1 / 68

Issue #2: Shift Invariance - PowerPoint PPT Presentation

  • Uploaded on

Issue #2: Shift Invariance. Backprop cannot handle shift invariance (it cannot generalize from 0011, 0110 to 1100) But the cup is on the table whether you see it right in the center or from the corner of your eyes (i.e. in different areas of the retina map)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Issue #2: Shift Invariance' - etoile

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Issue 2 shift invariance
Issue #2: Shift Invariance

  • Backprop cannot handle shift invariance (it cannot generalize from 0011, 0110 to 1100)

  • But the cup is on the table whether you see it right in the center or from the corner of your eyes (i.e. in different areas of the retina map)

  • What structure can we utilize to make the input shift-invariant?

Topological relations
Topological Relations

  • Separation

  • Contact

  • Coincidence:

    • Overlap

    • Inclusion

  • Encircle/surround


  • Scale

  • Uniqueness/Plausibility

  • Grammar

  • Abstract Concepts

  • Inference

  • Representation

How does activity lead to structural change
How does activity lead to structural change?

  • The brain (pre-natal, post-natal, and adult) exhibits a surprising degree of activity dependent tuning and plasticity.

  • To understand the nature and limits of the tuning and plasticity mechanisms we study

    • How activity is converted to structural changes (say the ocular dominance column formation)

  • It is centrally important for us to understand these mechanisms to arrive at biological accounts of perceptual, motor, cognitive and language learning

    • Biological Learning is concerned with this topic.

Learning and memory introduction







Learning and Memory: Introduction

memory of a situation

general facts


Learning and memory introduction1
Learning and Memory: Introduction

There are two different types of learning

  • Skill Learning

  • Fact and Situation Learning

    • General Fact Learning

    • Episodic Learning

  • There is good evidence that the process underlying skill (procedural) learning is partially different from those underlying fact/situation (declarative) learning.

  • Skill and fact learning involve different mechanisms
    Skill and Fact Learning involve different mechanisms

    • Certain brain injuries involving the hippocampal region of the brain render their victims incapable of learning any new facts or new situations or faces.

      • But these people can still learn new skills, including relatively abstract skills like solving puzzles.

    • Fact learning can be single-instance based. Skill learning requires repeated exposure to stimuli.

    • Implications for Language Learning?

    Short term memory
    Short term memory

    • How do we remember someone’s telephone number just after they tell us or the words in this sentence?

    • Short term memory is known to have a different biological basis than long term memory of either facts or skills.

      • We now know that this kind of short term memory depends upon ongoing electrical activity in the brain.

      • You can keep something in mind by rehearsing it, but this will interfere with your thinking about anything else. (Phonological Loop)

    Long term memory
    Long term memory

    • But we do recall memories from decades past.

      • These long term memories are known to be based on structural changes in the synaptic connections between neurons.

      • Such permanent changes require the construction of new protein molecules and their establishment in the membranes of the synapses connecting neurons, and this can take several hours.

    • Thus there is a huge time gap between short term memory that lasts only for a few seconds and the building of long-term memory that takes hours to accomplish.

    • In addition to bridging the time gap, the brain needs mechanisms for converting the content of a memory from electrical to structural form.

    Situational memory
    Situational Memory

    • Think about an old situation that you still remember well. Your memory will include multiple modalities- vision, emotion, sound, smell, etc.

    • The standard theory is that memories in each particular modality activate much of the brain circuitry from the original experience.

    • There is general agreement that the Hippocampal area contains circuitry that can bind together the various aspects of an important experience into a coherent memory.

    • This process is believed to involve the Calcium based potentiation (LTP).

    Models of learning
    Models of Learning

    • Hebbian ~ coincidence

    • Recruitment ~ one trial

    • Supervised ~ correction (backprop)

    • Reinforcement ~ delayed reward

    • Unsupervised ~ similarity

    Hebb s rule
    Hebb’s Rule

    • The key idea underlying theories of neural learning go back to the Canadian psychologist Donald Hebb and is called Hebb’s rule.

    • From an information processing perspective, the goal of the system is to increase the strength of the neural connections that are effective.

    Ltp and hebb s rule



    LTP and Hebb’s Rule

    • Hebb’s Rule: neurons that fire together wire together

    • Long Term Potentiation (LTP) is the biological basis of Hebb’s Rule

    • Calcium channels are the key mechanism

    Chemical realization of hebb s rule
    Chemical realization of Hebb’s rule

    • It turns out that there are elegant chemical processes that realize Hebbian learning at two distinct time scales

      • Early Long Term Potentiation (LTP)

      • Late LTP

    • These provide the temporal and structural bridge from short term electrical activity, through intermediate memory, to long term structural changes.

    Long term potentiation ltp
    Long Term Potentiation (LTP)

    • These changes make each of the winning synapses more potent for an intermediate period, lasting from hours to days (LTP).

    • In addition, repetition of a pattern of successful firing triggers additional chemical changes that lead, in time, to an increase in the number of receptor channels associated with successful synapses - the requisite structural change for long term memory.

