See Release Notes for the record of previously released features.

0.6.1+ Further buildout of axle.game (2021H1)

Missing functionality

• moveStateStream
  • rename to moveStatePath or traceGame
  • unless we give this job to State…
    • Record history Seq[(M, S)] in State (and display to user in interactiveMove)
  • stop using chain?
• Should be part of State displaying evGameIO.displayMoveTo(game, evGame.maskMove(game, move, mover, observer), mover, observer)
• Display to player the elapsed moves /and/ the state diff

Motivating Examples

• Generalize OldMontyHall.chanceOfWinning

• GuessRiffle.md
  • Walk through game
  • Plot distribution of sum(entropy) for both strategies
  • Plot entropy by turn # for each strategy
  • Plot simulated score distribution for each strategy

• GuessRiffleSpec: use moveFromRandomState

• Gerrymandering sensitivity

• “You split, I choose” as game

Deeper changes

• aiMover.unmask prevents MontyHallSpec “AI vs. AI game produces moveStateStream” from working
  • will be an issue for all non-perfect information

• Identify all uses of spire.random.Generator (and other random value generation)

• See uses of seed in GuessRiffleProperties

• Eliminate entropy consumption of rng side-effect (eg applyMove(Riffle()))
  • Chance should be its own player
  • Consider whether PM should be a part of Strategy type (MS => PM[M, V])
    • More abstractly, more many intents and purposes, all we are about is that resolving PM to M consumes entropy
    • In which cases should the PM be retained?
  • Each N bits consumed during Riffle() is its own move
  • Chance moves consume UnittedQuantity[Information, N]
• perceive could return a lower-entropy probability model
  • Perhaps in exchange for a given amount of energy
  • Or ask for a 0-entropy model and be told how expensive that was

• Game theory axioms (Nash, etc)

• axle.game: Observable[T]

Hygeine

• Replace axle.game.moveFromRandomState.mapToProb

• Clean up axle.game.playWithIntroAndOutcomes

• The references to movesMap in MoveFromRandomStateSpec.scala illustrate a need for a cleaner way to create a hard-coded strategy – which could just be in the form of a couple utility functions from movesMap to the data needed by evGame.{moves,applyMove} and rm strategy

• Generalize ConditionalProbabilityTable.uniform into typeclass

• Simplify GuessRiffleProperties (especially second property)
• stateStreamMap only used in GuessRiffleProperties – stop using chain?

• stateStrategyMoveStream only used in GuessRiffleProperties

• Game.players should be a part of GameState (or take it as an argument)? Will wait for pressing use case.

0.7.x Factoring and Bayesian Networks

• Reorder Probability mdoc (Creation, Kolmogorov/Region, Sampler, Bayes, Monad)
  • Footnotes (Giry, etc)
• {CPT,TD}.tailRecM then ScalaCheck Monad[CPT,TD]

• Functor for CPT, TD

• SigmaAlgebra for the CPT
  • Clean up expressions like RegionIf[TWOROLLS](_._1 == '⚃)
  • Laws for Region (“Sigma Algebra”? video)
  • OrderedRegion for the Order used in RegionLTE and RegionGTE?

• Measure Theory

• Test: start with ABE.jointProbabilityTable (monotype tuple5[Boolean])
  • Factor out each variable until original 5-note network is reached
  • Basically the inverse of factor multiplication
  • bn.factorFor(B) * bn.factorFor(E) should be defined? (It errors)
  • MonotypeBayesanNetwork.filter collapase into a single BNN

• Rename ConditionalProbabilityTable?

