOP e-graphs, the optimization space grows quickly in practice. Hence, we also show how a feedback-guided search strategy dubbed Iterative Contraction and Expansion on E-graphs (ICEE) can keep the size of the e-graph manage-able and direct the search toward promising candidates. We illustrate the advantages of our pipeline through examples from the carpentry domain.

cs.GR↗

arXiv2021

Pure Tensor Program Rewriting via Access Patterns (Representation Pearl)

Tensor kernels in machine learning (ML) often correspond to pure mathematical expressions, making term rewriting an attractive strategy for optimization and mapping to specialized hardware accelerators. However, existing ML intermediate representations (IRs) tend to either be \textit{pure but high-level}, making low-level rewrites to hardware targets inexpressible, or \textit{low-level but impure}, hampering the use of term rewriting altogether. This paper introduces Glenside, a pure IR whose core abstraction -- the \textit{access pattern} -- enables low-level, layout-aware, hardware-centric program rewrites. We demonstrate how term rewriting in Glenside can be used to map program fragments to hardware accelerator invocations and automatically discover classic data layout transformations like \texttt{im2col}. Glenside establishes a new foundation for exploring further term rewriting techniques in optimizing low-level tensor programs.

cs.PL↗

arXiv2021

Dynamic Tensor Rematerialization

Checkpointing enables the training of deep learning models under restricted memory budgets by freeing intermediate activations from memory and recomputing them on demand. Current checkpointing techniques statically plan these recomputations offline and assume static computation graphs. We demonstrate that a simple online algorithm can achieve comparable performance by introducing Dynamic Tensor Rematerialization (DTR), a greedy online algorithm for checkpointing that is extensible and general, is parameterized by eviction policy, and supports dynamic models. We prove that DTR can train an $N$-layer linear feedforward network on an $Ω(\sqrt{N})$ memory budget with only $\mathcal{O}(N)$ tensor operations. DTR closely matches the performance of optimal static checkpointing in simulated experiments. We incorporate a DTR prototype into PyTorch merely by interposing on tensor allocations and operator calls and collecting lightweight metadata on tensors.

cs.LG↗

arXiv2021

Nimble: Efficiently Compiling Dynamic Neural Networks for Model Inference

Modern deep neural networks increasingly make use of features such as dynamic control flow, data structures and dynamic tensor shapes. Existing deep learning systems focus on optimizing and executing static neural networks which assume a pre-determined model architecture and input data shapes--assumptions which are violated by dynamic neural networks. Therefore, executing dynamic models with deep learning systems is currently both inflexible and sub-optimal, if not impossible. Optimizing dynamic neural networks is more challenging than static neural networks; optimizations must consider all possible execution paths and tensor shapes. This paper proposes Nimble, a high-performance and flexible system to optimize, compile, and execute dynamic neural networks on multiple platforms. Nimble handles model dynamism by introducing a dynamic type system, a set of dynamism-oriented optimizations, and a light-weight virtual machine runtime. Our evaluation demonstrates that Nimble outperforms state-of-the-art deep learning frameworks and runtime systems for dynamic neural networks by up to 20x on hardware platforms including Intel CPUs, ARM CPUs, and Nvidia GPUs.

cs.PL↗

arXiv2020

egg: Fast and Extensible Equality Saturation

An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, e-graphs remain unspecialized for this newer use case. Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites. This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation. A new amortized invariant restoration technique called rebuilding takes advantage of equality saturation's distinct workload, providing asymptotic speedups over current techniques in practice. A general mechanism called e-class analyses integrates domain-specific analyses into the e-graph, reducing the need for ad hoc manipulation. We implemented these techniques in a new open-source library called egg. Our case studies on three previously published applications of equality saturation highlight how egg's performance and flexibility enable state-of-the-art results across diverse domains.

cs.PL↗

arXiv2020

Synthesizing Structured CAD Models with Equality Saturation and Inverse Transformations

Recent program synthesis techniques help users customize CAD models(e.g., for 3D printing) by decompiling low-level triangle meshes to Constructive Solid Geometry (CSG) expressions. Without loops or functions, editing CSG can require many coordinated changes, and existing mesh decompilers use heuristics that can obfuscate high-level structure. This paper proposes a second decompilation stage to robustly "shrink" unstructured CSG expressions into more editable programs with map and fold operators. We present Szalinski, a tool that uses Equality Saturation with semantics-preserving CAD rewrites to efficiently search for smaller equivalent programs. Szalinski relies on inverse transformations, a novel way for solvers to speculatively add equivalences to an E-graph. We qualitatively evaluate Szalinski in case studies, show how it composes with an existing mesh decompiler, and demonstrate that Szalinski can shrink large models in seconds.

cs.PL↗

arXiv2020

QED at Large: A Survey of Engineering of Formally Verified Software

Development of formal proofs of correctness of programs can increase actual and perceived reliability and facilitate better understanding of program specifications and their underlying assumptions. Tools supporting such development have been available for over 40 years, but have only recently seen wide practical use. Projects based on construction of machine-checked formal proofs are now reaching an unprecedented scale, comparable to large software projects, which leads to new challenges in proof development and maintenance. Despite its increasing importance, the field of proof engineering is seldom considered in its own right; related theories, techniques, and tools span many fields and venues. This survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.

