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[Arith] linear system and equation solver #5171

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tqchen merged 7 commits into apache:master from yzhliu:linear_solver

Apr 10, 2020

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yzhliu commented Mar 30, 2020

Co-authored-by: Sergei Grechanik [email protected]

Linear system data structures and linear equations solver (via Smith Normal Form)

this is part of tensor level autodiff. will be used by #5121

Originally implemented by @sgrechanik-h in #2634 I modified a bit to make it more mathematical. @sgrechanik-h please help to check if the math is correct and whether SuperSimplify is required (I use tir::Simplify instead in this PR, I think it is only required in condition lift)

@sgrechanik-h @tqchen @MarisaKirisame @junrushao1994 @hzfan Please review

yzhliu added the status: need review label

yzhliu force-pushed the linear_solver branch from 0a75caf to 2b0ad1a Compare

March 30, 2020 08:05

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tqchen commented Mar 30, 2020

NOTE: please try to rewrite to directly use the auxiliary class arith::Analyzer instead of the Simplify function, so that the temp data structure can be created only once

tqchen mentioned this pull request

[TVM] Zero elimination #2634

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yzhliu force-pushed the linear_solver branch from 2b0ad1a to 5a9c022 Compare

March 31, 2020 23:19

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yzhliu commented Mar 31, 2020

@tqchen changed to use arith::Analyzer

sergei-grechanik reviewed

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include/tvm/arith/linear_system.h Outdated

+              /*!
+               * \brief Represent a linear system including variables, their ranges and
+               *        the linear relations between them (either equations or inequalities)

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sergei-grechanik Apr 1, 2020

I think it's worth mentioning that the system is integer.

Also I'm not sure if LinearSystem is a good name, because it may be useful to have non-linear (in)equalities in relations (which doesn't break the algorithms that work on the linear part).

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yzhliu Apr 2, 2020 •

edited

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good suggestion. how about Formulas, Constraints, RelationSet, IntRelationSet, or InequalitySet (if we make term "inequality" to also include equations)? @sergei-grechanik

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sergei-grechanik Apr 3, 2020

IntegerSet or IntegerSystem maybe?

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yzhliu Apr 3, 2020

sounds good. There's IntSet in tvm, so I'll do IntegerSystem.

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yzhliu Apr 3, 2020

think it a bit more, should we use a more general name? as in solver, we will check the relation and ignore the non-integer equations, which implies it is valid to contain non-integer relations inside. @sergei-grechanik

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sergei-grechanik Apr 4, 2020

If variables are integer, I think it's still ok to call it IntegerSystem. But if we allow non-integer variables (I doubt it is a good idea), then I don't know, Set and System sound too unspecific, Constraints may be ok.

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tests/python/unittest/test_arith_solve_linear_system.py Outdated Show resolved Hide resolved

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sergei-grechanik commented Apr 1, 2020

About SuperSimplify: it was a combination of the canonical simplifier and the rewriting simplifier that worked best for autodiff (I actually ran it with different combinations and rewrite->canonical->rewrite turned out to be the best, although canonical->rewrite was good too). I think currently the default Simplify function is rewrite->canonical, not sure if this order has a good justification.

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yzhliu commented Apr 1, 2020

@sergei-grechanik do you have example that we have to end with rewrite?

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MarisaKirisame left a comment

LGTM, although i have essentially zero expertise in numerical algorithm, so I didnt really understand what is going on.

src/arith/linear_system.cc Outdated

+                node->variables = std::move(variables);
+                node->ranges = std::move(ranges);
+                node->relations = std::move(relations);
+                data_ = std::move(node);

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MarisaKirisame Apr 1, 2020

what is data_?

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yzhliu Apr 3, 2020

it's ObjectRef->data_ whose type is ObjectPtr

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tqchen commented Apr 1, 2020

cc @Hzfengsy @spectrometerHBH @merrymercy please also take a look if you have time, should be relevant to your areas

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sergei-grechanik commented Apr 1, 2020

@yzhliu Unfortunately I don't have an example. It's written in my notes that "we should end with rw because it factors multipliers out". If it's only that, it's probably not that important.

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src/arith/solve_linear_equation.cc Show resolved Hide resolved

src/arith/solve_linear_equation.cc

+                // Transform formulas into rows of the matrix
+                // S_{mxn} V^{-1}_{nxn} x_{nx1} = U y, in which n is # of variables
+                // here we initialize S_{mxn} to be A, U to be identity matrix.

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hzfan Apr 2, 2020

V to be identity matrix?

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yzhliu Apr 3, 2020

V was described above. here what I mean is
U^{-1} S V^{-1} x = y = [coefs] => S V^{-1} x = U [coefs]
which implies U is identity.

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yzhliu force-pushed the linear_solver branch 2 times, most recently from c58057b to c2678f8 Compare

April 5, 2020 06:05

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yzhliu commented Apr 5, 2020

@sergei-grechanik I rename it to IntConstraints, and also add checker to ensure the variables to be integers. please take a review again.

yzhliu force-pushed the linear_solver branch from c2678f8 to 3ccd472 Compare

April 5, 2020 06:11

sergei-grechanik reviewed

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include/tvm/arith/int_solver.h

+               * \param V  an identity matrix, it will be modified to V_{nxn}
+               * \param x  the x in A x = y. it will be modified to V^{-1}_{nxn} x_{nx1}
+               * \param y  the y in A x = y. it will be modified to U_{mxm} y_{mx1}
+               */

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sergei-grechanik Apr 8, 2020

I was thinking about this and came to conclusion that computing the proper Smith normal form may improve stability of automatic differentiation (I mean generating the same gradient code for slightly different but equivalent input code). However, I'm not sure if it's worth it (and not in this PR of course).