• Laws for Factor

• Review InteractionGraph, EliminationGraph, JoinTree and the functions they power

• Consider a “case” to be a Map vs a Vector

• Consider usefulness of Factor in terms of Region

• MonotypeBayesanNetwork.{pure, map, flatMap, tailRecR}
• Reconcile MBN combine1 & combine2

• Monad tests for MonotypeBayesanNetwork[Alarm-Burglary-Earthquake]

• Bayes[MonotypeBayesanNetwork] – could be viewed as “belief updating” (vs “conditioning”)
  • If it took a ProbabilityModel itself
• QuantumCircuit.md
• QBit2.factor
• Fix and enable DeutschOracleSpec

• QBit CCNot

• Review complex analysis

0.8.x Bugs and adoption barriers

• Fix LogisticRegression and move LogisticRegression.md back

• Fix GeneticAlgorithmSpec

• Featurizing functions should return HLists or other typelevel sequences in order to avoid being told # features

• Redo Logic using Abstract Algebra

• Simple graph implementation so that axle-core can avoid including axle-jung

• svgJungDirectedGraphVisualization move to a axle-jung-xml jar?
  • Will require externalizing the layout to its own…. typeclass?
  • Layout of bayesian network is quite bad – check ABE SVG
• axle-png to avoid Xvfb requirement during tests

• Chicklet borders / colors on site

• move ast view xml (how is it able to refer to xml.Node?)
  • ast.view.AstNodeFormatter (xml.Utility.escape)
  • ast.view.AstNodeFormatterXhtmlLines
  • ast.view.AstNodeFormatterXhtml
• Tests for axle.ast
• axle-ast-python

• cats.effect for axle.ast.python2

• Factor axle.algebra.chain in terms of well-known combinators

After that

It’s likely that a 1.0 release will be made at this time.

Future backlog organized by theme are below. At this point Axle will have enough building blocks to do the research that has been its goal since inception.

Game Theory and Examples

• Factor axle.game.moveFromRandomState in terms of a random walk on a graph.
  • See “TODO scale mass down”
  • Compare to Brownian motion, Random walk, Ito process, …
  • Provide some axoms
    • no outgoing with path in from non-zero mass monotonically increases
    • no incoming with path out monotonically decreases
  • possibly provide a version for acyclic graphs
• Iterative game playing algorithm is intractible, but shares intent with sequential monte carlo
• Think about Information Theory’s “Omega” vis-a-vis Sequential Monte Carlo
• Improve axle.stats.rationalProbabilityDist as probabilities become smaller
• SimpsonsParadox.md
• Axioms of partial differentiation
  • https://math.ucr.edu/home/baez/mathematical/ACTUCR/Plotkin_Partial_Differentiation.pdf
• Conal Elliott: Efficient automatic differentiation made easy via category theory
• Max bet for Poker
• syntax for Game typeclass

Quantum Circuits

• Property test reversibility (& own inverse)
• Typeclass for “negate” (etc), Binary, CBit
• Typeclass for unindex
• Deutsch-Jozsa algorithm (D.O. for n-bits) (Oracle separation between EQP and P)
• Simon’s periodicity problem (oracle separation between BQP and BPP)
• Shor’s algorithm
• Grover’s algorithm
• Quantum cryptographic key exchange

Algorithm / Concept breadth

• LSA
• LDA
• GLM
• MCMC
• Metropolis Hastings
• Sequential Monte Carlo (SMC)
• Hamiltonian Monte Carlo (HMC)
• Neural Networks
• t-distributed stochastic neighbor embedding (t-SNE)
• Support Vector Machines
• Gradient Boosted Trees
• Decision Trees
• Random Forest
• A* Search
• Conditional Random Fields (CRF)
• Hidden Markov Models
• N Queens
• Multi-armed bandit
• Connection between dynamic programming and semiring
• Recursive grid search
• P-values
• z & t scores
• Correlation
• Regression
• Accuracy, Precision
• Bias, Variance
• Cohen’s Kappa
• Normalizer axioms
• Fourier transformations
• Abadi Plotkin pathology
• JVP: Jacobian

Compute Engines

• Bring back Spark spoke – Solve the Spark ClassTag issue (see Frameless?)
• Performance benchmarking
• netlib-java Matrix
• GPU/CUDA support
• Algebird/Scalding for distributed matrices, HyperLogLog, etc
• Most MapRedicible witnesses are inefficient (eg calling toVector, toSeq, etc)