      • There are also related processes for weakening synapses and also for strengthening pairs of synapses that are active at about the same time.

    The hebb rule is found with long term potentiation ltp in the hippocampus
    The Hebb rule is found with long term potentiation (LTP) in the hippocampus

    Schafer collateral pathway

    Pyramidal cells

    1 sec. stimuli

    At 100 hz

    Computational models based on hebb s rule
    Computational Models based on the hippocampusHebb’s rule

    The activity-dependent tuning of the developing nervous system, as well as post-natal learning and development, do well by following Hebb’s rule.

    Explicit Memory in mammals appears to involve LTP in the Hippocampus.

    Many computational systems for modeling incorporate versions of Hebb’s rule.

    • Winner-Take-All:

      • Units compete to learn, or update their weights.

      • The processing element with the largest output is declared the winner

      • Lateral inhibition of its competitors.

  • Recruitment Learning

    • Learning Triangle Nodes

  • LTP in Episodic Memory Formation

  • Hebb s rule is not sufficient
    Hebb’s rule is not sufficient the hippocampus

    • What happens if the neural circuit fires perfectly, but the result is very bad for the animal, like eating something sickening?

      • A pure invocation of Hebb’s rule would strengthen all participating connections, which can’t be good.

      • On the other hand, it isn’t right to weaken all the active connections involved; much of the activity was just recognizing the situation – we would like to change only those connections that led to the wrong decision.

    • No one knows how to specify a learning rule that will change exactly the offending connections when an error occurs.

      • Computer systems, and presumably nature as well, rely upon statistical learning rules that tend to make the right changes over time. More in later lectures.

    Models of learning1
    Models of Learning the hippocampus

    • Hebbian ~ coincidence

    • Recruitment ~ one trial

    • Supervised ~ correction (backprop)

    • Reinforcement ~ delayed reward

    • Unsupervised ~ similarity

    LTP and one-shot memory the hippocampus

    Twin requirements of LTP induction:

    • presynaptic activity + postsynaptic depolarization:

      • LTP requires synchronous activity at multiple synapses of a postsynaptic cell (cooperativity)

      • ideal for transforming a transientsynchronous-activitybased expression of a relation between multiple items into a persistentsynaptic-efficacy based encoding of the relation (Shastri, 2001)

    Recruiting connections
    Recruiting connections the hippocampus

    • Given that LTP involves synaptic strength changes and Hebb’s rule involves coincident-activation based strengthening of connections

      • How can connections between two nodes be recruited using Hebbs’s rule?

    The idea of recruitment learning

    K the hippocampus





    F = B/N

    the point is, with a fan-out of1000,

    if we allow 2 intermediate layers,

    we can almost always find a path

    The Idea of Recruitment Learning

    • Suppose we want to link up node X to node Y

    • The idea is to pick the two nodes in the middle to link them up

    • Can we be sure that we can find a path to get from X to Y?

    Finding a connection
    Finding a Connection the hippocampus

    P = (1-F) **B**K

    P = Probability of NO link between X and Y

    N = Number of units in a “layer”

    B = Number of randomly outgoing units per unit

    F = B/N , the branching factor

    K = Number of Intermediate layers, 2 in the example


    106 107 108


    # Paths = (1-Pk-1)*(N/F) = (1-Pk-1)*B

    X the hippocampus


    X the hippocampus


    Finding a Connection in Random Networks the hippocampus

    For Networks with N nodes and branching factor,

    there is a high probability of finding good links.

    (Valiant 1995)

    Recruiting the hippocampus a Connection in Random Networks

    • Informal Algorithm

    • Activate the two nodes to be linked

    • Have nodes with double activation strengthen their active synapses (Hebb)

    • There is evidence for a “now print” signal based on LTP (episodic memory)

    Triangle nodes and feature structures

    A the hippocampus



    Triangle nodes and feature structures




    Recruiting triangle nodes
    Recruiting triangle nodes the hippocampus

    • Let’s say we are trying to remember a green circle

    • currently weak connections between concepts (dotted lines)







    Strengthen these connections
    Strengthen these connections the hippocampus

    • and you end up with this picture








    Has-color the hippocampus




    Has-color the hippocampus




    Models of learning2
    Models of Learning the hippocampus

    • Hebbian ~ coincidence

    • Recruitment ~ one trial

    • Supervised ~ correction (backprop)

    • Reinforcement ~ delayed reward, soon

    • Unsupervised ~ similarity

    5 levels of neural theory of language
    5 the hippocampuslevels of Neural Theory of Language

    Pyscholinguistic experiments

    Spatial Relation

    Motor Control



    Cognition and Language


    Structured Connectionism


    Neural Net and learning


    Triangle Nodes

    Computational Neurobiology


    Neural Development




    Tinbergen’s Four Questions the hippocampus

    How does it work?

    How does it improve fitness?

    How does it develop and adapt?