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yzhliu Apr 8, 2020

I see. I'll put a todo here.

yzhliu force-pushed the linear_solver branch 2 times, most recently from 3f7424e to 0010a64 Compare

April 8, 2020 07:27

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yzhliu and others added 6 commits

April 9, 2020 17:17


          [arith] linear system and equation solver

0aa5115

Co-authored-by: Sergei Grechanik <[email protected]>


          avoid constructing analyzer every time

42317d9


          generate random test cases and address comments

ff42ed1

Co-authored-by: Sergei Grechanik <[email protected]>


          rename linear_system to int_constraints


          add comments and use random seed

8cac9e3


          message for reporting failure with seed

2d89fef


          add SEqualReduce to IntConstraints; allow variables & ranges to be None

dc76eac

yzhliu force-pushed the linear_solver branch from 0010a64 to dc76eac Compare

April 10, 2020 00:17

sergei-grechanik approved these changes

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sergei-grechanik left a comment

Ok, looks good to me

tqchen approved these changes

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tqchen merged commit e21f268 into apache:master

tqchen added status: accepted and removed status: need review labels

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tqchen commented Apr 10, 2020

Thanks @yzhliu @sgrechanik-h @hzfan @MarisaKirisame

trevor-m pushed a commit to trevor-m/tvm that referenced this pull request


          [Arith] linear system and equation solver (apache#5171)

* [arith] linear system and equation solver

Co-authored-by: Sergei Grechanik <[email protected]>

* avoid constructing analyzer every time

* generate random test cases and address comments

Co-authored-by: Sergei Grechanik <[email protected]>

* rename linear_system to int_constraints

* add comments and use random seed

* message for reporting failure with seed

* add SEqualReduce to IntConstraints; allow variables & ranges to be None

Co-authored-by: Sergei Grechanik <[email protected]>
Co-authored-by: Sergei Grechanik <[email protected]>

zhiics pushed a commit to neo-ai/tvm that referenced this pull request


          [Arith] linear system and equation solver (apache#5171)

bde2419

* [arith] linear system and equation solver

Co-authored-by: Sergei Grechanik <[email protected]>

* avoid constructing analyzer every time

* generate random test cases and address comments

Co-authored-by: Sergei Grechanik <[email protected]>

* rename linear_system to int_constraints

* add comments and use random seed

* message for reporting failure with seed

* add SEqualReduce to IntConstraints; allow variables & ranges to be None

Co-authored-by: Sergei Grechanik <[email protected]>
Co-authored-by: Sergei Grechanik <[email protected]>

dpankratz pushed a commit to dpankratz/incubator-tvm that referenced this pull request


          [Arith] linear system and equation solver (apache#5171)

1ee5937

* [arith] linear system and equation solver

Co-authored-by: Sergei Grechanik <[email protected]>

* avoid constructing analyzer every time

* generate random test cases and address comments

Co-authored-by: Sergei Grechanik <[email protected]>

* rename linear_system to int_constraints

* add comments and use random seed

* message for reporting failure with seed

* add SEqualReduce to IntConstraints; allow variables & ranges to be None

Co-authored-by: Sergei Grechanik <[email protected]>
Co-authored-by: Sergei Grechanik <[email protected]>

ZihengJiang mentioned this pull request

TVM v0.7 Release Note Candidate #6486

Closed

monklof pushed a commit to monklof/incubator-tvm that referenced this pull request


          Merge pull request apache#3 in DATA/tvm from ~WANGXIN66/tvm_clone_fro…

f6767fd

…m_data:master to master

* commit 'cd0d52daa6942bdafa9363ff6cfa3d25fcd5b8d6': (824 commits)
  [Intrinsic] Add log1p, ldexp, atan2, hypot, nextafter, copysign (apache#5312)
  [Rust][CI] Restore Rust CI (apache#5137)
  Remove PrimExpr from String (apache#5311)
  [Requantize] Cleanup and Optimize Lowering (apache#5286)
  [IR][TRANSFORM] Enable CopyOnWrite for passes. (apache#5309)
  [PYTORCH]Abs, Arange, Softplus ops (apache#5295)
  [LLVM] Fix generation of LLVM intrinsics (apache#5282)
  [BYOC] Add example of Composite + Annotate for DNNL fused op (apache#5272)
  [Frontend][TensorFlow]Improve TensorFlow Static Shape Tensor Array (apache#5243)
  [RUNTIME] Introduce RValue reference(move) support to TypedPackedFunc (apache#5271)
  [RELAY][FRONTEND][CAFFE2] add Mul and ConvTranspose operator (apache#5302)
  [BYOC] Refine AnnotateTarget and MergeCompilerRegion Passes (apache#5277)
  [CI] Fix the hexagon string (apache#5304)
  [Arith] linear system and equation solver (apache#5171)
  [PYTORCH]Repeat, Reciprocal & Reshape Op support (apache#5280)
  [FRONTEND][TENSORFLOW] Fix gather_nd indices (apache#5279)
  Update device_annotation.cc (apache#5291)
  [REFACTOR][IR] Move to runtime::String (apache#5276)
  [NDArray] Set shape_ in NDArray::FromDLPack (apache#5301)
  [RUNTIME] Initial implementation of Hexagon runtime support (apache#5252)
  ...

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status: accepted