Deeper exploration

• Bettings odds
• Rainbow Tables
• Blockchain
• Nerod Partition
• Finish Angluin Learner
• Motivation for Gold Paradigm, Angluin Learner
• Stochastic Lambda Calculus
• Game Theory: information sets, equilibria
• Redo axle.ast.* (rm throws, more typesafe)
• Shapeless for compound Quanta and Bayesian Networks
• Physics (eg, how Volume relates to Flow)
• Topoi
• do-calculus (Causality)
• Eigenvector
• Σ ⊣ Δ ⊣ Π means “sums are left adjoint to diagonals, which are left adjoint to products.”

Hygiene

• Get rid of implicit arg passing to KMeans in ClusterIrises.md (and KMeansSpecification)
• Factor tics and tics-{joda,algebra,spire} into separate libs?
• remove unnecessary implicit Field, R{,i}ng, {Additive, Multiplicative}Monoid once spire/cats play well
• Fix “unreachable” default pattern match cases
• Review remaining usage of: asInstanceOf, ClassTag, and Manifest
• Review groupBy uses – they use university equality. Replace with Eq
• axle.algorithms coverage > 80%
• axle.core coverage > 80%
• Rm throws from axle.quanta.UnitConverterGraph
• Rm throws from axle.jung
• Rm throws from axle.pgm.BayesianNetwork
• Rm throws from axle.stats.TallyDistribution
• Unchecked constraint in PlotDataView

Visualization

• WebGL
• SVG Animation
• Box Plot
• Candlestick Chart
• Honor graph vis params in awt graph visualizations
• axle.web.Table and HtmlFrom[Table[T]]
• Log scale
• SVG[Matrix]
• BarChart Variable width bars
• Horizontal barchart
• KMeansVisualization / ScatterPlot similarity (at least DataPoints)
• SVG[H] for BarChart hover (wrap with <g> to do getBBox)
• Background box for ScatterPlot hover text?
• Fix multi-color cube rendering
• Bloom filter surface
• Factor similarity between SVG and Draw?
• Re-enable axle-jogl
  • May require jogamop 2.4, which is not yet released
  • Or possibly use jogamp archive
  • See processing’s approach in this commit

Mathematics

• Collatz Conjecture vis
• Demo Mandelbrot with Rational
• Scrutinize axle.math and move out less reusable functions

Types and Axioms

• Replace Finite with Shapeless’s version (eg Sized[Vector[_], nat.2])
• Delete Finite conversions for jung (replace with NaturalTransformation?)
• Replace with Cats: FoldLeft, Bijection, FunctionPair, Endofunctor
• Define laws for Scanner, Aggregator, Zipper, Indexed, Talliable, Finite?
• Sort out MapFrom, FromStream, FromSet
• Test axle.algebra.tuple2Field
• similarity syntax for SimilaritySpace (see axle.bio.*)
• Projections of jung graphs for Finite
• kittens or magnolia
  • pattern match in FirstOrderPredicateLogic
  • subtyping for Suit and Rank
• Machinist?
• Type-level matrix dimension using -Yliteral-types and singleton-ops in LinearAlgebra typeclass
• Make the Int abstract in KMeans{,Visualization}, LinearAlgebra, etc

Docs, Site, CI/CD

• Friend of Spire

• Experiment with pandoc

• Use sbt-ci-release (rm sbt-release)

• Configure makeSite to preview: previewFixedPort := Some(9999)
• Copy css using makeSite (not update-docs.sh)
• Fix markdown lint warnings

• Figure out better way to reference images in docs

• Site
  • meta tag with keywords: axle, scala, dsl, data, analysis, science, open-source, adam pingel
  • Remove jekyll from publishing pipeline
    • sbt-site
    • sbt-s3