cs.LO↗

arXiv2020

Enumerating Hardware-Software Splits with Program Rewriting

A core problem in hardware-software codesign is in the sheer size of the design space. Without a set ISA to constrain the hardware-software interface, the design space explodes. This work presents a strategy for managing the massive hardware-software design space within the domain of machine learning inference workloads and accelerators. We first propose EngineIR, a new language for representing machine learning hardware and software in a single program. Then, using equality graphs -- a data structure from the compilers literature -- we suggest a method for efficiently enumerating the design space by performing rewrites over our representation.

cs.DC↗

arXiv2019

Relay: A High-Level Compiler for Deep Learning

Frameworks for writing, compiling, and optimizing deep learning (DL) models have recently enabled progress in areas like computer vision and natural language processing. Extending these frameworks to accommodate the rapidly diversifying landscape of DL models and hardware platforms presents challenging tradeoffs between expressivity, composability, and portability. We present Relay, a new compiler framework for DL. Relay's functional, statically typed intermediate representation (IR) unifies and generalizes existing DL IRs to express state-of-the-art models. The introduction of Relay's expressive IR requires careful design of domain-specific optimizations, addressed via Relay's extension mechanisms. Using these extension mechanisms, Relay supports a unified compiler that can target a variety of hardware platforms. Our evaluation demonstrates Relay's competitive performance for a broad class of models and devices (CPUs, GPUs, and emerging accelerators). Relay's design demonstrates how a unified IR can provide expressivity, composability, and portability without compromising performance.

cs.LG↗

arXiv2018

Relay: A New IR for Machine Learning Frameworks

Machine learning powers diverse services in industry including search, translation, recommendation systems, and security. The scale and importance of these models require that they be efficient, expressive, and portable across an array of heterogeneous hardware devices. These constraints are often at odds; in order to better accommodate them we propose a new high-level intermediate representation (IR) called Relay. Relay is being designed as a purely-functional, statically-typed language with the goal of balancing efficient compilation, expressiveness, and portability. We discuss the goals of Relay and highlight its important design constraints. Our prototype is part of the open source NNVM compiler framework, which powers Amazon's deep learning framework MxNet.

cs.PL↗

arXiv2018

Finding Root Causes of Floating Point Error with Herbgrind

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform. This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to a simplified program fragment whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries, and tracking error across function boundaries and through the heap.

cs.PL↗

arXiv2018

A Graphical Interactive Debugger for Distributed Systems

Designing and debugging distributed systems is notoriously difficult. The correctness of a distributed system is largely determined by its handling of failure scenarios. The sequence of events leading to a bug can be long and complex, and it is likely to include message reorderings and failures. On single-node systems, interactive debuggers enable stepping through an execution of the program, but they lack the ability to easily simulate failure scenarios and control the order in which messages are delivered. Oddity is a graphical, interactive debugger for distributed systems. It brings the power of traditional step-through debugging---fine-grained control and observation of a program as it executes---to distributed systems. It also enables exploratory testing, in which an engineer examines and perturbs the behavior of a system in order to better understand it, perhaps without a specific bug in mind. A programmer can directly control message and failure interleaving. Oddity supports time travel, allowing a developer to explore multiple branching executions of a system within a single debugging session. Above all, Oddity encourages distributed systems thinking: rather than assuming the normal case and attaching failure handling as an afterthought, distributed systems should be developed around the certainty of message loss and node failure. Graduate and undergraduate students used Oddity in two distributed systems classes. Usage tracking and qualitative surveys showed that students found Oddity useful for both debugging and exploratory testing.

cs.DC↗

arXiv2018

Combining Tools for Optimization and Analysis of Floating-Point Computations

Recent renewed interest in optimizing and analyzing floating-point programs has lead to a diverse array of new tools for numerical programs. These tools are often complementary, each focusing on a distinct aspect of numerical programming. Building reliable floating point applications typically requires addressing several of these aspects, which makes easy composition essential. This paper describes the composition of two recent floating-point tools: Herbie, which performs accuracy optimization, and Daisy, which performs accuracy verification. We find that the combination provides numerous benefits to users, such as being able to use Daisy to check whether Herbie's unsound optimizations improved the worst-case roundoff error, as well as benefits to tool authors, including uncovering a number of bugs in both tools. The combination also allowed us to compare the different program rewriting techniques implemented by these tools for the first time. The paper lays out a road map for combining other floating-point tools and for surmounting common challenges.

cs.PL↗

arXiv2011

Equality Saturation: A New Approach to Optimization

Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for structuring the optimization phase of a compiler. In our approach, optimizations take the form of equality analyses that add equality information to a common intermediate representation. The optimizer works by repeatedly applying these analyses to infer equivalences between program fragments, thus saturating the intermediate representation with equalities. Once saturated, the intermediate representation encodes multiple optimized versions of the input program. At this point, a profitability heuristic picks the final optimized program from the various programs represented in the saturated representation. Our proposed way of structuring optimizers has a variety of benefits over previous approaches: our approach obviates the need to worry about optimization ordering, enables the use of a global optimization heuristic that selects among fully optimized programs, and can be used to perform translation validation, even on compilers other than our own. We present our approach, formalize it, and describe our choice of intermediate representation. We also present experimental results showing that our approach is practical in terms of time and space overhead, is effective at discovering intricate optimization opportunities, and is effective at performing translation validation for a realistic optimizer.

cs.PL↗