    How did it evolve?

    postsynaptic the hippocampus


    Brains computers

    1000 operations/sec the hippocampus

    100,000,000,000 units

    10,000 connections/

    graded, stochastic


    fault tolerant

    evolves, learns

    1,000,000,000 ops/sec

    1-100 processors

    ~ 4 connections

    binary, deterministic



    designed, programmed

    Brains ~ Computers

    Flexor- the hippocampus










    Painful Stimulus

    Neural tissue
    Neural Tissue the hippocampus

    • The skin and neural tissue arise from a single layer, known as the ectoderm

      • in response to signals provided by an adjacent layer, known as the mesoderm.

      • A number of molecules interact to determine whether the ectoderm becomes neural tissue or develops in another way to become skin

    Critical periods in development
    Critical Periods in Development the hippocampus

    • There are critical periods in development (pre and post-natal) where stimulation is essential for fine tuning of brain connections.

    • Other examples of columns

      • Orientation columns

    Pre natal tuning internally generated tuning signals
    Pre-Natal Tuning: Internally generated tuning signals the hippocampus

    • But in the womb, what provides the feedback to establish which neural circuits are the right ones to strengthen?

      • Not a problem for motor circuits - the feedback and control networks for basic physical actions can be refined as the infant moves its limbs and indeed, this is what happens.

      • But there is no vision in the womb. Recent research shows that systematic moving patterns of activity are spontaneously generated pre-natally in the retina. A predictable pattern, changing over time, provides excellent training data for tuning the connections between visual maps.

    • The pre-natal development of the auditory system is also interesting and is directly relevant to our story.

      • Research indicates that infants, immediately after birth, preferentially recognize the sounds of their native language over others. The assumption is that similar activity-dependent tuning mechanisms work with speech signals perceived in the womb.

    Post natal environmental tuning
    Post-natal environmental tuning the hippocampus

    • The pre-natal tuning of neural connections using simulated activity can work quite well –

      • a newborn colt or calf is essentially functional at birth.

      • This is necessary because the herd is always on the move.

      • Many animals, including people, do much of their development after birth and activity-dependent mechanisms can exploit experience in the real world.

    • In fact, such experience is absolutely necessary for normal development.

    • As we saw, early experiments with kittens showed that there are fairly short critical periods during which animals deprived of visual input could lose forever their ability to see motion, vertical lines, etc.

      • For a similar reason, if a human child has one weak eye, the doctor will sometimes place a patch over the stronger one, forcing the weaker eye to gain experience.

    Learning rule gradient descent on an root mean square rms

    O = the hippocampusoutput layer

    Learning Rule – Gradient Descent on an Root Mean Square (RMS)

    • Learn wi’s that minimize squared error

    Backpropagation algorithm
    Backpropagation Algorithm the hippocampus

    • Initialize all weights to small random numbers

    • For each training example do

      • For each hidden unit h:

      • For each output unit k:

      • For each output unit k:

      • For each hidden unit h:

      • Update each network weight wij:


    Distributed vs localist rep n

    What are the drawbacks of each representation? the hippocampus

    Distributed vs Localist Rep’n

    Distributed vs localist rep n1

    What happens if you want to represent a group? the hippocampus

    How many persons can you represent with n bits? 2^n

    What happens if one neuron dies?

    How many persons can you represent with n bits? n

    Distributed vs Localist Rep’n

    Word superiority effect
    Word Superiority Effect the hippocampus

    Modeling lexical access errors
    Modeling lexical access errors the hippocampus

    • Semantic error

    • Formal error (i.e. errors related by form)

    • Mixed error (semantic + formal)

    • Phonological access error

    Phonological access error selection of incorrect phonemes
    Phonological access error: Selection of incorrect phonemes the hippocampus







    On Vo Co













    Adapted from Gary Dell, “Producing words from pictures or from other words”

    Mri and fmri
    MRI and fMRI the hippocampus

    • MRI: Images of brain structure.

    • fMRI: Images of brain function.

    • Tissues differ in magnetic susceptibility (grey matter, white matter, cerebrospinal fluid)

    Mirror neurons area f5
    Mirror Neurons: Area F5 the hippocampus

    Cortical mechanism for action recognition
    Cortical Mechanism for the hippocampusAction Recognition

    adds additional somatosensory information to

    the movement to be imitated

    provides an early

    description of the action




    Parietal mirror neurons (PF)

    (inferior parietal lobule)

    Frontal mirror neurons (F5) (BA 44)

    copies of the motor plans necessary to imitate actions for monitoring purposes

    codes the goal of the

    action to be imitated

    Somatotopy of Action Observation the hippocampus

    Foot Action

    Hand Action

    Mouth Action

    Buccino et al. Eur J Neurosci 2001

    The wcs color chips
    The WCS Color Chips the hippocampus

    • Basic color terms:

      • Single word (not blue-green)

      • Frequently used (not mauve)

      • Refers primarily to colors (not lime)

      • Applies to any object (not blonde)


    English has 11 basic color terms